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Answer = C. 475

Total automobile instalment credit = 57*3 = 171

Total consumer instalment credit \(= 171*\frac{100}{36} = 475\)
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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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ppravin88
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.
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ppravin88
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
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ppravin88
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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ppravin88
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

Answer: C
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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.
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ppravin88
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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Hi.. Just wanted to check if such questions actually come for a 700-level quant?
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ppravin88
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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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.
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At that time automobile finance companies extended $57 billion of credit, or \small \frac{1}{3} of the automobile installment credit

475 billion is what was at the end of year.
After extending 57b or 1/3, it means 2/3rd was not extended.

don't we need to reduce : 475-2*57 = 361?
please confirm why not

at that time and end of year - may not be same
what happens after financial companies extended.
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I just took a simple approach to solve it fast without using a pen.

57B $ = 0.12x of the total
60 = 12*5 (57B would be little less than 5B when divided by 12)

Hence the answer would be lesser than 500 i.e 475.

Posted from my mobile device
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rimcovinay2552
I just took a simple approach to solve it fast without using a pen.

57B $ = 0.12x of the total
60 = 12*5 (57B would be little less than 5B when divided by 12)

Hence the answer would be lesser than 500 i.e 475.

Posted from my mobile device


How many billion dollars of consumer installment credit was outstanding at that time?

what time?
At end of year ? OR at the time when automobile finance companies extended $57 billion of credit?
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rimcovinay2552
I just took a simple approach to solve it fast without using a pen.

57B $ = 0.12x of the total
60 = 12*5 (57B would be little less than 5B when divided by 12)

Hence the answer would be lesser than 500 i.e 475.

Posted from my mobile device


How many billion dollars of consumer installment credit was outstanding at that time?

what time?
At end of year ? OR at the time when automobile finance companies extended $57 billion of credit?



There is only one time given and that is end of the year.
The whole question mentions at the end of the year and then mentions at that time which refers to the same moment.
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PAVANIJOSHI374
Hi.. Just wanted to check if such questions actually come for a 700-level quant?

I believe so. In exam conditions, this question has some tough terminology to set up the initial equation. I'd say most students would get freaked out by the wording and guess.

I do agree though, once the initial equation is indeed set up, it is fairly straight forward.
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ppravin88
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!


Automobile installment credit accounted for 36% of all outstanding consumer installment credit. We need to find the total of installment credit , let it be x.

As given, 36% of x =Automobile installment credit.
Credit extended was $57 billion of credit, or 1/3 of the automobile installment credit.

Therefore, 1/3 (36% of x)= $57 billion
1/3*36/100*x=57
x=5700/12
x=475.
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