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# At the end of year X, automobile installment credit accounte

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At the end of year X, automobile installment credit accounte  [#permalink]

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11 Nov 2013, 13:31
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00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:13) correct 32% (02:17) wrong based on 615 sessions

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At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time? A. 62 B. 171 C. 475 D. 513 E. 684 Kindly help in solving this! ##### Most Helpful Community Reply Manager Joined: 26 Sep 2013 Posts: 184 Concentration: Finance, Economics GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: Automobile Installment Credit [#permalink] ### Show Tags 11 Nov 2013, 18:12 10 11 ppravin88 wrote: At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended$57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?

A. 62
B. 171
C. 475
D. 513
E. 684

Kindly help in solving this!

So we're trying to find ALL consumer installment credit, let's call that Q.

So at the end of the year we know that 36% of Q comes from automobile installment credit. So we need to figure out the number for automobile installment credit, and then we can solve for Q. We're told that 57 billion is 1/3 of the automobile installment credit amount. So the full amount of automobile installment credit (in billions) is: 57*3 (since 1/3 of the amount is 57 billion, we multiply by 3 to find the full amount. This gives 171 (billion).

So going back to the stem we know that 36% of outstanding consumer credit (which we are calling Q) comes from automobile credit. So 171 is 36% of what number?

.36*Q=171

Q=171/.36

Q=475

so answer is C. Are you sure that was a 700 level problem?
##### General Discussion
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Re: At the end of year X, automobile installment credit accounte  [#permalink]

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29 Dec 2014, 19:39
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4
System of Equations
a = (36/100) c
(1/3) a = 57 --> a = 171

Substitution
171 = (36/100) c
c = (100/36) 171

You now have 2 ways
- You can do the ugly calculation 171/36 * 100
- Or you can notice that 100/36 is slightly smaller than 3. That way 171 * (100/3) will be slightly smaller than 171 * 3.

THE TRAP!
- 171 * 3 is actually 513, the reason why the test makers placed this trap-answer.

- The correct answer will be slightly smaller than 513. Therefore, the correct answer is 475.
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Re: At the end of year X, automobile installment credit accounte  [#permalink]

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30 Dec 2014, 21:30
2

Total automobile instalment credit = 57*3 = 171

Total consumer instalment credit $$= 171*\frac{100}{36} = 475$$
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Re: At the end of year X, automobile installment credit accounte  [#permalink]

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25 Feb 2016, 17:01
1
The way I minimized the time it took is by saving all the calculations until the end.

I wrote: (57*3)/3*2*3*2 and you'll get 57/12 which the first number when you divide starts with a 4 so I clicked C.
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At the end of year X, automobile installment credit accounte  [#permalink]

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22 Jun 2016, 23:08
AccipiterQ wrote:
ppravin88 wrote:
At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time? A. 62 B. 171 C. 475 D. 513 E. 684 Kindly help in solving this! So we're trying to find ALL consumer installment credit, let's call that Q. So at the end of the year we know that 36% of Q comes from automobile installment credit. So we need to figure out the number for automobile installment credit, and then we can solve for Q. We're told that 57 billion is 1/3 of the automobile installment credit amount. So the full amount of automobile installment credit (in billions) is: 57*3 (since 1/3 of the amount is 57 billion, we multiply by 3 to find the full amount. This gives 171 (billion). So going back to the stem we know that 36% of outstanding consumer credit (which we are calling Q) comes from automobile credit. So 171 is 36% of what number? .36*Q=171 Q=171/.36 Q=475 so answer is C. Are you sure that was a 700 level problem? 1/3 extended, 3+1= total 4 parts, 1 part=57 billion then total automobile installment credit=45*4=228 billion , instead of 57*3 anybody pls help me to make it clear. _________________ please press "+1 Kudos" if useful Director Status: I don't stop when I'm Tired,I stop when I'm done Joined: 11 May 2014 Posts: 525 Location: Bangladesh Concentration: Finance, Leadership GPA: 2.81 WE: Business Development (Real Estate) Re: At the end of year X, automobile installment credit accounte [#permalink] ### Show Tags 23 Jun 2016, 02:21 1 jasimuddin wrote: AccipiterQ wrote: ppravin88 wrote: At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended$57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?

A. 62
B. 171
C. 475
D. 513
E. 684

Kindly help in solving this!

So we're trying to find ALL consumer installment credit, let's call that Q.

So at the end of the year we know that 36% of Q comes from automobile installment credit. So we need to figure out the number for automobile installment credit, and then we can solve for Q. We're told that 57 billion is 1/3 of the automobile installment credit amount. So the full amount of automobile installment credit (in billions) is: 57*3 (since 1/3 of the amount is 57 billion, we multiply by 3 to find the full amount. This gives 171 (billion).

So going back to the stem we know that 36% of outstanding consumer credit (which we are calling Q) comes from automobile credit. So 171 is 36% of what number?

.36*Q=171

Q=171/.36

Q=475

so answer is C. Are you sure that was a 700 level problem?

1/3 extended, 3+1= total 4 parts, 1 part=57 billion then total automobile installment credit=45*4=228 billion , instead of 57*3

anybody pls help me to make it clear.

IMO,You missed a point

The question asked you to find the amount of consumer installment credit NOT the amount of automobile installment credit

According to question,

$$\frac{1}{3}$$ of automobile installment credit=$57 billion,so total automobile installment credit=57*3=$171 billion

So,$171 billion=36% of consumer installment credit,Now we can calculate to find consumer installment credit=$$\frac{171*100}{36}$$=475 Correct Answer C _________________ Md. Abdur Rakib Please Press +1 Kudos,If it helps Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges Manager Joined: 23 Dec 2013 Posts: 138 Location: United States (CA) GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44 GPA: 3.76 Re: At the end of year X, automobile installment credit accounte [#permalink] ### Show Tags 22 Jul 2017, 19:23 1 ppravin88 wrote: At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended$57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?

A. 62
B. 171
C. 475
D. 513
E. 684

Kindly help in solving this!

C = outstanding consumer installment credit

auto = 36C/100

57 = 36C/300

57 = 12C/100

57 = 6C/50
57=3C/25

C = 475
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Re: At the end of year X, automobile installment credit accounte  [#permalink]

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11 Dec 2017, 10:52
ppravin88 wrote:
At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time? A. 62 B. 171 C. 475 D. 513 E. 684 We are given that at the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit and that at that time, automobile finance companies extended$57 billion of credit, or 1/3 of the automobile installment credit.

If we let A = the amount of automobile credit, we can create the following equation:

57 billion = (1/3)A

171 billion = A

Since automobile credit or A = 171 billion, and automobile installment credit accounted for 36% of all outstanding consumer installment credit, we can create the following equation in which N = all outstanding credit.

0.36N = 171 billion

N = (171 billion)/0.36

N = 475 billion

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At the end of year X, automobile installment credit accounte  [#permalink]

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27 Dec 2017, 13:50
I set this up essentially the same way as everyone else did BUT avoided algebra by leveraging number properties.

36% Total = Auto Credit
1/3 Auto Credit = $57B Substitute & re-arrange I get 9/25 * x = 171. I want to solve for X. Now this is how one can avoid some algebra: namely, number properties. Looking at the answers (something one should do in any PS problems before diving straight in) one would notice that all are integers. The only way for a Fraction * Integer = Integer is if the denominator of that fraction cancels out. In this case we have 25 (primes of 5s only), so I look for an answer that is a multiple of 5 (last digit either 0 or 5). There is only one answer which is C. GMAT Club Legend Joined: 12 Sep 2015 Posts: 4015 Location: Canada Re: At the end of year X, automobile installment credit accounte [#permalink] ### Show Tags 10 Jan 2018, 13:17 1 Top Contributor ppravin88 wrote: At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended$57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?

A. 62
B. 171
C. 475
D. 513
E. 684

This questions illustrates the importance of ALWAYS checking the answer choices BEFORE getting bogged down with time-consuming calculations. For more on this important strategy, watch the video below.

IMPORTANT: Notice that the answer choices are reasonably spread apart. This means we may be able to use some ESTIMATION to find the answer quickly.

$57 billion of credit equals 1/3 of the automobile installment credit So, the automobile installment credit = (3)($57 billion) = $171 billion Automobile installment credit accounted for 36% of all outstanding consumer installment credit IMPORTANT ESTIMATION CONCEPTS: If x is 25% of y, then y = 4x If x is 33 1/3% of y, then y = 3x If x is 50% of y, then y = 2x Since 36% is a little more than 33 1/3% we can conclude the following: if x is 36% of y, then y = a little less than 3x The question tells us that automobile installment credit (worth$171 billion) accounts 36% of all outstanding consumer installment credit.
In other words, $171 billion is 36% of all outstanding consumer installment credit. So, all outstanding consumer installment credit = little less than 3($171)
3(171) = 513, so the correct answer is a little less than $513 billion. Answer choice C is a little less than$513 billion, so it must be the correct answer.

RELATED VIDEO

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Re: At the end of year X, automobile installment credit accounte  [#permalink]

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13 May 2019, 11:31
Hi.. Just wanted to check if such questions actually come for a 700-level quant?
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Re: At the end of year X, automobile installment credit accounte  [#permalink]

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30 Aug 2019, 11:35
ppravin88 wrote:
At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended \$57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?

A. 62
B. 171
C. 475
D. 513
E. 684

Kindly help in solving this!

Its marked as a medium to hard question simply because of the disorganized way the information is given to us. If we are a little organized about it and go step by step we can do this question (and others like this one) within 30 seconds in our heads.

• First thing: 57=1/3rds of the total auto credit so total auto credit must be 57*3 (no need to do the math on this for now because we will divide again, we're doing this in our heads remember! so best to keep things simple)
• Now we are also told that auto credit formed 36% of total consumer credit so $$57*3*\frac{100}{36}$$, now we can just reduce the fractions quickly, 3 goes once with 36 and then 57 and 12 go once with 3, leaving you with $$19*\frac{100}{4}$$ which 25*19
• Now scan the options, the only multiple of 25 in the list is C, so that will be your answer. (You can also work out that 25*20=500 so 25*19 must be 500-25=475)
• But as I said before, if you reduce the steps and keep things simple you can work these supposedly complex problems that are supposed to take a lot of time in under 30 seconds in your head by staying organized and going step by step. You save precious time and scratch paper space in the actual exam.
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Re: At the end of year X, automobile installment credit accounte  [#permalink]

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21 Sep 2019, 14:14
Ai=(36/100) * Ci
57= (1/3)Ci
Ci =? ---- requirement.

57*3=Ai
57*3=(36/100) * Ci
(57*3*100)/36 = Ci
19*25 = Ci
Ci = 475 ------------------ Only option C has a last digit of 5. So no need to finish the calculation.
Re: At the end of year X, automobile installment credit accounte   [#permalink] 21 Sep 2019, 14:14
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