
622 F.3d 761 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Teodulo PINEDA-BUENAVENTURA, Otoniel Mendoza, Gerardo Pineda-Soria, and Arturo Pineda-Lopez, Defendants-Appellants.
Nos. 09-1500, 09-1525, 09-1875, 09-2431.
United States Court of Appeals, Seventh Circuit.
Argued March 31, 2010.
Decided September 15, 2010.
As Amended on Denial of Rehearing October 6, 2010.
*764 Paul W. Connell, Attorney (argued), Office of the United States Attorney, Madison, WI, for Plaintiff-Appellee.
Robert A. Handelsman, Attorney (argued), Chicago, IL, for Teodulo Pineda-Buenaventura Defendant-Appellant.
Mark P. Maciolek, Attorney, MNM Law Office, Madison, WI, for Arturo Pineda-Lopez Defendant-Appellant
Susan Kister, Attorney (argued), St. Louis, MO, for Otoniel Mendoza Defendant-Appellant.
Megan M. Keleher, Attorney (argued), Wildman, Harrold, Allen & Dixon, Chicago, IL, for Gerardo Pineda-Soria Defendant-Appellant.
Before MANION and WILLIAMS, Circuit Judges, and DARRAH, District Judge.[*]
*765 WILLIAMS, Circuit Judge.
This is a consolidated appeal of four defendants involved in a large cocaine distribution conspiracy that operated in Jefferson County, Wisconsin. Following an investigation involving wiretap surveillance, controlled purchases, and confidential informants, sixteen individuals were charged in two separate indictments for conduct related to the conspiracy. The four defendants involved hereTeodulo Pineda-Buenaventura, Otoniel Mendoza, Gerardo Pineda-Soria, and Arturo Pineda-Lopezeach pled guilty to possessing or conspiring to possess with intent to distribute cocaine. Each now appeals. Teodulo Pineda-Buenaventura challenges his sentence, arguing that the drug amount calculation in his presentence investigation report was insufficient to support the statutory mandatory minimum sentence he received. Otoniel Mendoza challenges the validity of his guilty plea, arguing that his plea colloquy did not satisfy the requirements of Federal Rule of Criminal Procedure 11. Gerardo Pineda-Soria appeals the denial of his motion to suppress drugs found in his apartment and statements he made thereafter, arguing that the search violated the Fourth Amendment. And Arturo Pineda-Lopez's attorney has filed an Anders brief, seeking to withdraw on the basis that there are no non-frivolous arguments to be made by Pineda-Lopez on appeal.
For the reasons explained below, we vacate Pineda-Buenaventura's sentence and remand for resentencing because the district court's drug quantity findings did not support the sentence he received. We also vacate Mendoza's conviction because his plea colloquy did not satisfy the requirements of Rule 11, and so we remand for further proceedings. Furthermore, we affirm the district court's denial of Pineda-Soria's motion to suppress because he and his co-tenants gave valid consent to search his apartment. Finally, we grant Pineda-Lopez's counsel permission to withdraw because a challenge to the reasonableness of his sentence would be frivolous.

I. TEODULO PINEDA-BUENAVENTURADRUG AMOUNT FINDING
Teodulo Pineda-Buenaventura was a "runner" in the drug conspiracy who delivered cocaine at the direction of his cousin, Efrain Pineda-Buenaventura, one of the co-leaders of the conspiracy.[1] On June 19, 2008, after wiretap surveillance, police executed a search warrant at his home and recovered cocaine, a digital scale, a firearm, and $16,000 in cash. He was arrested, admitted to his involvement in the conspiracy, and on December 10, 2008, pled guilty pursuant to a written plea agreement to a single count of conspiracy to possess with intent to distribute at least 500 grams of cocaine. The plea agreement provided that he was subject to a 60-month mandatory minimum term of imprisonment pursuant to 21 U.S.C. § 841(b)(1)(B), but offered no details as to the specific amount of drugs to which he was admitting responsibility. At the plea hearing, the government acknowledged that while the count to which Pineda-Buenaventura was pleading was based on an amount of at least 500 grams, if the presentence investigation resulted in a finding that he was responsible for less, he would only be held accountable for that lower amount.
*766 Pineda-Buenaventura's presentence investigation report ("PSR") stated that 105 grams of cocaine were recovered from his home during the execution of the search warrant and that wiretap surveillance showed he had made deliveries totaling approximately 300 grams of cocaine. The PSR also found that Pineda-Buenaventura made 22 additional deliveries in which the drug quantities "could not be determined." Based on these findings, the PSR stated that "[t]he probation office believes that Teodulo's relevant conduct involves at least 400 grams to 500 grams of cocaine, resulting in a base offense level of 24. This is a conservative estimate."
At Pineda-Buenaventura's sentencing hearing, the district judge imposed the statutory minimum sentence of 60 months based on responsibility for 500 or more grams of cocaine. The district court appeared to agree with the findings in the PSRincluding, presumably, its estimate that Pineda-Buenaventura was responsible for "at least" 400 to 500 grams of cocainebut then stated "[y]our relevant conduct involves at least 400 grams but less than 500 grams of cocaine." (emphasis added). Apparently, the district judge believed that Pineda-Buenaventura was responsible for at least 500 grams (given that she sentenced him to a mandatory minimum based on that amount), but then made an express finding that he was responsible for less than that amount.
Pineda-Buenaventura contends that his PSR does not establish that he was responsible for at least 500 grams of cocaine in the conspiracy, the amount necessary for the charge to which he pled. Because he forfeited this argument by failing to challenge the PSR's amount determinations below (he admits this), the sentence is reviewed for plain error.[2]United States v. Jacques, 345 F.3d 960, 962 (7th Cir.2003). We find that while the PSR may support a finding that Pineda-Buenaventura was responsible for at least 500 grams under the evidentiary standards applicable at sentencing, remand is necessary because the sentencing judge made a finding on the record that Pineda-Buenaventura was responsible for less than that amount. This constitutes plain error that affected Pineda-Buenaventura's substantial rights and seriously affected the fairness of the proceedings. See United States v. Garrett, 528 F.3d 525, 527 (7th Cir.2008).
Evidentiary standards at sentencing are not as stringent as those at trial. United States v. Taylor, 72 F.3d 533, 543 (7th Cir.1995). A district court can determine drug quantities attributable to a defendant based only on a preponderance of the evidence, United States v. Salinas, 62 F.3d 855, 859 (7th Cir.1995), and can rely on the findings set forth in a PSR so long as the information has "sufficient indicia of reliability to support its probable accuracy." U.S.S.G. § 6A1.3(a). That said, we have encouraged courts to "make conservative estimates [of drug amounts], especially when presented with generalized testimony, as a way to . . . approximate drug quantities." United States v. Henderson, 58 F.3d 1145, 1152 (7th Cir.1995). Here, while the facts set forth in Pineda-Buenaventura's PSR would arguably support a finding that he was responsible for over *767 500 grams of cocaine under the standard we just described, the sentencing judge's express statement that his relevant conduct involved "less than 500 grams" forecloses any such interpretation and compels remand.
"A sentencing based on an incorrect Guidelines range constitutes plain error and warrants a remand for resentencing, unless we have reason to believe that the error in no way affected the district court's selection of a particular sentence." United States v. Farmer, 543 F.3d 363, 375 (7th Cir.2008). Here, relevant conduct involving an amount between 400 and 499 gramsthe amount expressly referenced by the district judgewould have generated an advisory Guideline range of 46-57 months, not the 60-month minimum set forth in § 841(b)(1). This was plain error that seriously affected the integrity of the proceedings, because Pineda-Buenaventura was sentenced based on an incorrect Guideline range. See Farmer, 543 F.3d at 375; see also United States v. Avila, 557 F.3d 809, 822 (7th Cir.2009)("It appears that the district court simply applied the wrong range, which constitutes plain error.").
Remand will provide the district court with an opportunity to clarify its findings regarding the drug amount attributable to Pineda-Buenaventura and to impose an appropriate sentence for that amount. See, e.g., Garrett, 528 F.3d at 530 (finding plain error and remanding to district court when "we have no reason to believe its error in the application of the Guideline range did not affect its selection of the particular sentence."). It is possible that the sentencing judge merely misspoke when making the finding that Pineda-Buenaventura's relevant conduct involved "less than 500 grams," but there is no way to be sure of this, especially when the PSR on its own terms does not unequivocally establish that Pineda-Buenaventura was responsible for at least 500 grams of drugs. See United States v. Salem, 597 F.3d 877, 888 (7th Cir.2010)(if court relies on PSR to make a finding as to certain conduct, the PSR must actually define that conduct); see also Farmer, 543 F.3d at 375 ("We have no reason to believe that the district court would not have selected an even lower sentence if given the opportunity to do so, thus, we must remand.").

II. OTONIEL MENDOZARULE 11 PLEA COLLOQUY
Otoniel Mendoza was another "runner" that delivered cocaine in the conspiracy. A search warrant executed at Mendoza's home yielded 339 grams of cocaine and 9 grams of methamphetamine. Wiretap surveillance revealed that he had delivered an additional 283 grams of cocaine, and made 21 additional deliveries for which the amount could not be determined. On December 12, 2008, Mendoza pled guilty to a single count of conspiracy to possess at least 500 grams of cocaine with intent to distribute, pursuant to a written plea agreement. The agreement stated that he was subject to a 60-month mandatory minimum term of imprisonment per 21 U.S.C. § 846, but did not discuss any relevant conduct to which he was pleading.
Mendoza makes two arguments on appeal: (1) that his plea colloquy did not satisfy Rule 11's requirement that his plea be knowing and voluntary, and (2) that the facts upon which his mandatory minimum sentence was based must be found by a jury. We address each in turn.

A. Mendoza's Plea Colloquy Did Not Satisfy Rule 11
Mendoza claims that his guilty plea to conspiring to distribute cocaine fell short of Rule 11's requirement that it be knowing and voluntary. He argues that the district court failed to ensure that he understood *768 the nature of the conspiracy charge to which he was pleading, that he never clearly pled guilty to specific acts in furtherance of that conspiracy, and that he was never clearly told he was pleading to an offense with a five-year mandatory minimum sentence.
A careful review of Mendoza's colloquy with the court at his plea hearingrelevant portions of which we quote belowdemonstrates that Mendoza was indeed confused with the concept of the conspiracy to which he was pleading, and was equivocal in many of his answers to the court regarding his conduct. We cannot say with confidence that Mendoza ever truly understood the nature of the conspiracy to which he was admitting involvement, nor can we determine exactly what acts Mendoza believed he was admitting to. We conclude that the plea colloquy fell short of Rule 11(b)(1)(G)'s requirement that Mendoza understand the nature of the charge to which he pled guilty.

1. The Plea Colloquy
Problems began early in Mendoza's exchange with the court, which took place through a translator due to Mendoza's limited English. Asked by the district judge whether he understood that the government was charging him with agreeing with others to distribute drugs, he answered "Yes. But the one thing about us coming to an agreement isn't so"displaying a lack of agreement with a critical element of a conspiracy. Noticing Mendoza's apparent confusion, the district court attempted to clarify Mendoza's understanding of the conspiracy, and the following exchange occurred:
THE COURT: When you talk about a conspiracy, it's not saying that you all sat around a table and agreed on each and every part of the conspiracy. The Government has to show that you did agree to something that carried out the conspiracy. The Government says that this conspiracy involved cocaine and it involved at least 500 grams of cocaine. That doesn'tthe Government isn't saying that you yourself were responsible for distributing 500 grams, but it does say that the conspiracy, all of the people involved conspired to distribute 500 grams or more.
MENDOZA: I just have one question.
THE COURT: Yes.
MENDOZA: Could you tell me more or less how many people are in the conspiracy?
THE COURT: According to the Indictment, there's seven that are named. That includes you, but then the Indictment also talks about others who may or may not be known to the grand jury.
MENDOZA: Well, the thing is that I wasn't in contact with those people. I don't know those people, and I can't name them here in the papers.
The district judge again attempted to clarify by explaining that Mendoza need not have specifically reached agreement with each member of the conspiracy, to which he vaguely replied "[w]ell, maybe I'm pleading guilty because I did sell a few times." When the court attempted to again determine whether Mendoza understood the government's allegations as to what he had done, Mendoza's answer was still equivocal: "Yes, I do understand, but I need to see a little bit more. I don't know how much the Government may have."
Later in the hearing, the government proffered some of the evidence it would have introduced had Mendoza chosen to go to trial. The government referred to intercepted telephone calls between Mendoza and Efrain Pineda-Buenaventura in which Mendoza was directed to deliver cocaine; Mendoza's own admission at the time of his arrest that he had delivered cocaine; and evidence that had been seized *769 at Mendoza's apartment, including 200 grams of cocaine, a digital scale, and packaging materials. Asked whether he disputed any of the evidence the government said it could prove, Mendoza said that he did not.
Mendoza was then asked to describe in his own words what he had done in connection with the conspiracy, however, and this is where things again got problematic. Mendoza began by vaguely describing his relationship with Efrain Pineda-Buenaventura, but did not initially describe any activity involving the delivery of cocaine. The court sought to focus matters and the following exchange ensued:
THE COURT: Did youdid you deliver drugs to [Efrain] Pineda-Buenaventura? Did you pick up drugs from him?
MENDOZA: No.
THE COURT: Did you do any of the things that Mr. Connell [government lawyer] talked about?
MENDOZA: I don't remember too well what it was that he said, but
The government lawyer then offered to assist by reiterating some of the government's proof against Mendoza, which the court invited him to do. The government lawyer again referred to intercepted telephone calls in which Efrain Pineda-Buenaventura instructed Mendoza to deliver drugs to various persons, and also again referred to Mendoza's own statement at his arrest that he had in fact delivered drugs at Efrain Pineda-Buenaventura's direction. When the court turned back to Mendoza and sought to confirm his understanding of this, this exchange occurred, which we quote at length:
THE COURT: Did [Efrain] Pineda-Buenaventura call you and ask you or tell you to deliver drugs?
MENDOZA: He told me to go and deliver some CDs that some people had lent to him.
THE COURT: All right. I'm not going any farther with this. Mr. Mendoza, if you don't agree that you did any of the things that Mr. Connell says you did, we'll continue this trialthis for trial.
MENDOZA: Well, there is a part that I am guilty of there, but the thing is though in part they are pinning a lot of stuff on me and I don't believe I did all of that.
THE COURT: All right. I'll startI'll give you one last chance and then I have other matters that I need to take care of, Mr. Mendoza, and I'm not interested in spending more time with you if you're not willing to take any responsibility. We'll just go to trial. We'll have a jury decide what happened in this case. I'll ask you once again, did you deliver any cocaine at the request of any of the people that you conspired with? Mr. Delyea [defense counsel].
DEFENSE COUNSEL: Actually the point I made is did you ever just do it one time. Apparently there were times when they delivered CDs and DVDs.
THE COURT: I'm not interested in that.
DEFENSE COUNSEL: I understand.
THE COURT: I just want to know whether he ever delivered cocaine.
DEFENSE COUNSEL: If there was ever one occasion.
THE COURT: Ever. Any occasion on which he delivered cocaine with any of the people named in the Indictment or others.
MENDOZA: Yes, there was one time. But not specifically in the calls, but one time, yes.
THE COURT: And who called you and asked you to deliver cocaine?
MENDOZA: Well, it wasn't directlyit wasn't directly somebody calling me and saying well, let's deliver cocaine to so-and-so. *770 I think it was cocainewell, I never had this, but I think it was cocaine.
THE COURT: But who asked you to deliver it?
MENDOZA: Well they called me and had meEfrain called me to have me take that over to someone who I guess had ordered it from him. I don't know how they ordered the stuff from him.
THE COURT: You don't need to know that. Who called you? [Efrain] Pineda-Buenaventura?
MENDOZA: Yes, him.
THE COURT: All right. Then on the basis of this extended discussion with counsel and with Mr. Mendoza and upon the basis of the entire record in the case, I find and conclude, Mr. Mendoza, that you have entered a plea of guilty knowingly, understandingly, and voluntarily. . . .

2. Analysis
Mendoza claims that his plea colloquy did not comply with Rule 11 because he never understood the nature of the charge against him. Because Mendoza never sought to withdraw his plea in the district court, our review is for plain error. United States v. Vonn, 535 U.S. 55, 63, 122 S.Ct. 1043, 152 L.Ed.2d 90 (2002); United States v. Burnside, 588 F.3d 511, 520 (7th Cir.2009). We review Mendoza's claim of a Rule 11 violation to determine whether (1) an error has occurred; (2) it was plain; (3) it affected Mendoza's substantial rights; and (4) it seriously affected the fairness, integrity, or public reputation of the judicial proceedings. See Burnside, 588 F.3d at 520.
Rule 11 requires that "before the court accepts a plea of guilty or nolo contendere.. . the court must address the defendant personally in open court . . . [and] inform the defendant of, and determine that the defendant understands . . . the nature of each charge to which the defendant is pleading." Fed.R.Crim.P. 11(b)(1)(G). It requires that a district court "ensure that [the defendant] understands the law of his crime in relation to the facts of his case." Vonn, 535 U.S. at 62, 122 S.Ct. 1043. Unless a defendant "fully comprehends the elements of the crime to which he is confessing, his plea cannot be said to have been knowingly and voluntarily entered." United States v. Fernandez, 205 F.3d 1020, 1025 (7th Cir. 2000) (quotation and citation omitted). To determine whether a defendant in fact understands the nature of a charge, we take a totality-of-the-circumstances approach and consider (1) the complexity of the charge; (2) the defendant's intelligence, age, and education; (3) whether the defendant was represented by counsel; (4) the district judge's inquiry during the plea hearing and the defendant's own statements; and (5) the evidence proffered by the government. Id. (citing United States v. LeDonne, 21 F.3d 1418, 1423 (7th Cir. 1994)).
Our assessment of these factors in Fernandez is instructive here. In Fernandez, a native Spanish-speaking defendant with a fifth grade education and limited English pled guilty to conspiring to distribute marijuana. 205 F.3d at 1022. At his plea hearing, Fernandez, like Mendoza here, demonstrated confusion both with the concept of the conspiracy and the specific acts to which he was pleading guilty. Id. at 1025-27. In his exchanges with the court, Fernandez gave ambiguous, partial, and even contradictory answers, and at times appeared confused. Id. For example, when asked by the court whether he had done the things set forth in the government's proffer, Fernandez gave inconsistent and unclear answers, varying from "Yes, your Honor, I did," to "[n]ot everything. I thought I was pleading guilty *771 partially," to "[n]ot all of the acts, partially." Id. at 1026-27.
On appeal, Fernandez argued his plea was not voluntary, and we agreed, finding the guilty plea to have been "enveloped in confusion and misunderstanding." Id. at 1026. Reviewing the record, we found that Fernandez exhibited confusion over the nature of the conspiracy, and that "like most lay people, Fernandez would not understand the term `conspiracy' without some further explanation." Id. at 1026. We also found that there was general confusion regarding "precisely what acts Fernandez admitted." Id. at 1027. We concluded that "Fernandez' accounts of what acts he admitted and those he denied were very murky. Based on this record, it is impossible to ascertain precisely what acts Fernandez admits and which he denies." Id. Evaluating the totality of the circumstances, we held that "we cannot conclude that Fernandez was fully aware of the nature of the crime to which he pleaded guilty" and remanded the case to the district court for a new plea. Id. at 1026, 1030.
Reviewing the record here (especially the portions quoted above) in light of Fernandez and the relevant factors, we cannot say with confidence that Mendoza ever truly understood the nature of the conspiracy to which he was pleading. Mendoza demonstrated confusion with the concept of the conspiracy, and that confusion was never fully resolved by the court. Nor can we clearly determine exactly what acts Mendoza admitted.
The first two factors in our totality-of-the-circumstances approachcomplexity of the charge and defendant's age and educationmitigate against a finding that Mendoza understood exactly what he was pleading to. Conspiracy is not a concept immediately understandable to a layperson. See United States v. Blalock, 321 F.3d 686, 689 (7th Cir.2003) ("[C]onspiracy is generally considered a rather complicated offense."); see also United States v. Wetterlin, 583 F.2d 346, 350 (7th Cir.1978) (charge of conspiracy "is not a self-explanatory legal term"). The relative complexity of a conspiracy charge, coupled with Mendoza's sixth-grade education level and limited English, favor a finding that Mendoza did not comprehend the charge to which he was pleading. See Fernandez, 205 F.3d at 1026.
The fact that Mendoza was represented by counselthe third factor in our inquirydid not alleviate the problems we perceive here. At certain points during the plea hearing, Mendoza's lawyer did attempt to clarify matters for his client and the court, but those attempts are not a substitute for Mendoza himself actually indicating an understanding of the charge to which he was pleading. At certain points during the hearing, counsel's presence almost seems to have complicated matters at times when meaningful follow-up questions might have confirmed Mendoza's understanding, counsel instead stepped in and offered comments that took the court in another direction. Moreover, Mendoza himself indicated at the beginning of the hearing that there had been some communication problems with his lawyer. Asked by the court whether counsel had answered all of his questions, Mendoza answered, "Well, I'm not really clear on some of them, but others, yes." Mendoza indicated that he was not sure if his lawyer had understood him in their conversations, stating that "[h]e doesn't speak my Spanish." And counsel himself informed the court at the close of the plea hearing that he and Mendoza had had "some difficulty communicating."
The fourth factorthe district judge's inquiry during the plea hearing and the defendant's own statementsis the most troubling. A careful review of the plea *772 colloquy demonstrates that Mendoza never seemed to have a real grasp of what the conspiracy was. The court made attempts to clarify and explain the conspiracy to Mendoza, but the record shows that he at best indicated only partial understanding, and at times made statements that entirely undercut it-such as "the one thing about us coming to an agreement isn't so" and "I wasn't in contact with those people." Further attempts were made to clarify matters, to which Mendoza only stated that he would "need to see a little bit more" in order to understand, because he didn't "know how much the Government may have."
And when it came time for Mendoza to explain in his own words what he did, his accounts were noncommital, vague, and evasive. Mendoza repeatedly hedged in his answers and descriptions of his conduct to the court, prompting numerous (fruitless) clarifying questions from the court. At one point, he even discussed delivering compact discs for Efrain Pineda-Buenaventura instead of drugs. Eventually, after significant back-and-forth with the courtduring which time the district judge told Mendoza that he had "one last chance," that she had "other matters . . . to take care of," and that "I'm not interested in spending more time with you if you're not willing to take any responsibility"Mendoza finally stated that Efrain Pineda-Buenaventura had on one occasion instructed him to deliver drugs to someone. This lone statement is eclipsed in context by the significant confusion that preceded it. At any point during the colloquy, the district court could have taken a brief recess in order to allow counsel to talk with his client confidentially, address Mendoza's apparent confusion, and determine if he did indeed wish to proceed with a plea. Such a conference might have helped to avoid the problems that occurred here. But based on this record, we cannot be confident that Mendoza understood the nature of the crime to which he was pleading guilty, or exactly which acts he was admitting having committed. See Fernandez, 205 F.3d at 1027. The fourth factor in our totality-of-the-circumstances inquiry favors Mendoza.
The fifth factor in our inquiry examines the government's proffered evidence. Examining this factor in Fernandez, we found that "while there was nothing wrong with the AUSA's factual proffer on its face, the surrounding chaos at this change of plea hearing significantly negated any confidence in Fernandez' understanding of and admission to those facts." Id. The same could be said here. The government's explanation of its evidence against Mendoza was sufficient, but Mendoza's various reactions to it undermine our confidence that he understood the acts to which he was admitting. While Mendoza initially said that what the government had proffered was "fair," he then later stated that he did not remember what the government's evidence was. Even when the proffer was reiterated, he showed further confusion and was evasive. Just as in Fernandez, where we were concerned with a defendant who admitted to, in his words, "[n]ot all of the acts, partially," here Mendoza was similarly noncommital, saying "there is a part that I am guilty of there, but the thing is.. . I don't believe I did all of that." See id. ("Because we cannot glean a clear understanding of Fernandez' participation in the crime charged, it is impossible to determine whether Fernandez himself understood the nature of the crime to which he was pleading guilty."). Mendoza's tentative, qualified responses to the government's proffered evidence undermine our confidence that he really did understand exactly what to which he was pleading guilty. See id.
We find that the Rule 11 errors that occurred during the plea colloquy in *773 this case were plain and affected Mendoza's substantial rights. See Vonn, 535 U.S. at 62, 122 S.Ct. 1043; see also United States v. Bradley, 381 F.3d 641, 647 (7th Cir.2004) ("Misunderstanding of the nature of the charge . . . is not harmless error."). That a plea be knowing and voluntary is a "core concern" of Rule 11. United States v. Pena, 314 F.3d 1152, 1157 (9th Cir. 2003). "[A] defendant's clear understanding of the nature of the charge to which he is pleading guilty relates to the very heart of the protections afforded by the Constitution and Rule 11." Fernandez, 205 F.3d at 1027. Looking at the totality of the circumstances, we conclude that the variances from Rule 11 that occurred during Mendoza's plea colloquy warrant vacatur of his conviction and a remand for further proceedings.[3]
B. Whether Facts Triggering Mendoza's Mandatory Minimum Sentence Needed to Be Proven Beyond a Reasonable Doubt
Mendoza also appeals his sentence on the basis that a jury, not a sentencing court, must find facts sufficient to trigger the application of the mandatory minimum sentence to which he was subjected. Because we are vacating Mendoza's conviction on the basis set forth above, we need not reach this issue. We note, however, that this argument is foreclosed in the Seventh Circuit, because our precedent is clear that judges may determine drug amounts by a preponderance of the evidence that subject a defendant to a statutory mandatory minimum. See, e.g., United States v. Clark, 538 F.3d 803, 811-12 (7th Cir.2008); United States v. Price, 516 F.3d 597, 605 (7th Cir.2008). Mendoza acknowledges this, but states in his brief that he raises the issue to "preserve it for further review" in light of the Supreme Court having granted certiorari in United States v. O'Brien, 560 U.S. ___, 130 S.Ct. 2169, 176 L.Ed.2d 979 (2010) (the case has been decided since the time Mendoza filed his brief). It is unclear why Mendoza hedged a bet on the outcome of O'Brien. O'Brien involved a provision of 18 U.S.C. § 924(c)a statute not at issue in this casethat provides for a 30-year mandatory minimum sentence when the firearm used in the offense is a machine gun. 18 U.S.C. § 924(c)(1)(B)(ii). The O'Brien court ruled that the fact that a gun is a machine gun is an element of the § 924(c) offense that must be proved to a jury beyond a reasonable doubt, as opposed to a sentencing factor to be proven to the judge. O'Brien, 130 S.Ct. at 2180. The holding has no bearing on the validity of Mendoza's sentence under 21 U.S.C. *774 § 841(b)(1)(B). As we have repeatedly held, the amount of drugs a defendant possessed is not an element of a § 841 offense and the sentencing judge can find facts that trigger a mandatory minimum sentence. See Clark, 538 F.3d at 811-12; see also United States v. Washington, 558 F.3d 716, 720 (7th Cir.2009); Price, 516 F.3d at 605. Amount findings need be determined beyond a reasonable doubt only when they implicate a statutory maximum prison term, which is not the case here. See United States v. Kelly, 519 F.3d 355, 363 (7th Cir.2008); see also Harris v. United States, 536 U.S. 545, 122 S.Ct. 2406, 153 L.Ed.2d 524 (2002).

III. GERARDO PINEDA-SORIAMOTION TO SUPPRESS
Gerardo Pineda-Soria was a supplier of cocaine to the conspiracy. He pled guilty to possessing with intent to distribute cocaine in violation of 21 U.S.C. § 841(a), subject to a plea agreement in which he retained his ability to appeal the district court's denial of his motion to suppress drugs that had been found during a search of his residence. He was sentenced to 30 months' imprisonment. He now appeals the denial of his motion to suppress.
When considering a motion to suppress, we review the district court's legal conclusions de novo, and factual findings and credibility determinations for clear error. United States v. Lewis, 608 F.3d 996, 999 (7th Cir.2010). We are particularly deferential to credibility findings, and "unless the trial court has credited testimony that is contrary to the laws of nature or so internally inconsistent or implausible on its fact that no reasonable factfinder would credit it, we defer to the trial court's finding." United States v. Collins, 604 F.3d 481, 486 (7th Cir.2010).

A. The Search of Pineda-Soria's Apartment
On June 18, 2008, Drug Enforcement Agency ("DEA") agents obtained a search warrant for Pineda-Soria's residence at 253 South High Street, Apartment A, in Janesville, Wisconsin. The doorway of 253 South High Street opens into a two-story foyer, and the building is divided into two apartments, A and B. The entrance to Apartment A is on the first floor, and an open staircase leads up to the door for Apartment B. Neither door has a letter, however, so it would not necessarily be clear to someone that they were separate apartments. Based on information that the upstairs apartment was empty, agents limited their warrant application only to Apartment A, and the warrant itself was similarly limited. An arrest warrant for Pineda-Soria was issued at the same time.
At 6:01 a.m. the next morning, DEA agents and Janesville police officers executed the warrant. None of the DEA agents that were aware of the Apartment A/B distinction were present at the search, and apparently had not informed any of the searching officers that the warrant was limited to the downstairs unit. Unaware of the warrant's limitation or the distinction between the units, the entry team entered both Apartments A and B. In performing a preliminary sweep of Apartment B, agents found three men sleeping: Pineda-Soria, along with Hoguer Pineda and Adrian Lazcano (the "co-tenants"). The three were taken downstairs and outside. Pineda-Soria was taken to the Janesville police station to be interviewed, while Pineda and Lazcano remained on the premises.
Before any contraband was found, a DEA agent became aware that Apartment B was a separate unit after speaking with residents of the downstairs unit. Realizing the error, searching officers immediately *775 ceased the nascent search and withdrew to the front lawn to wait for further instructions. It was decided to ask Pineda-Soria and the co-tenants for consent to search, and DEA agents also contacted an Assistant United States Attorney regarding the possibility of obtaining another search warrant for Apartment B at the same time.
At approximately 6:45 a.m., a Spanish-speaking Janesville police officer asked each co-tenant separately whether he would consent to a search of Apartment B. Both men had by this point been allowed to get dressed, and were not handcuffed. The interviewing officer first asked the co-tenants if they lived in the unit and both stated that they did. The officer then told them it was up to them whether or not to allow a search and both individually gave oral consent to search. Police decided it would be advisable to also obtain written consent from each co-tenant, and telephoned another officer to bring a written consent form that he could translate into Spanish for them to read and sign.
In the meantime, at the Janesville police station, DEA agents and police advised Pineda-Soria of his rights and asked for his cooperation. He signed a Miranda waiver form, and at 7:08 a.m. he filled out a written consent form consenting to a search of Apartment B. The record is not clear as to whether officers resumed searching the upstairs unit once the co-tenants consented at 6:45 a.m., or whether they also waited for Pineda-Soria's consent that came approximately 25 minutes later. In any event, officers re-entered Apartment B, and found a kilogram of cocaine under Pineda-Soria's bed.[4]
By this time, agents had completed an initial interview with Pineda-Soria, who had to that point denied any involvement in the alleged conspiracy. When they brought him back to the apartment building, they learned that cocaine had been found in the search of Apartment B. This update was shared with Pineda-Soria, and he was reminded of his Miranda rights. Pineda-Soria agreed to cooperate, and confronted with the evidence that had been found, admitted to involvement in the conspiracy.
Pineda-Soria moved to suppress the physical evidence found in his apartment and the statements that he had made, arguing that the search of Apartment B occurred without a valid warrant and that there had been no valid consent, and on December 8, 2008, an evidentiary hearing was held. On February 11, 2009, a magistrate judge issued a Report and Recommendation that the district court deny the motion to suppress, finding (1) that the consents to search Apartment B were valid, and (2) that the inevitable discovery doctrine also applied. On March 5, 2009, the district court adopted the Report and Recommendation and denied the motion to suppress. Pineda-Soria then entered into a conditional plea to one count of possessing with intent to distribute cocaine, reserving his right to appeal the denial of his motion to suppress.

B. Whether the Consents Were Voluntary
Pineda-Soria appeals the denial of his motion to suppress on two grounds. First, he argues that none of the consents given to search Apartment B were voluntary. Second, he asserts that the inevitable discovery doctrine should not apply, arguing that the government failed to meet its burden of proof to benefit from that doctrine.
*776 No one disputes that the initial search of the upstairs unit was illegal; officers entered Apartment B armed with a warrant that only gave them permission to search Apartment A. Nothing was found in the brief initial sweep, however. It was not until officers re-entered the unit, after receiving consent to do so, that contraband was discovered. The Fourth Amendment's warrant requirement does not apply in circumstances where an authorized party voluntarily consents to a search. United States v. Parker, 469 F.3d 1074, 1077 (7th Cir.2006); see also Schneckloth v. Bustamonte, 412 U.S. 218, 219, 93 S.Ct. 2041, 36 L.Ed.2d 854 (1973). The relevant question here is whether the consents from Pineda-Soria and his co-tenants to search Apartment B were valid.[5]
Whether a defendant voluntarily consented to a search is a question of fact determined by examining the totality of the circumstances. Lewis, 608 F.3d at 999. In making this determination, we consider (1) the defendant's age, intelligence, and education; (2) whether the defendant was advised of his constitutional rights; (3) how long the defendant was detained prior to giving consent; (4) whether the consent was immediate, or was prompted by repeated requests by authorities; (5) whether any physical coercion was used; and (6) whether the defendant was in police custody when he gave his consent. United States v. Risner, 593 F.3d 692, 694 (7th Cir.2010); see also United States v. Figueroa-Espana, 511 F.3d 696, 704-05 (7th Cir.2007). We review a district court's finding of voluntary consent for clear error. United States v. Santiago, 428 F.3d 699, 704 (7th Cir.2005). And when consent is given after an illegal search has occurred, we must also be sure that the illegality did not taint any consent that was given. To determine whether the taint from an initial illegal search has been purged, we examine (1) the temporal proximity of the illegal entry and the consent; (2) the presence of intervening circumstances; and (3) the purpose and flagrancy of the official misconduct. Brown v. Illinois, 422 U.S. 590, 603-04, 95 S.Ct. 2254, 45 L.Ed.2d 416 (1975); see also United States v. Robeles-Ortega, 348 F.3d 679, 681 (7th Cir.2003). Viewing the circumstances in light of these standards, we find that the consents given in this case were valid and were not tainted by the initial warrantless search, and that the district court properly denied Pineda-Soria's motion to suppress.

1. The Co-Tenants' Consents
We first examine the consents given by the co-tenants, Pineda and Lazcano. Approximately 45 minutes transpired between the time that they were rousted out of bed to when they gave their initial oral consent. They were permitted to get dressed, initially sat on a couch in Apartment A, then were relocated to the yard outside of the house. They were not handcuffed, and were in the company of other people that they knew. The record is not clear on their age or education level, but we know that officers communicated with them in their native Spanish. When asked for consent, both co-tenants were informed that they did not have to give permission, both orally and on the written consent forms they signed. See United States v. Valencia, 913 F.2d 378, 381 (7th Cir.1990) *777 (finding it significant that defendant had been told he did not have to consent to search). The record shows that each man gave his consent immediately, and there is no evidence of repeated prodding or questioning by police. While being awoken by armed officers and made to leave their dwelling certainly must have been an intimidating experience, there is no evidence that any subsequent events took place that were coercive in any way.
Nor do we think that the initial illegal entry tainted the co-tenants' consent in any way. Considering the Brown factors, we find that the temporal proximity of the illegal entry and consent, taken together with the intervening circumstances, support the district court's finding that there was no taint. Brown, 422 U.S. at 603-04, 95 S.Ct. 2254. Forty-five minutes transpired between the time of the illegal entry and the co-tenants' verbal consents, and an hour and forty minutes passed between the entry and the written consent. See Valencia, 913 F.2d at 382. There is no evidence of any coercion taking place during that time; conversely, both Pineda and Lazcano were told they did not have to consent if they did not want to. Finally, consideration of the "purpose and flagrancy of the official misconduct" weighs heavily in favor of finding that any taint was purged. The initial entry into Apartment B was a mistake on the part of the searching officers, none of whom were aware of the limitation on the warrant. Once the mistake was discovered, officers immediately withdrew from the upstairs unit to determine what should be done next. The initial entry does not appear to have been at all flagrant or purposeful, and it did not taint the co-tenants' subsequent consent. The district court's determination that the co-tenants' consents were voluntary is not clearly erroneous.
Pineda-Soria contends that even if the consents were voluntary, neither co-tenant had any authority to actually give it. By failing to object to the magistrate judge's recommendation finding that they had authority, Pineda-Soria has waived this issue on appeal. United States v. Moore, 563 F.3d 583, 585 (7th Cir.2009). And in any event, the co-tenants did have apparent authority to consent to the search. A police officer asked both men, in Spanish, if they lived in the unit, and both answered that they did. Pineda-Soria argues that officers have a duty to inquire further as to a third party's authority, but that is only true when the circumstances make the authority questionable in the first place. See United States v. Goins, 437 F.3d 644, 649 (7th Cir.2006). An officer can conduct a search when the facts available at the time "warrant a man of reasonable caution in the belief that the consenting party had authority over the premises." Illinois v. Rodriguez, 497 U.S. 177, 188, 110 S.Ct. 2793, 111 L.Ed.2d 148 (1990) (quotation omitted). Here, the facts clearly warranted such a belief. Pineda and Lazcano had authority to grant consent to search Apartment B.

2. Pineda-Soria's Consent
Having reached this conclusion, we need not address the voluntariness of Pineda-Soria's consent, but do so anyway. We are more concerned with the voluntariness of Pineda-Soria's consent than we are with that of the co-tenants. He was rousted out of bed and whisked away to a police station for interrogation, and was thus in a far more restrictive and potentially coercive setting than the co-tenants were. And unlike the co-tenants, Pineda-Soria was not on the premises and had no knowledge of what was transpiring there. For all Pineda-Soria knew, contraband could already have been found at the location, and he may well have felt pressure to appear cooperative and consent when he *778 otherwise would not have. See, e.g., Brown, 422 U.S. at 605 n. 12, 95 S.Ct. 2254. At the same time, he was given Miranda warnings, spoken to in his native Spanish, and chose to sign a written consent form agreeing to the search. While the question of the voluntariness of Pineda-Soria's consent is a closer call than that of his co-tenants, we are not "left with the definite and firm conviction that a mistake has been made" by the district court, and we find no clear error in its finding that Pineda-Soria's consent was also voluntary. Lewis, 608 F.3d at 1000 (quotation and citation omitted).
Having found that the district court did not err in concluding that the consents from Pineda-Soria and the co-tenants were valid, we need not reach the question of whether the inevitable discovery doctrine would also have justified the warrantless search. See United States v. Patterson, 65 F.3d 68, 72 (7th Cir.1995). We affirm the district court's denial of Pineda-Soria's motion to suppress the contraband found in his apartment and the statements he made in connection therewith.

IV. ARTURO PINEDA-LOPEZCOUNSEL'S MOTION TO WITHDRAW
Arturo Pineda-Lopez was another "runner" in the conspiracy and was overheard on wiretaps delivering cocaine for Efrain Pineda-Buenaventura. Evidence showed he delivered somewhere between 500 grams and 2 kilograms of drugs. He pled guilty pursuant to a plea agreement to conspiracy to possess with intent to distribute 500 grams of cocaine, in violation of 21 U.S.C. § 846. Pineda-Lopez's PSR determined that he had a base offense level under the sentencing guidelines of 21, after a 3-level downward adjustment based on acceptance of responsibility and a 2-level downward adjustment because he met the "safety valve" provision, 18 U.S.C. § 3553(f). Coupled with a criminal history category of I, Pineda-Lopez's advisory guideline range was 37-46 months. At sentencing, the district court gave him the bottom of the range: 37 months. Pineda-Lopez's trial counsel has filed an Anders brief seeking permission to withdraw on the basis that there are no non-frivolous arguments to be made on appeal. See Anders v. California, 386 U.S. 738, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967).
Pineda-Lopez did not respond to his counsel's submission, and so we review the potential issues counsel has identified in his brief. See United States v. Garcia, 580 F.3d 528, 543 (7th Cir.2009). Counsel represents that Pineda-Lopez would challenge the reasonableness of his sentence by arguing that his 37-month term is unduly harsh in light of his limited involvement in the conspiracy and his lack of criminal history. Counsel claims that while Pineda-Lopez may view the sentence as harsh, it was well within the district court's discretion to impose it, and points out that the sentence is at the bottom of the advisory guideline range. Therefore, counsel argues, Pineda-Lopez's argument would be frivolous if raised on appeal.
Having reviewed the record and counsel's Anders brief, we agree. The court reviews the reasonableness of a sentence under an abuse of discretion standard. United States v. Poetz, 582 F.3d 835, 837 (7th Cir.2009). We apply a presumption of reasonableness to a sentence that reflects proper application of the guidelines. Rita v. United States, 551 U.S. 338, 347, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007). Here, the sentence was reasonable. The district court properly calculated and considered the applicable Sentencing Guidelines range, did not clearly err in its factual findings, and imposed a sentence at the bottom of the range after considering the § 3553(a) factors. We conclude that there are no non-frivolous *779 issues on appeal, grant counsel's motion to withdraw, and dismiss Pineda-Lopez's appeal. See United States v. Recendiz, 557 F.3d 511, 534 (7th Cir.2009).

CONCLUSION
We VACATE Teodulo Pineda-Buenaventura's sentence and REMAND to the district court for resentencing consistent with this opinion. We VACATE Otoniel Mendoza's conviction and REMAND for further proceedings. We AFFIRM the district court's denial of Gerardo Pineda-Soria's motion to suppress. And we GRANT Pineda-Lopez's counsel's motion to withdraw and DISMISS his appeal.
NOTES
[*]  The Honorable John W. Darrah, United States District Court for the Northern District of Illinois, Eastern Division, sitting by designation.
[1]  "Pineda-Buenaventura" refers to defendant-appellant Teodulo Pineda-Buenaventura. When we refer to Efrain Pineda-Buenaventura, we do so using his full name so as to avoid confusion.
[2]  The government argues that Pineda-Buenaventura waived, not merely forfeited, appeal on this issue. But waiver is an intentional, strategic decision not to raise a challenge, whereas an argument is forfeited when the issue is not raised negligently or accidentally. See United States v. Cooper, 243 F.3d 411, 416 (7th Cir.2001). We can discern no tactical reason behind Pineda-Buenaventura's failure to raise this argument. See United States v. Jaimes-Jaimes, 406 F.3d 845, 848 (7th Cir. 2005) ("Waiver principles should be construed liberally in favor of the defendant.").
[3]  Mendoza also argues that his plea was not knowing and voluntary because he did not have a clear understanding of the mandatory minimum sentence he faced and that he never actually pled guilty to responsibility for the requisite 500 grams or more of drugs to support that sentence. Because we vacate the plea on other grounds, we need not reach this argument. We note, however, that in this respect "Rule 11 only requires that the court inform the defendant of the maximum and minimum penalties . . . as well as the fact that the particular sentence imposed will be determined by reference to the federal sentencing guidelines." Blalock, 321 F.3d at 689 (holding that plea was voluntary when court had not determined drug amount at time of hearing, and told defendant amount would be subsequently determined); see also Fed. R.Crim.P. 11(b)(1)(I). That requirement was satisfied here. The government specifically referred to the potential five-year mandatory minimum at the hearing, and Mendoza's lawyer himself clarified with the court that the drug amount was not being established at that hearing, and instead would occur later when the PSR was written. See, e.g., United States v. Wagner, 996 F.2d 906, 912 (7th Cir. 1993) (rejecting claim that plea was involuntary on basis that specific amount had not been determined, noting that parties had acknowledged exact drug amounts would be calculated later).
[4]  At some point during the search, a Spanish translation of a written consent form was produced for the co-tenants, which each signed at 7:40 a.m.
[5]  While none of the officers on the scene were aware of the warrant's limitation to Apartment A, under the collective knowledge doctrine the fact that some DEA agents were aware of the distinction forecloses the good faith exception here. See United States v. Harris, 585 F.3d 394, 400 (7th Cir.2009). We agree with the district court's conclusion that the DEA's failure to properly inform or supervise the executing police of this fact was reckless, meaning the exclusionary rule is in play. Herring v. United States, ___ U.S. ___, 129 S.Ct. 695, 702, 172 L.Ed.2d 496 (2009).
