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

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11 Nov 2013, 12:31

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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?

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?

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

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29 Dec 2014, 18:39

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

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22 Jun 2016, 22:08

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.
_________________

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

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23 Jun 2016, 01:21

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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

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

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22 Jul 2017, 18:23

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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?

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

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27 Dec 2017, 12:50

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.

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.