
523 F.3d 110 (2008)
Stella Chukwudumebi EMOKAH, Petitioner,
v.
Michael B. MUKASEY, Attorney General of the United States,[1] Respondent.
Docket No. 07-3115-ag.
United States Court of Appeals, Second Circuit.
Argued: April 7, 2008.
Decided: April 22, 2008.
*112 Roberto Tschudin Lucheme, Glastonbury, CT, for Petitioner.
Russell J.E. Verby, (Jeffrey S. Buckholtz, Acting Assistant Attorney General on the brief, Barry J. Pettinato, Assistant Director, of counsel), Office of Immigration Litigation, Civil Division, U.S. Department of Justice, Washington, DC, for Respondent.
Before: WALKER, CABRANES AND RAGGI, Circuit Judges.
JOSÉ A. CABRANES, Circuit Judge:
Petitioner Stella Chukwudumebi Emokah, a native and citizen of Nigeria, seeks review of a June 16, 2005 decision of Immigration Judge ("IJ") Michael W. Straus denying her applications for a waiver of inadmissibility pursuant to 8 U.S.C. § 1182(i)[2] and an adjustment of status under 8 U.S.C. § 1255(a).[3]See In re Emokah, No. A XX-XXX-XXX (Imm. Ct. Hartford June 16, 2005). The Board of Immigration Appeals ("BIA") affirmed the IJ's decision in an opinion issued on June 22, 2007. See In re Emokah, No. A XX-XXX-XXX (BIA June 22, 2007). On appeal, petitioner contends that she did not need a *113 waiver of inadmissibility to adjust her status because her knowing use of a fraudulent surname to obtain a visa did not amount to a willful misrepresentation of a material fact within the meaning of 8 U.S.C. § 1182(a)(6)(C)(i), see note 2 ante (text of provision). In the alternative, petitioner contends: first, that her possession of an approved I-360 visa petition[4] obviated the need for a section 1182(i) waiver; and, second, that if the section 1182(i) waiver was required, her circumstances were such that the waiver should have been granted. We find these arguments to be without merit but write to clarify that, where an alien whose previous visa application has been denied receives a visa after providing false information about her identity, that conduct constitutes willful misrepresentation of a material fact for purposes of 8 U.S.C. § 1182(a)(6)(C)(i).

I. BACKGROUND
Petitioner entered the United States in August 2000, on a B-2 non-immigrant visa[5] that was valid until February 2001. She married Peter Emokah, a U.S. citizen, in October 2000. Emokah filed an I-130 visa petition[6] on petitioner's behalf in December 2000 but withdrew the petition in May 2001 based on suspicions that petitioner was already married to someone else in Nigeria. In June 2001, the then-Immigration and Naturalization Service initiated removal proceedings against petitioner on the basis that she had remained in the United States past the expiration of her nonimmigrant visa. Four months later, petitioner and Peter Emokah separated and later divorced. In October 2001, petitioner filed an I-360 petition, see ante note 4, on her own behalf. Petitioner then appeared before the IJ for a removal hearing in October 2002 wherein she conceded her removability but sought a continuance of the removal proceedings to allow for the adjudication of her I-360 petition. The IJ granted petitioner's request for a continuance on this occasion, in June 2003, and again in January 2004.
At a hearing held on June 15, 2004, petitioner's counsel informed the IJ that the I-360 petition had been approved. The IJ asked whether petitioner's counsel anticipated any issues with petitioner's application for adjustment of status and petitioner's counsel answered "[p]ossibly one," relating to "[m]isrepresentation at the embassy" where petitioner obtained her B-2 visa. J.A. 59. The IJ then adjourned proceedings so that petitioner's counsel could file an application for a waiver of inadmissibility pursuant to section 1182(i), *114 see note 2 ante. At petitioner's fifth appearance before the IJ, on May 6, 2005, the IJ noted that petitioner's counsel had not yet filed the application for a section 1182(i) waiver on her behalf and reminded petitioner's counsel that petitioner bore the burden of proof on the issue of her admissibility. Petitioner's counsel agreed to submit the application for a section 1182(i) waiver within ten days.
On June 16, 2005, the IJ held a merits hearing on petitioner's applications for a waiver of admissibility and adjustment of status. At the hearing, petitioner testified that, prior to taking the name of her U.S. citizen husband, her surname was Limogou. She also acknowledged that she had provided a different surname  "Oke"  when applying for her B-2 visa in Lagos, Nigeria. On direct examination, she explained that "Oke" was the surname of a wealthy and well-connected Nigerian businessman with whom she had been romantically involved for several years. She further explained that she had a child with Oke but was not married to him because he was already married to someone else. Petitioner testified that, to obtain a visa for travel to the United States, she had gone with Oke and their son to the American embassy in Lagos. The consular official in charge of visa interviews called them up as "Ok[e]'s family" and they were interviewed together. J.A. 85. Oke stated that the visa was for him and that he was traveling with his family. According to petitioner, "because of the . . . bank statements[] [and] all the things that he provided,. . . [the embassy officials] did not ask any further questions. They just said, come tomorrow, pick up your passports by 12 noon." Id. These events occurred in 1994, shortly before petitioner's first trip to the United States. Thereafter, whenever petitioner's visa expired, Oke would fill out a new visa application on her behalf and take it, along with petitioner's passport, to the American embassy in Lagos. It was in this way that petitioner obtained the visa on which she traveled to the United States in August 2000.
Petitioner further testified that Oke had paid for her to visit the United States in 1994, 1997, and 1998. Her August 2000 visit, however, was undertaken without Oke's knowledge and motivated by her desire to leave him. Shortly after arriving in the United States, she met and married Peter Emokah. Nevertheless, she continued to call Oke periodically to discuss matters relating to their son, who was living in Nigeria with petitioner's sister. Petitioner testified that these communications, and the surname "Oke" on her passport, caused Emokah to suspect that a "marriage [had been] contracted" between petitioner and Oke. Id. at 105. In response to these suspicions, Emokah withdrew the I-130 visa petition he had filed on petitioner's behalf; they separated several months later and subsequently divorced.
Petitioner also testified about the hardships she would face if she were returned to Nigeria. Specifically, she stated that she did not have any prospects for employment and feared retaliation from Oke. She also testified that her "[l]ife would not be safe, generally" based on country conditions. Id. at 94. Petitioner submitted a number of documents to corroborate her testimony. Among these were a letter from her father to Emokah, reassuring Emokah that petitioner was not married to Oke but had used his surname in order to obtain a visa for travel to the United States after a prior visa application in her own surname had been rejected;[7] and a *115 letter from Emokah to the Immigration and Naturalization Service stating that petitioner had told him that "she used . . . Mr Oke's name to get [her] visa because of financial verification purposes." Id. at 181.
At the close of the hearing, the IJ issued an oral decision finding that (1) petitioner had "committed visa fraud on several occasions by using the name Oke when she, in fact, did not have that name"; and (2) "there is some discrepancy as to why she used the name Oke."[8]See In re Emokah, No. A XX-XXX-XXX, at 6 (Imm. Ct. Hartford June 16, 2005). Evaluating whether petitioner had satisfied the "extreme hardship" requirement for a waiver of inadmissibility pursuant to section 1182(i), the IJ determined that "[c]onsidering all the factors," petitioner had not presented "sufficient evidence to establish extreme hardship." Id. Rather, petitioner's claim of hardship is "generally the hardship that happens based on anyone who departs the United States." Id. The IJ also concluded that, "based on the underlying fraud and the clear discrepancies in the [evidence presented by petitioner], . . . the favorable exercise of discretion is not warranted." Id. at 7. Accordingly, the IJ denied petitioner's applications for a waiver of inadmissibility and adjustment of status and ordered petitioner returned to Nigeria.
Petitioner then appealed to the BIA. On appeal she claimed that (1) she did not need to obtain a section 1182(i) waiver of inadmissibility prior to adjusting her status because her use of Oke's name on her visa application did not constitute misrepresentation or fraud; (2) her possession of an approved I-360 visa petition rendered her admissible under 8 U.S.C. § 1182(a)(6)(A)(ii)(II),[9] obviating the need for a section 1182(i) waiver; and (3) if the section 1182(i) waiver was required, her circumstances were such that the section 1182(i) waiver should have been granted.
In an opinion issued on June 22, 2007, the BIA explained that:
In our review [of the record], we concur with the Immigration Judge's finding that [petitioner] committed fraud or a willful misrepresentation within the scope of [8 U.S.C. § 1182(a)(6)(C)(I)] which necessitated a section [1182(i)] waiver. [Petitioner] acknowledged that she used the surname of her child's father to facilitate her obtaining a visa and. . . signed the visa application knowing the use of the surname . . . [was] a willful misrepresentation.
[W]e also concur in the Immigration Judge's analysis denying [petitioner's] request for a section [1182(i)] waiver. Although [petitioner] apparently has a lawful permanent resident mother in the United States, the record does not contain evidence of hardship to [the mother] or [petitioner], other than the emotional *116 hardships of separation which are implied by their separation. [Petitioner] herself does not have a very lengthy residence in the United States and her return to Nigeria will reunite her family there, especially her son. We also concur in the Immigration Judge's denial of the waiver in the exercise of discretion.
In re Emokah, No. A XX-XXX-XXX (B.I.A. June 22, 2007) (internal citations omitted).
The BIA rejected petitioner's claim that she fell within the exception for battered women set forth in section 1182(a)(6)(A)(ii)(II) on the basis that "[h]er marital troubles began when her U.S. husband found out about her entry and purported marriage in Nigeria." Id. Specifically, the BIA concluded that petitioner could not demonstrate a "nexus between her fraudulent entry and her abusive marriage [because] . . . [she] entered prior to even meeting her citizen husband," id.; nor could she satisfy the requirements of section 1182(a)(6)(A)(ii)(II), see note 6 ante (text of provision), with evidence of "mistreatment of her by the Nigerian father of her son as they were not married," id. Accordingly, the BIA "adopt[ed] and affirm[ed]" the IJ's decision. Id.

II. DISCUSSION
Because the BIA fully adopted the IJ's decision, we review the decisions of both the BIA and IJ. See, e.g., Yan Chen v. Gonzales, 417 F.3d 268, 271 (2d Cir.2005) ("Where the BIA adopts the decision of the IJ and merely supplements the IJ's decision, . . . we review the decision of the IJ as supplemented by the BIA."). Pursuant to Chevron U.S.A. Inc. v. Natural Res. Def. Council, Inc., 467 U.S. 837, 844, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), we defer to the agency's interpretations of ambiguous provisions of the Immigration and Nationality Act, unless those interpretations are "arbitrary, capricious, or manifestly contrary to the statute." See, e.g., Singh v. Gonzales, 468 F.3d 135, 138-39 (2d Cir.2006). We review an agency's factual findings under the substantial evidence standard, treating them as "conclusive unless any reasonable adjudicator would be compelled to conclude to the contrary." 8 U.S.C. § 1252(b)(4)(B). See, e.g., Corovic v. Mukasey, 519 F.3d 90, 95 (2d Cir.2008).

A. The agency's determination that petitioner's conduct rendered her inadmissible under 8 U.S.C. § 1182(a)(6)(C)(i)
The bar on admissibility established by section 1182(a)(6)(C)(i) applies to "[a]ny alien who, by fraud or willfully misrepresenting a material fact, seeks to procure (or has sought to procure or has procured) a visa, other documentation, or admission into the United States. . . ." The agency determined that petitioner misrepresented a fact in her visa application; that her misrepresentation was willful; that the fact in question was material; and that petitioner's material misrepresentation allowed her to procure a visa for travel to the United States. Accordingly, it concluded that petitioner's conduct rendered her inadmissible under 8 U.S.C. § 1182(a)(6)(C)(i).
On appeal, petitioner acknowledges that she knowingly used the wrong name in connection with her visa application but contends that her conduct "does not amount to fraud" because she lacked "fraudulent intent." Petitioner's Br. 7. Petitioner does not, however, dispute that her conduct amounted to "misrepresentation." We therefore turn to the question of whether this misrepresentation was (1) willful and (2) material.
"[A]n act is done willfully if [it is] done intentionally and deliberately and if it *117 is not the result of innocent mistake, negligence or inadvertence." United States v. Dixon, 536 F.2d 1388, 1397 (2d Cir.1976) (internal quotation marks omitted); see also United States v. Temple, 447 F.3d 130, 137 (2d Cir.2006) (noting that "`[w]illful' repeatedly has been defined in the criminal context as intentional, purposeful, and voluntary, as distinguished from accidental or negligent"); Forbes v. INS, 48 F.3d 439, 442 (9th Cir.1995) (noting that, for purposes of the INA, "the requirement. . . of fraud or willful misrepresentation is satisfied by a finding that the misrepresentation was deliberate and voluntary[;] [p]roof of an intent to deceive is not required; [r]ather, knowledge of the falsity of a representation is sufficient" (internal citations omitted)). By petitioner's own admission, her use of the name "Oke" on her visa application was a deliberate act, "not the result of innocent mistake, negligence or inadvertence." Dixon, 536 F.2d at 1397 (internal quotation marks omitted). We therefore conclude, as a matter of law, that the evidence was sufficient to support the agency's finding that petitioner's misrepresentation was "willful" in nature.
"[A] concealment or misrepresentation is material if it `has a natural tendency to influence or was capable of influencing, the decision of the decisionmaking body to which it was addressed.'" Monter v. Gonzales, 430 F.3d 546, 553 (2d Cir.2005) (quoting Kungys v. United States, 485 U.S. 759, 770, 108 S.Ct. 1537, 99 L.Ed.2d 839 (1988)). To obtain a B-2 visa, an alien must satisfy the consular official issuing the visa that
the alien qualifies under the provisions of INA 101(a)(15)(B), [8 U.S.C. § 1101(a)(15)(B)], and that:
(1) The alien intends to leave the United States at the end of the temporary stay . . .
(2) The alien has permission to enter a foreign country at the end of the temporary stay.
(3) Adequate financial arrangements have been made to enable the alien to carry out the purpose of the visit to and departure from the United States.
22 C.F.R. § 41.31(a). To qualify for non-immigrant status under section § 1101(a)(15)(B), an alien must "hav[e] a residence in a foreign country which he has no intention of abandoning and [be] visiting the United States temporarily." At the time that petitioner applied for her B-2 visa, she was a secretary at the Merchant Bank of Africa with several family members in the United States. Petitioner's presentation of herself as the wife of a wealthy businessman with strong ties to Nigeria was, therefore, undoubtedly a misrepresentation "capable of influencing[ ]the decision of the decisionmaking body," Monter, 430 F.3d at 553, responsible for evaluating her B-2 visa application.
Proof that an alien has made a material misrepresentation in the course of applying for an immigration benefit creates a rebuttable presumption that the alien procured the benefit by means of this misrepresentation. Id. at 557-58. To rebut this presumption, the alien must demonstrate that knowledge of his true circumstances would not have led to the denial of the benefit. Id. In other words, for purposes of section 1182(a)(6)(C)(i), an alien has procured an immigration benefit through material misrepresentation when that misrepresentation was determinative to the alien's success in obtaining the benefit sought. The IJ  noting that (1) petitioner's submissions revealed "some discrepancy as to why she used the name Oke" and that (2) petitioner's explanation was "in conflict with her father's . . . letter"  determined that petitioner had *118 failed to rebut the presumption that she had procured her visa through willful misrepresentation. The record reveals no evidence sufficient to compel a different conclusion. Indeed, petitioner's inability to secure a visa in her true name reinforces the conclusion that her misrepresentation of her name was both willful and material.
Accordingly, we conclude that the agency committed no legal error in holding that petitioner's conduct rendered her inadmissible under 8 U.S.C. § 1182(a)(6)(C)(i).

B. The agency's determination that petitioner did not fall within the exception set forth in 8 U.S.C. § 1182(a)(6)(A)(ii)
In her submissions to our Court, as before the BIA, petitioner contends that her possession of an approved I-360 visa petition rendered her admissible under 8 U.S.C. § 1182(a)(6)(A)(ii), obviating the need for a section 1182(i) waiver. Section 1182(a)(6)(A) applies to aliens "present in the United States without being admitted or paroled, or who arrive[] in the United States at any time or place other than as designated by the Attorney General." Id. § 1182(a)(6)(A)(i). Accordingly, we begin our analysis by considering whether the circumstances of petitioner's entry conform to any of the qualifying circumstances set forth in section 1182(a)(6)(A).
Petitioner contends that, if we determine that she obtained her visa through fraud or misrepresentation, we must also conclude "that she was present without admission."[10] Petitioner's Br. 6. We disagree. The Immigration and Nationality Act ("INA") defines "[t]he terms `admission' and `admitted' [to] mean, with respect to an alien, the lawful entry of the alien into the United States after inspection and authorization by an immigration officer." 8 U.S.C. § 1101(a)(13)(A). Accordingly, an alien who enters the United States after inspection and authorization has been "admitted" even if he was, "at the time of entry . . . within one or more of the classes of aliens inadmissible by the law." See 8 U.S.C. § 1227(a) & (a)(1). Petitioner traveled to the United States on a B-2 tourist visa issued to her in Nigeria and was permitted entry after inspection and authorization by an immigration officer in the United States. The manner in which she procured her admission rendered her inadmissible at the time of entry, see supra II.A, but does not change the fact that she was, indeed, admitted. Petitioner is, therefore, plainly outside the exception set forth in section 1182(a)(6)(A)(ii).
Even if we were to conclude otherwise, however, we identify no error in the agency's conclusion that petitioner failed to demonstrate a "substantial connection," see 8 U.S.C. § 1182(a)(6)(A)(ii)(III), between her fraudulent entry and any abuse she may have suffered at the hands of her U.S. citizen husband after her entry. The language of the statute makes clear that it applies where mistreatment somehow prompts or leads to illegal entry, not where a petitioner claims unrelated mistreatment following such entry.

C. The agency's denial of petitioner's application for a waiver of inadmissibility
The IJ denied petitioner's application for a waiver of inadmissibility pursuant to 8 *119 U.S.C. § 1182(i) upon concluding that petitioner's evidence did not suggest that (1) she would suffer "extreme hardship" if removed to Nigeria or (2) a favorable exercise of discretion was otherwise warranted. In her submissions to our Court, petitioner contends that the record does not support the agency's conclusion that she would not suffer severe hardship if removed to Nigeria. She also contends that the agency lacked a valid reason for denying her the benefit of a favorable exercise of discretion.
The determination that an applicant for section 1182(i) relief has failed to meet the "extreme hardship" requirement set forth therein involves "factual and discretionary decisions." See, e.g., Camara v. Dep't of Homeland Sec., 497 F.3d 121, 124 (2d Cir.2007). As we have observed on numerous occasions, "we lack jurisdiction to review challenges to factual and discretionary determinations . . . unless the petitioner raises a constitutional claim or a question of law." Id. "[Petitioner's] arguments that the agency's decision was not supported by substantial evidence and was clearly erroneous represent `quarrels over the [exercise of discretion and the] correctness of the factual findings' reached by the agency." Id. (quoting Xiao Ji Chen v. U.S. Dept. of Justice, 471 F.3d 315, 329 (2d Cir.2006)). Accordingly, we lack jurisdiction to review petitioner's challenge to the denial of her application for section 1182(i) relief.

III. CONCLUSION
For the reasons given above, the petition for review is (1) denied as to the agency's determination that petitioner's conduct rendered her inadmissible under 8 U.S.C. § 1182(a)(6)(C)(i) and (2) dismissed as to the agency's denial of petitioner's application for section 1182(i) relief.
NOTES
[1]  Pursuant to Federal Rule of Appellate Procedure 43(c)(2), Attorney General Michael B. Mukasey is automatically substituted for former Attorney General Alberto R. Gonzales as a respondent in this case.
[2]  Section 1182(i), which relates to the "[a]dmission of [an] immigrant inadmissible for fraud or willful misrepresentation of material fact," states, in relevant part, that "[t]he Attorney General may, in the discretion of the Attorney General, waive the application of clause (i) of subsection (a)(6)(C) of this section. . . in the case of a VAWA [Violence Against Women Act] self-petitioner, [if] the alien demonstrates extreme hardship to the alien . . ."

Section 1182(a)(6)(C)(i) provides that "[a]ny alien who, by fraud or willfully misrepresenting a material fact, seeks to procure (or has sought to procure or has procured) a visa, other documentation, or admission into the United States or other benefit provided under this chapter is inadmissible."
[3]  Section 1255(a) provides, in relevant part, that:

[t]he status of an alien . . . having an approved petition for classification as a VAWA self-petitioner may be adjusted by the Attorney General, in his discretion and under such regulations as he may prescribe, to that of an alien lawfully admitted for permanent residence if (1) the alien makes an application for such adjustment, (2) the alien is eligible to receive an immigrant visa and is admissible to the United States for permanent residence, and (3) an immigrant visa is immediately available to him at the time his application is filed.
[4]  The I-360 petition is a form that relatives of U.S. citizensincluding abused spouses of such personsmust file in order to obtain immigrant status based on their "qualifying relationship to a citizen," 8 C.F.R. § 204.1(a)(3). See 8 U.S.C. § 1154(a)(1)(A)(iii)(I) & (II)(aa)(CC)(ccc) (setting forth the procedure for adjustment to immigrant status by an alien whose marriage to a U.S. citizen terminated on account of "battering or extreme cruelty by the United States citizen spouse"); 8 C.F.R § 204.2(c)(1)(i)(E) (same).
[5]  As we noted in Ibragimov v. Gonzales:

A B-2 visa, often referred to as a "tourist" visa, may be issued to a "visitor for pleasure" so that such a person may remain legally in the United States for a temporary period. The initial period of authorization of a B-2 visa may not exceed one year, but may be extended in increments of six months.
476 F.3d 125, 128 n. 2 (2d Cir.2007) (citing 8 C.F.R. § 214.2(b)(1)).
[6]  The I-130 petition is a form that a U.S. citizen must file in order to obtain immigrant status for an alien spouse based on their marital relationship. See 8 U.S.C. § 1154(a)(1)(A)(i) (setting forth the procedure whereby a U.S. citizen may petition for an adjustment to immigrant status for his or her alien spouse); 8 C.F.R. § 204.1(a) (same).
[7]  The letter states, in relevant part: "In the process of seeking answers to your questions, I learn[ed] that way back in 1989 when Stella applied for an American [v]isa and was turned down, she agreed to Mr. Oke's suggestion to make a fresh application using his name. She subsequently did and was issued the said visa." J.A. 323.
[8]  As the IJ observed, petitioner testified that she "changed her name [to `Oke'] because her child couldn't get into school because he was illegitimate." J.A. 32, 83-84. The IJ, however, "f[ou]nd that [explanation] hard to believe," noting that it "conflict[ed]" with the explanation provided in the letter from petitioner's father, which stated that petitioner used the Oke name to secure a visa after failing to secure one in her own name. Id. at 32.
[9]  Section 1182(a)(6)(A) establishes the inadmissibility of "[a]liens present without admission or parole" but recognizes an exception for "battered women," id. § 1182(a)(6)(A)(ii), who can demonstrate, inter alia, that "there was a substantial connection between the battery [they experienced] . . . and [their] unlawful entry into the United States," id. § 1182(a)(6)(A)(ii)(III).
[10]  Petitioner does not allege that she arrived at a time or place not contemplated by her visa, or that she was ever a parolee within the meaning of section 1182(a)(6)(A). Cf. Ibragimov, 476 F.3d at 131 ("`Parole' is an administrative practice whereby the government allows an arriving alien who has come to a port-of-entry without a valid entry document to be temporarily released from detention and to remain in the United States pending review of . . . his immigration status.").
