#### UNITED STATES of America, Plaintiff-Appellee, v. Billy Miranda FLORES, Defendant-Appellant.

No. 12-30078.

United States Court of Appeals, Ninth Circuit.

Argued and Submitted June 7, 2013.

Filed Aug. 2, 2013.

*1031Jonathan I. Edelstein, Law Office of Alan Ellis, New York, NY, for Defendant-Appellant.

Teal Luthy Miller, Assistant United States Attorney (argued), and Jenny A. Durkan, United States Attorney, Office of the United States Attorney, Seattle, WA, for Plaintiff-Appellee.

Before: ARTHUR L. ALARCÓN, RONALD LEE GILMAN,* and SANDRA S. IKUTA, Circuit Judges.

*

 The Honorable Ronald Lee Gilman, Senior Circuit Judge for the U.S. Court of Appeals for the Sixth Circuit, sitting by designation.

OPINION

ALARCÓN, Circuit Judge:

Billy Miranda Flores (“Flores”) was convicted on one count of conspiracy to distribute oxycodone, three counts of distribution of oxycodone, one count of possession with intent to distribute metha*1032done, and one count of possession of a firearm in furtherance of the methadone charge. The district court sentenced Flores to 240 months imprisonment—180 months for the drug charges and 60 months for the firearm charge, imposed consecutively. Flores appeals his conviction of the gun charge and his sentence. We have jurisdiction under 28 U.S.C. § 1291 and 18 U.S.C. § 3742(a). In this opinion, we consider only Flores’s challenges to his sentence. In a concurrently filed memorandum disposition, we address Flores’s separate challenges to his conviction. *See United States v. Flores,*— Fed.Appx. -, 2013 WL 3963793 (9th Cir.2013).

Flores argues that in imposing the sentence, the district court erred in estimating the quantity of drugs attributable to the conspiracy under the United States Sentencing Guidelines, and in applying a two-level sentencing enhancement under United States Sentencing Guidelines Manual § 3B1.4 for use of a person less than eighteen years of age in the conspiracy to distribute oxycodone.1 We conclude that any error in estimating the quantity of drugs attributable to the conspiracy was harmless, but that the district court erred in imposing the sentencing enhancement without an adequate factual basis. We accordingly vacate Flores’s sentence and remand for resentencing.

I

This case arises out of a joint Federal Bureau of Investigation (“FBI”) and Drug Enforcement Agency (“DEA”) investigation into oxycodone2 and methadone trafficking on Puyallup tribal land in Washington State. Sometime before the summer of 2008,3 law enforcement began investigating Flores and the smoke shop he managed, the Indian Smoke Shop (the “Shop”), which is located on the Puyallup reservation. The investigation employed physical and electronic surveillance, telephone toll records, trap and trace devices on target telephones, a pole camera installed outside the Shop, confidential informants, and controlled purchases of pills by undercover *1033agents and cooperators. The investigation ended on October 20, 2009, when law enforcement officers arrested Flores and his codefendants: Bill C. Flores (“Flores Senior”), Flores’s father; Tiny Bean-Flores (“Tiny Bean”), Flores’s half-brother and an employee of the Shop; Danny Lee Sherwood (“Sherwood”), Flores’s relative and an employee of the Shop; Timothy More-head, a purchaser; and Shelbie Ingham (“Ingham”), Flores’s girlfriend at the time.

The same day, law enforcement officers searched the Shop and Flores’s house pursuant to search warrants and uncovered evidence of a drug conspiracy. Officers discovered cash and two bottles of methadone, and a loaded Smith and Wesson, Model 29, .44 Magnum revolver in an unlocked drawer approximately one foot from a safe where the officers recovered the bottles of methadone. The search of Flores’s house yielded approximately seven empty prescription bottles—five of which were for oxycodone and all of which were prescribed to persons other than Flores.

Based on this evidence, Flores and his codefendants were indicted and charged in 34 counts. Flores was indicted with one count of conspiring to distribute oxycodone and methadone in violation of 21 U.S.C. § 841(a)(1), (b)(1)(C), and 846, five counts of substantive distribution of oxycodone in violation of 21 U.S.C. § 841(a)(1), (b)(1)(C), one count of possession with intent to distribute methadone in violation of 18 U.S.C. § 2 and 21 U.S.C. §§ 841(a)(1), (b)(1)(C), and one count of possession of a firearm in furtherance of the methadone count in violation of 18 U.S.C. §§ 2, 924(c)(1)(A). Tiny Bean, Ingham, Morehead, and Flores Senior entered into plea agreements. Flores and Sherwood proceeded to trial. A jury found Flores guilty of conspiring to distribute oxycodone, distributing oxycodone, possessing methadone with intent to distribute it, and possessing a gun in furtherance of the methadone charge.4

In calculating Flores’s base offense level, Flores’s Presentence Report (“PSR”) adopted a start date for the conspiracy of October 2007 and estimated that the conspiracy sold 1,000 to 1,500 80-milligram pills of oxycodone per day. PSR recommended a two-level upward adjustment for use of Shelbie Ingham, a person under eighteen years of age, in the conspiracy. Flores filed objections to the PSR in his sentencing memorandum. Specifically, he asserted that (1) the PSR’s estimate of the quantity of drugs attributable to the conspiracy was too high, and (2) there was no evidence to support the enhancement for use of a minor.

At Flores’s sentencing hearing, Sherwood testified that he joined the conspiracy in May 2009 and eventually sold up to 1,000 pills daily for Flores. The district court concluded that a “conservative estimate” placed the start date of the conspiracy in December 2007, based on an unindicted coconspirator’s trial testimony. The court noted that it had heard “a lot of testimony about the volume of the sales” and concluded that 500 80-milligram pills of oxycodone was a “conservative! ]” estimate of the amount of pills that moved through the conspiracy daily between December 2007 and October 2009.

The district court explained that the marijuana equivalent for that amount of oxycodone was “well over” 30,000 kilograms of marijuana, which is the smallest quantity that triggers the highest base offense level, 38, in the Drug Quantity Table. *See*U.S. Sentencing Guidelines Manual § 2D1.1 (Drug Quantity Table).5*1034The district court therefore concluded that Flores’s base offense level was 38. The district court imposed a four-level enhancement for Flores’s leadership role in the conspiracy and a two-level enhancement for use of a minor. However, the district court did not make an express finding as to Ingham’s age at the time of her involvement in the conspiracy. The court imposed a two-level downward adjustment for Flores’s acceptance of responsibility, resulting in a total offense level of 42. The court correctly stated that the Guidelines range for an offense level 42 and criminal history category I is 360 months to life.

The district court did not rely solely on the Guidelines range in determining its ultimate sentence. Noting that the Federal Sentencing Guidelines are advisory, the court explained that the “big issue is not so much the math, the calculations; it’s the qualitative issues that are so distressing. ... Maybe Shelbie Ingham was broken before Billy Miranda Flores got his claws in her, but she is definitely broken now.” The court also stated:

> There is a lot of human wreckage in this case, and we don’t even know how pervasive the reach of this conspiracy went, not those who agreed to perform sales, but just the reach of the conspiracy, the people who bought, the people who sold and more—most importantly, those people who used.

The district court further opined that the “biggest challenge for any judge who sentences someone” is determining the difference between a criminal “who is ignorant or dumb or stupid ... [and] in need of a break” and those who “are really bad.” “I put Billy Miranda Flores among that [latter] group” because Flores “preys on people,” “has no empathy for other people,” and “has harmed so many people.” Based on “the seriousness of the offense, the personal characteristics, the need to promote the rule of law and to deter people from committing the same offenses that he has committed,” the court imposed a total of 240 months of imprisonment—180 months of imprisonment on the drug charges, half of the low-end of the advisory Guidelines range, and 60 months on the firearm offense, which is the mandatory minimum sentence for a violation of 18 U.S.C. § 924(c).

Flores raises two issues on appeal relating to the calculation of his Federal Sentencing Guidelines range. First, Flores argues the district court erred in calculating the amount of drugs attributable to the conspiracy by employing a method that was not sufficiently reliable and by failing to “err on the side of caution” as required by Ninth Circuit precedent. Second, Flores asserts that the two-level enhancement for use of a person under eighteen *1035years of age in the conspiracy was not supported by the record.

II

We first address Flores’s challenge to the district court’s calculation of the drug quantity attributable to the conspiracy. “When we review a sentence, the first step is to determine if the district court made a material error in its Guidelines calculation that serves as the starting point for its sentencing decision.” *Kilby,*443 F.3d at 1140 (citing *United States v. Cantrell,*433 F.3d 1269, 1280 (9th Cir.2006)). If we find a material error in the Guidelines calculation, “we will remand for resentencing, without reaching the question of whether the sentence as a whole is reasonable.” *Kilby,*443 F.3d at 1140 (citation omitted). If the district court did not err in applying the Guidelines, we then consider challenges to the reasonableness of the overall sentence in light of the factors specified in 18 U.S.C. § 3553(a). *Id.*

This Court reviews *de novo*“whether a district court’s method of approximation of the relevant drug quantity conforms to the Guidelines.” *Id.*(citing *United States v. Rosacker,*314 F.3d 422, 425 (9th Cir.2002)). After *United States v. Booker,*543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), we review a district court’s sentencing decisions, including its factual findings, for abuse of discretion. *Gall v. United States,*552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007); *United States v. Carty,*520 F.3d 984, 993 (9th Cir.2008) (en banc). Under the law of this Circuit, a district court is required to resolve factual disputes regarding drug quantity by applying the preponderance of the evidence standard. *Kilby,*443 F.3d at 1140; see *Rosacker,*314 F.3d at 429-30 (holding the clear and convincing standard that applies to cases where a sentencing factor has an extremely disproportionate effect on the sentence does not apply to drug quantity approximations).

Several different witnesses testified about the quantity of drugs sold by the conspiracy. Most of the evidence at trial relating to the quantity of drugs over the life of the conspiracy came from codefendant Tiny Bean, unindicted coconspirators Leslie Larson (“Larson”) and Dennis Hilsendeger (“Hilsendeger”), law enforcement officers who surveilled the Shop, and an undercover officer who made three controlled buys from Flores. In addition, Sherwood testified at Flores’s sentencing hearing regarding the amount of drugs Sherwood sold for the conspiracy.

A short summary of the coconspirators’ testimony relating to the quantity of drugs they individually sold for Flores is useful here. Larson testified she began selling drugs for Flores in approximately February of either 2007 or 2008, while the other coconspirators testified they began selling for Flores as early as January 2008 and as late as mid-2009. Larson testified that she sold drugs for Flores for approximately one year until her arrest on April 16, 2009. Over this one-year period, Larson testified she started selling a few pills per day and eventually increased to selling hundreds of pills per day. Hilsendeger testified he sold pills for Flores for approximately six months, starting with a few pills a day in January or February 2008 and eventually increasing to 50 or 100 pills per day. Tiny Bean testified he sold pills for Flores when Flores was out of town and sold approximately 100 to 300 pills over ten or twelve weekends, or 50 to 100 pills per day, but once sold around 1,000 pills over one weekend. Sherwood testified he sold pills for Flores for around six months starting in May 2009, though he believed that Flores began selling pills in 2007. Sherwood testified he sold hundreds of pills per day when he started and even*1036tually increased to 1,000 pills per day. Sherwood estimated that eight to ten other persons sold drugs for Flores. The witnesses testified they primarily sold 80-milligram pills.

The PSR estimated that the conspiracy sold 1,000 to 1,500 80-milligram pills per day from October 2007 through October 2009. The district court adopted December 2007 as the start date of the conspiracy and used 500 80-milligram pills as a “conservative” estimate of the volume of oxycodone pills moved by the conspiracy per day.

The accuracy of this estimate is important because the applicable Guidelines range for a drug trafficking crime depends upon the weight of drugs involved. *United States v. Culps,*300 F.3d 1069, 1076 (9th Cir.2002); U.S. Sentencing Guidelines Manual § 2Dl.l(a), (c) (2004). Where, as here, none6 of the total drugs allegedly sold by the conspiracy were seized, the district court may approximate the weight of the drugs. *Kilby,*443 F.3d at 1141 (citing *United States v. August,*86 F.3d 151, 154 (9th Cir.1996); U.S. Sentencing Guidelines Manual § 2D1.1, cmt. n.5).7 Because a sentence will vary greatly based on these approximations, courts must exercise caution in selecting the method of calculation and meet the following criteria: (1) “the government is required to prove the approximate quantity by a preponderance of the evidence ... [which means that] [t]he district court must conclude that the defendant is more likely than not actually responsible for a quantity greater than or equal to the quantity for which the defendant is being held responsible”; (2) “the information which supports an approximation must possess sufficient indicia of reliability to support its probable accuracy”; and (3) because the defendant’s “sentence depends in large part upon the amount of drugs ... and approximation is by definition imprecise, the district court *must err on the side of caution*” in approximating the drug quantity. *Culps,*300 F.3d at 1076 (emphasis added) (internal quotation marks and citation omitted); *United States v. Walton,*908 F.2d 1289, 1302 (6th Cir.1990) (“[W]hen choosing between a number of plausible estimates of drug quantity, none of which is more likely than not the correct quantity, a court must err on the side of caution.”).

This Court previously has approved the “multiplier method” employed by the district court, which estimates the total quantity of drugs sold by “selecting a time period over which it is more likely than not that the defendant was dealing in that quantity and multiplying these two factors together.” Culps, 300 F.3d at 1077 (holding the multiplier method is an acceptable means of calculating drug quantity “[p]rovided that the approximation has a reliable evidentiary basis and that the court proceeds with caution”). Applying the multiplier method in this case required the district court to determine three data points: the length of the conspiracy, the number of pills sold by the conspiracy per day, and the tablet strength of the pills. We examine the district court’s findings as to each data point.

*1037We begin with the easiest data point first: the tablet strength. Several witnesses involved in the conspiracy testified they primarily sold 80-milligram pills, and no witness contradicted this testimony. In addition, Flores sold 70 to 100 80-milli-gram pills to an undercover agent during three controlled buys. Consequently, the district court’s adoption of an average tablet strength of 80-milligrams was not an abuse of discretion.

The next data point we consider is the quantity of drugs attributable to the conspiracy per day. The district court discounted its baseline estimate of 1,000 pills per day by fifty percent to satisfy its duty to account for a margin of error. *See id.*at 1081 (stating fifty percent reduction of baseline estimate ordinarily will “satisfy the district court’s duty to err on the side of eaution[,]” assuming the amount being discounted is founded on reliable evidence); cf*. August,*86 F.3d at 154 (permitting the method of calculating “lab capacity” as an approximation of the relevant amount of drugs that “could have been produced *during the course of the offense*”) (emphasis in original). There was scant evidence at trial relating to the quantity of drugs sold during the earliest months of the district court’s selected time frame for the conspiracy.8 There was, however, coconspirator testimony attributing hundreds of pills per day to the conspiracy from January 2008 through mid-2008 and then even higher amounts for the months thereafter. The district court’s estimate of 500 80-milligram pills per day is supported by a preponderance of the evidence. Thus, the district court did not abuse its discretion in estimating the daily drug quantity attributable to the conspiracy-

Finally, as to the last data point, the length of the conspiracy, the district court adopted a start date of December 2007. In selecting that date, the district court stated that it relied on Larson’s testimony. Larson testified that she purchased oxycodone from Flores for approximately one year. At the sentencing hearing, the district court stated that Larson was arrested in August 2008 and that nine or twelve months before her arrest would place her entrance into the conspiracy in “October to December 2007.” Later, the court stated:

> I believe the conspiracy began on or before December 2007. Leslie Larson was arrested in August [2008]. She was buying up to 300 pills per day from Billy Flores for 9 to 12 months at that time. Taking the conservative estimate would put that in December 2007.

Thus, to arrive at December 2007 as the start date of the conspiracy, the district court relied on August 2008 as the date Larson was arrested and then counted backwards nine months to reach December 2007.

The evidence at trial, however, does not support a finding that Larson was arrested in August 2008. Although Larson testified that law enforcement searched her apartment at some unspecified date before her arrest, she stated that her “first arrest” for selling drugs for Flores was not until April 16, 2009. Larson testified that she *1038was arrested again in November 2009 (the day after Thanksgiving) for not appearing in court and then served six months of imprisonment.

A district court may rely on a coconspirator’s testimony where, as here, the testimony is given under oath and is subject to cross-examination. *See, e.g., United States v. Alvarez,*358 F.3d 1194, 1213 (9th Cir.2004) (holding three coconspirators’ estimates of drug weight were sufficiently reliable where they testified under oath and were subject to cross-examination); *United States v. Melchor-Zaragoza,*351 F.3d 925, 929 (9th Cir.2003) (holding that a coconspirator’s testimony that twenty-three aliens were taken hostage by conspirators was sufficient to support court’s finding, for sentencing purposes, that twenty-three victims were involved in the conspiracy to commit hostage taking). However, there is no evidence in the record to support the district court’s finding that Larson was arrested in August 2008. Consequently, the district court’s December 2007 start date of the conspiracy, which was based on the purported August 2008 arrest, also is not supported by Larson’s testimony.

Sherwood was the only other witness who testified that Flores was selling drugs in 2007. In response to Government questioning at the sentencing hearing, Sherwood confirmed that he was not “aware of any time period from [an unspecified date in 2007] until [Sherwood’s] arrest in 2009 when Billy Flores wasn’t selling pills.” The remaining witnesses testified to entering the conspiracy in 2008 or 2009. Of those witnesses, Hilsendeger testified to the earliest involvement—in January or February of 2008.

The PSR placed the start date of the conspiracy in October 2007, two months before the date the district court adopted. A “court may adopt the factual findings of the presentence report ... [but] may not ... adopt conclusory statements unsupported by facts or the Guidelines.” *United States v. Navarro,*979 F.2d 786, 789 (9th Cir.1992); *see United States v. Garcia-Sanchez,*189 F.3d 1143, 1149 (9th Cir.1999) (reversing estimate of conspiracy’s weekly drug sales where government offered only agent’s unexplained conclusions that did not contain “sufficient indicia of reliability to support its probable accuracy” (citation omitted)). Sherwood’s testimony gives the district court’s determination that the conspiracy started in December 2007 some slight support. But even if the district court erred in determining the start date, any error in the district court’s calculation of the length of the conspiracy is harmless beyond a reasonable doubt. *See Alvarez,*358 F.3d at 1213 (holding any error was harmless where, in order to lower defendant’s base offense level, the quantity of drugs would have to drop below an amount that was not supported by the record). Selecting a start date, based on Hilsendeger’s testimony, of January or February 2008 would result in the same base offense level, as would adopting Flores’s suggested start date of September 25, 2008. Indeed, even if the length of the conspiracy were cut in half, the number of pills sold by the conspiracy daily would have to drop below 170 80-milligram pills to lower Flores’s base offense level from 38 to 36. Such a drop is not supported by the record. Thus, a recalculation of the Guidelines range by the district court based on a shorter conspiracy length would not lead to a lesser base offense level. *See id.*Consequently, any error by the district court in calculating the quantity of drugs attributable to the conspiracy is harmless. *See Cantrell,*433 F.3d at 1280; *United States v. Scheele,*231 F.3d 492, 499-500 & n. 4 (9th Cir.2000).

*1039III

Flores next argues that the district court committed procedural error in imposing a sentencing enhancement for use of a person under eighteen years of age in the conspiracy. Flores maintains there was no evidence in the record as to Shelbie Ingham’s age at the time she entered the conspiracy. We agree that the district court abused its discretion in imposing this sentencing enhancement because the court failed to set forth its reasons for finding that Ingham was a minor when she participated in the conspiracy.

A

At trial, Flores testified that he met Shelbie Ingham around November or December 2008. After meeting Ingham, Flores said he did not see her for four to six months because Ingham made his girlfriend at the time, Larson, “very upset,” and Larson told Flores not to talk to Ingham. Flores started talking to Ingham again after she brought her car to the Shop for repairs. In his testimony, Flores admitted to selling Ingham oxycodone in the summer of 2009, when she was around eighteen years old. Tiny Bean testified he sold drugs to Ingham sometime before he stopped selling drugs for Flores in June 2009. In August or September 2009, law enforcement made a controlled buy from Ingham. Flores admitted to being intimate with Ingham “at the end,” before he was arrested on October 20, 2009. Flores estimated that Ingham turned eighteen about four months before she was arrested, placing her birthday around June 2009.

The PSR recommended a two-level upward adjustment for Flores’s use of “a person ... less than 18 years of age to commit the offense.” Flores’s PSR referred to Ingham as a minor and stated that Ingham was addicted to pills and became a member of the conspiracy to support her addiction. Flores objected to the PSR’s characterization of Ingham as a minor at the time she was involved in the conspiracy, arguing there was no evidence to support that finding. The probation office declined to amend the PSR, however, stating that its information of Ingham’s age was based on the following language from Ingham’s PSR: “Flores provided a residence and vehicle for Ingham, who was the youngest member of the conspiracy, and barely seventeen when she became involved with Oxycontin and met Flores.”

In its Sentencing Memorandum, the Government did not request an enhancement for use of a minor pursuant to § 3B1.4, nor did it allege facts demonstrating that Ingham was a minor. It indicated at the sentencing hearing, however, that it did not “disagree with the Court that there is evidence there to find it.”

The district court failed to point to any evidence in the record establishing Ingham’s age at the time of her involvement in the conspiracy. During the sentencing hearing, defense counsel argued that the enhancement for use of a minor in the conspiracy should not apply, and the district court responded: “I can tell you that ... there’s a two-level increase on use of a person under [eighteen]. I know that from—I know [Ingham], and I know the circumstances.” After listening to Sherwood’s testimony, the argument of counsel, and Flores’s allocution, the district court imposed the two-level enhancement for using a person less than eighteen years of age in the conspiracy. The district court’s vague statement about knowing Ingham and the circumstances did not set forth any facts to justify the imposition of the enhancement.

B

Post *-Booker,*we review a district court’s sentencing decisions, including its factual findings, for abuse of discretion. *1040*Gall,*552 U.S. at 49, 128 S.Ct. 586; *Carty, 520 F.3d*at 993. A two-level sentencing enhancement may be imposed under United States Sentencing Guidelines Manual § 3B1.4 “[i]f the defendant used or attempted to use a person less than eighteen years of age to commit the offense or assist in avoiding detection of, or apprehension for, the offense,” meaning that the defendant directed, commanded, encouraged, intimidated, counseled, trained, procured, recruited, or solicited the minor. U.S.S.G. § 3B1.4 cmt. n.l (2001). The district court may impose the § 3B1.4 enhancement only if a preponderance of the evidence demonstrates that the defendant “acted affirmatively to involve the minor in the crime.” *United States v. Jimenez,*300 F.3d 1166, 1169 (9th Cir.2002) (quotation marks and citation omitted).

Because the district court did not provide a factual basis for imposing the enhancement for use of a minor in the conspiracy, we must determine whether an “adequate explanation” can be “inferred from the PSR or the record as a whole.” *Carty,*520 F.3d at 992; *see also United States v. Jordan,*291 F.3d 1091, 1099 (9th Cir.2002) (“A merely speculative logic cannot displace the need for evidence on [the question of whether a defendant’s conduct justified a leadership-role enhancement], which cannot be decided by assumption or inference not based on fact.”). Here, neither the PSR nor the record supply an adequate explanation for this enhancement.

At trial, Flores admitted that he conspired with Ingham to sell oxycodone but denied that she was a minor when she began selling for him. There was no other evidence at trial regarding Ingham’s age when she entered the conspiracy. The PSR refers to Ingham as a minor and states that Ingham was addicted to pills and became a member of the distribution conspiracy to support her own addiction. The Addendum to the PSR, created in response to Flores’s objection, copied language from Ingham’s PSR, which states that Flores provided Ingham a residence and a vehicle and that she was “barely seventeen when she became involved with Oxycontin and met Flores.” This factual assertion does not support a finding that she became a member of the conspiracy before she reached the age of eighteen.

The first question, then, is whether these statements in the PSR may serve as a proper basis for the district court’s decision. This Court has held that a district court may rely on an *unchallenged*PSR at sentencing to find by a preponderance of the evidence that the facts underlying a sentencing enhancement have been established. *See United States v. Charlesworth,*217 F.3d 1155, 1160-61 (9th Cir.2000) (where defendant failed to challenge accuracy of information in presentence report and failed to offer any evidence to contradict presentence report, sentencing court did not err in relying on presentence report in denying defendant’s request for sentence reduction); *United States v. Marin-Cuevas,*147 F.3d 889, 895 (9th Cir.1998). However, the district court “may not ... adopt conclusory statements unsupported by the facts or the Guidelines.” *Culps,*300 F.3d at 1078 (citations omitted) (holding a conclusory statement in a PSR regarding the average transaction size in a drug conspiracy could not sustain district court’s adoption of that size where “the factual underpinning for that assertion, if any, was not explained”).

The record does not provide an explanation of the factual underpinning for the assertion in the PSR that Ingham was a minor when she participated in the conspiracy. Flores objected to the PSR and argued there was no evidence of Ingham’s age when she joined the conspiracy. He did not submit evidence regarding her age *1041when she joined the conspiracy. Flores’s failure to submit such evidence is not dis-positive. We previously have held that “when a defendant raises objections to the PSR, *the district court is obligated*to resolve the factual dispute, and *the government bears the burden of proof....*The court may not simply rely on the factual statements in the PSR.” *United States v. Showalter,*569 F.3d 1150, 1160 (9th Cir.2009) (emphasis added) (citing *United States v. Ameline,*409 F.3d 1073, 1085-86 (9th Cir.2005) (en banc); Fed.R.Crim.P. 32(i)(3)(B) (requiring court to rule on disputed matters at sentencing)). Thus, Flores’s failure to provide additional evidentiary support for his contention did not alter the district court’s obligation to resolve this factual dispute nor excuse the Government’s failure to meet its burden of proof.

The evidence in the record similarly does not provide the necessary factual underpinning for imposing the enhancement. The only evidence in the record of Ingham’s age came from Flores, who estimated that she turned eighteen in June 2009.9 None of the events the Government relies on to connect Ingham to the conspiracy took place before June 2009. The Government identifies activities that took place in the “summer,” but “summer” falls both before and after Ingham’s birthday. Nor does evidence that Ingham was “close” with Flores or in a relationship with him before she turned eighteen establish by a preponderance of the evidence that she was involved in the conspiracy at that time. The only evidence affirmatively linking Ingham to the conspiracy—as opposed to merely linking her to Flores— was law enforcement’s controlled purchase from Ingham in September 2009, which occurred *after*June 2009, the month Flores testified that Ingham’s eighteenth birthday took place. In addition, the PSR does not, contrary to the Government’s assertion, state that Ingham was seventeen when she “became involved *in the conspiracy,”*only that she was seventeen when she became involved *with Oxycontin*and *met Flores.*Ingham’s addiction to OxyContin and her relationship with Flores when she was seventeen do not demonstrate that Ingham joined the conspiracy at that time. Therefore, we conclude that the Government did not meet its burden of establishing that Ingham was a minor when she participated in conspiracy.

When a party raises a specific, non-frivolous argument that is relevant to sentencing, “the judge should normally explain why he accepts or rejects the party’s position.” *Carty,*520 F.3d at 992-93 (citation omitted). The district court’s failure to do so is not procedural error where *1042“adequate explanation” may “be inferred from the PSR or the record as a whole.” *Id.*at 992. The factual basis for the district court’s imposition of the enhancement here cannot be inferred from the PSR or the record as a whole. *See Gall,*552 U.S. at 50, 128 S.Ct. 586 (“[A court] must adequately explain the chosen sentence to allow for meaningful appellate review----”). The district court provided no factual basis for its conclusion and failed to resolve a factual dispute raised by Flores. The facts in the PSR are inconclusive as to whether Ingham was a minor when she joined the conspiracy, and the trial record does not illuminate the issue. On this limited evidentiary record, we cannot conclude that this enhancement was supported by a preponderance of the evidence. Thus, we must conclude that the district court abused its discretion by imposing the enhancement without providing an adequate factual basis.

C

The Supreme Court has held that improperly calculating the Guidelines range may constitute “significant procedural error.” *Gall,*552 U.S. at 51, 128 S.Ct. 586. Thus, even where, as here, the district court imposes a sentence well below the Guidelines range, it is difficult, if not impossible, to determine whether the court would impose the same sentence if it were to heed its imperative to keep the Guidelines range “in mind throughout the process.” *Carty,*520 F.3d at 991; *Gall,*552 U.S. at 50 n. 6, 128 S.Ct. 586 (“[District courts must begin their analysis with the Guidelines and remain cognizant of them throughout the sentencing process.”); *United States v. Munoz-Camarena,*631 F.3d 1028, 1031 (9th Cir.2011) (declining to find harmless a district court’s incorrect application of an enhancement, even though the district court sentenced the defendant above the Guidelines range and stated it would have imposed the sentence no matter the Guidelines calculation, because the Ninth Circuit was not convinced that the district court would impose the same sentence if the correct Guidelines range were “kept in mind throughout the process”) (citation omitted).

In this case, the district court calculated Flores’s total offense level as 42, which resulted in a Guidelines range of 360 months to life. Removing the incorrect two-level enhancement would result in a correct total offense level of 40, with an associated Guidelines range of 292 to 365 months. Although the two Guidelines ranges overlap slightly and the district court sentenced Flores to 180 months for the drug charges, which is below both the original and the correct Guidelines ranges, we cannot say whether the district court would impose the same sentence if it kept the correct Guidelines range in mind throughout the process. *See Munoz-Camarena,*631 F.3d at 1031. Because we conclude that material errors affected the district court’s Guidelines calculation that served as the starting point for its sentencing decision, we must vacate Flores’s sentence and remand this matter for re-sentencing. Because we remand on a procedural error, we decline to reach Flores’s argument regarding the substantive reasonableness of his sentence. *See Gall,*552 U.S. at 51, 128 S.Ct. 586 (holding that “the appellate court must ... first ensure that the district court committed no significant procedural error” and should consider whether the sentence is substantively reasonable only if “the district court’s sentencing decision is procedurally sound”); *Kilby, 443 F.8d at 1140 (“If there is*a material error in the Guidelines calculation, we will remand for resentencing, without reaching the question of whether the sentence as a whole is reasonable ... in light of the factors specified in 18 U.S.C. § 3553(a).”).

*1043D

Finally, the parties dispute whether we should allow the district court to consider new evidence on remand. The default rule is that “if a district court errs in sentencing, we will remand for resentencing on an open record—that is, without limitation on the evidence that the district court may consider.” *United States v. Matthews,*278 F.3d 880, 885-86 (9th Cir.2002) (en banc) (“On remand, the district court generally should be free to consider any matters relevant to sentencing, even those that may not have been raised at the first sentencing hearing, as if it were sentencing de novo.” (citing *United States v. Ponce,*51 F.3d 820, 826 (9th Cir.1995); *United States v. Caterino,*29 F.3d 1390, 1394 (9th Cir.1994))). We may depart from this general rule where “ ‘additional evidence would not have changed the outcome or where there was a failure of proof after a full inquiry into the factual question at issue.’ ” *Culps,*300 F.3d at 1082 (quoting *Matthews,*278 F.3d at 886); *see also United States v. Reyes-Oseguera,*106 F.3d 1481, 1484 (9th Cir.1997) (remanding for resentencing on a closed record where government offered insufficient evidence to support a reckless endangerment enhancement).

Here, we cannot conclude that there was a full inquiry into the factual question at issue or that it would be futile to introduce additional evidence regarding Ingham’s birthday and her participation in the conspiracy. The Government did not request an enhancement for use of a minor in its sentencing memorandum. Rather, the enhancement was recommended by the probation office and imposed sua sponte by the district court at the sentencing hearing before the court heard argument from the Government. The Government stated it did not disagree with the district court that there was evidence to support the enhancement, but did not present any evidence in support of the district court’s finding. Under these circumstances, we leave it to the district court’s discretion to “assess the government’s right to submit further evidence on this issue.” *Jordan,*291 F.3d at 1092; *see also United States v. Gonzales,*307 F.3d 906, 914 (9th Cir.2002) (leaving the question whether to allow new evidence upon resentencing to the district court’s discretion where the court’s initial inquiry was incomplete). We remand to the district court with directions to reconsider its sentencing decision regarding the enhancement for use of a minor.

VACATED and REMANDED for re-sentencing.

1

. Flores also contends that the district court erred in imposing a substantively unreasonable sentence. Given our holding, we do not address the substantive reasonableness of the sentence. *See United States v. Kilby,*443 F.3d 1135, 1140 (9th Cir.2006) (holding that if a reviewing court finds a material error in the Guidelines calculation, it "will remand for resentencing, without reaching the question of whether the sentence as a whole is reasonable”).

2

. At trial, the attorneys and witnesses (and consequently the presentence report, transcripts, parties' papers, and orders) used the terms "oxycodone” and "OxyContin” interchangeably. "Oxycodone” is a generic opioid pain reliever found in a number of prescription medications and is the sole active ingredient in OxyContin, a widely used prescription narcotic manufactured by Purdue Pharma L.P. *See*U.S. Gov't Accountability Office, GAO-04-110, Prescription Drugs: OxyContin Abuse and Diversion Efforts to Address the Problem 1-2, 8-9, 11 (2003). Oxycodone is classified as a Schedule II controlled substance "because it has high potential for abuse and may lead to severe psychological or physical dependence.” *Id. at 2 &*n. 6. We use the terms "oxycodone” and "OxyContin” interchangeably in our opinion to reflect their usage in the record.

3

.The record is unclear as to the start date of the two separate investigations that eventually merged into the joint investigation. DEA Investigator Errin Jewell testified that he was informed of an ongoing DEA investigation in June 2008. He learned that the investigation "had potential to be very complex, a bigger investigation involving the Indian Smoke Shop ... and [he] was assigned as the lead investigator on the investigation.” FBI Special Agent Donald Treat testified that the FBI’s South Sound Gang Task Force was conducting an investigation before it joined with the DEA’s Tacoma Narcotics Enforcement Team task force around early to mid-2008.

4

. The jury acquitted Flores of conspiring to distribute methadone.

5

. Federal sentencing courts use the Drug Quantity Table in § 2D 1.1 of the Federal Sentencing Guidelines to calculate the base of*1034fense level for offenses involving controlled substances. Where, as here, an offense involves a drug that is not listed in the Drug Quantity Table, sentencing courts use the Drug Equivalency Tables in § 2D 1.1 to covert the drug into an equivalent amount of marijuana. *See*U.S. Sentencing Guidelines Manual § 2D1.1 cmt. n.8(A) (2012). The Drug Equivalency Tables provide that one gram of actual oxycodone equals 6,700 grams of marijuana.

Here, using the district court's start date of the conspiracy, December 2007, means the conspiracy lasted 689 days. Multiplying 689 days by the district court's estimate of 500 pills per day results in a total of 344,500 80-milligram pills. Multiplying this amount by the 80 milligrams in each pill results in 27,-560.000 milligrams, or 27,560 grams, of oxycodone. Finally, after converting oxycodone to its marijuana equivalent using the 1:6,700 gram ratio in the Drug Equivalency Tables, the district court’s adopted start date and daily quantity yield a total of 184,652 kilograms of marijuana. Pursuant to the Drug Quantity Table, any amount of marijuana over 30.000 kilograms results in the highest base offense level, which is 38.

6

. Although 332 methadone pills were seized from Flores’s office, the jury acquitted Flores of conspiring to distribute methadone. Thus, those pills are not included in the quantity drugs attributable to the conspiracy to distribute oxycodone.

7

. The comment provides:

> In making this determination, the court may consider, for example, the price generally obtained for the controlled substance, financial or other records, similar transactions in controlled substances by the defendant, and the size or capability of any laboratory involved.

U.S. Sentencing Guidelines Manual § 2D1.1, cmt. n.5.

8

. Only Larson both placed the date of the conspiracy during that time period *and*provided information regarding the quantity of pills she sold during that time. However, Larson stated she began selling pills in either February 2007 or February 2008. Sherwood is the only other witness who testified that the conspiracy began in 2007 (though he was not involved at that time), but he provided no information regarding the amount of drugs sold during that period. Several witnesses— Larson, Hilsendeger, and Sherwood'—testified they began selling small amounts of pills for Flores in 2008 or 2009 and eventually increased their sales dramatically.

9

. In its answering brief, the Government states that Ingham’s birthday "was in July 2009.” The Government determined Ingham’s birthday by looking at Ingham’s Presentence Report, “to which the district court had access.” Ingham's PSR is not properly before this Court, however, because it was not in the record below. The Government alternatively argues that the PSR Addendum provided Flores access to the relevant information from Ingham’s PSR regarding her age. This is incorrect, however, because the Addendum did not include Ingham’s birthday nor did it state that she was a minor when she became involved in the conspiracy. Additionally, the district court could not base its conelusions regarding Ingham’s age and her involvement in the conspiracy on information to which Flores was not privy. *See*Appellant's Opening Br. at 34 (noting that defense counsel did not have access to Ingham’s sealed PSR). During oral argument, the Government claimed that Ingham’s Sentencing Memorandum states that her birthday is July 9, 1991. This may be true, but even if that memorandum were part of the record in this case, whether Ingham’s birthday was in June or July 2009 is immaterial, because there is no evidence in the record that establishes by a preponderance that Ingham participated in the conspiracy before July 2009.