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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] New post 11 Nov 2013, 12:31
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Difficulty:

  35% (medium)

Question Stats:

66% (01:55) correct 34% (00:49) wrong based on 118 sessions
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!
[Reveal] Spoiler: OA
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Re: Automobile Installment Credit [#permalink] New post 11 Nov 2013, 17:12
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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?
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Re: At the end of year X, automobile installment credit accounte [#permalink] New post 15 Nov 2014, 09:13
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Re: At the end of year X, automobile installment credit accounte [#permalink] New post 29 Dec 2014, 18:39
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
- 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] New post 30 Dec 2014, 20:30
Answer = C. 475

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] 30 Dec 2014, 20:30
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