At the end of year \(X,\) automobile installment credit accounted for \(36\%\) of all outstanding consumer installment

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Sun Sep 12, 2021 9:06 am

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 \(\dfrac13\) 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

Answer: C

Source: GMAT Prep

This question 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.