Problem Solving

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

abhasjha wrote:

Automobile Installment Credit = (36/100) x all Outstanding Credit

Given $57 Billion = (1/3) x Automobile Installment Credit

i.e.$57 Billion = (1/3) x (36/100) x all Outstanding Credit

i.e. all Outstanding Credit = (100/36) x (3/1) x 57 = (25/3) x 57 = $475 Billion

Answer: Option C

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

An alternate approach is to convert the percentages to RATIOS.

Let A = automobile installment credit, C = all outstanding consumer installment credit, and E = extended credit.

Automobile installment credit accounted for 36% of all outstanding consumer installment credit.
Thus:
A:C = 36:100 = 9:25.

Finance companies extended 1/3 of the automobile installment credit.
In other words, $1 of credit was extended for every $3 of automobile installment credit.
Thus:
E:A = 1:3 = 3:9.

Combining the two ratios, we get:
E:A:C = 3:9:25
E:C = 3:25.

Since the actual value of E = 57, and 3*19 = 57, the multiplier for the ratio above is 19:
E:C = (3*19) : (25*19) = 57:475.
Thus, C = 475.

The correct answer is C.

1/3 of AIC= 57 Mn
AIC= 57*3= 171 Mn
AIC= 0.36 of CIC

So, CIC= AIC*100/36= 171*100/36= 171*25/9= 25*19= 475
Option C

total = A
end of X = 0.36 * A
57 = 1/3 * 0.36 * A
57/0.12 = A
5700/12 = A
just below 500

So, {C}