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# If a loan of P dollars, at an interest rate of r percent...

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If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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Updated on: 11 Oct 2013, 02:29
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If a loan of P dollars, at an interest rate of r percent per year compounded monthly, is payable in n monthly installments of m dollars each, then m is determined by the formula
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John and Sue took out loans whose monthly installments were determined by using the formula above. Both loans had the same interest rate and the same number of monthly installments. John's monthly installment was what percent of Sue's monthly installment?

(1) The amount of Sue's loan was 4 times the amount of John's loan.

(2) Sue's monthly installment was 4 times John's monthly installment.

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Originally posted by NeverSurrender on 11 Oct 2013, 02:27.
Last edited by Bunuel on 11 Oct 2013, 02:29, edited 1 time in total.
Edited the question.
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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11 Oct 2013, 02:38
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If a loan of P dollars, at an interest rate of r percent per year compounded monthly, is payable in n monthly installments of m dollars each, then m is determined by the formula

John and Sue took out loans whose monthly installments were determined by using the formula above. Both loans had the same interest rate and the same number of monthly installments. John's monthly installment was what percent of Sue's monthly installment?

Given that r and n are the same for John and Sue.

John's monthly installment was what percent of Sue's monthly installment? --> $$\frac{m_j}{m_j+m_s}=?$$

(1) The amount of Sue's loan was 4 times the amount of John's loan --> $$P_s=4*P_j$$ --> $$\frac{m_j}{m_j+m_s}=\frac{P_j}{P_j+4P_j}=0.2$$ (everything else get reduced). Sufficient.

(2) Sue's monthly installment was 4 times John's monthly installment --> $$\frac{m_j}{m_j+m_s}=\frac{m_j}{m_j+4m_j}=0.2$$. Sufficient.

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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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11 Oct 2013, 11:02
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Bunuel wrote:
If a loan of P dollars, at an interest rate of r percent per year compounded monthly, is payable in n monthly installments of m dollars each, then m is determined by the formula

John and Sue took out loans whose monthly installments were determined by using the formula above. Both loans had the same interest rate and the same number of monthly installments. John's monthly installment was what percent of Sue's monthly installment?

Given that r and n are the same for John and Sue.

John's monthly installment was what percent of Sue's monthly installment? --> $$\frac{m_j}{m_j+m_s}=?$$

(1) The amount of Sue's loan was 4 times the amount of John's loan --> $$P_s=4*P_j$$ --> $$\frac{m_j}{m_j+m_s}=\frac{P_j}{P_j+4P_j}=0.2$$ (everything else get reduced). Sufficient.

(2) Sue's monthly installment was 4 times John's monthly installment --> $$\frac{m_j}{m_j+m_s}=\frac{m_j}{m_j+4m_j}=0.2$$. Sufficient.

Bunuel,

[ m(j)/m(s) ] * 100?
and thats 25%.

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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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11 Oct 2013, 11:46
1
Bunuel wrote:
If a loan of P dollars, at an interest rate of r percent per year compounded monthly, is payable in n monthly installments of m dollars each, then m is determined by the formula

John and Sue took out loans whose monthly installments were determined by using the formula above. Both loans had the same interest rate and the same number of monthly installments. John's monthly installment was what percent of Sue's monthly installment?

Given that r and n are the same for John and Sue.

John's monthly installment was what percent of Sue's monthly installment? --> $$\frac{m_j}{m_j+m_s}=?$$

(1) The amount of Sue's loan was 4 times the amount of John's loan --> $$P_s=4*P_j$$ --> $$\frac{m_j}{m_j+m_s}=\frac{P_j}{P_j+4P_j}=0.2$$ (everything else get reduced). Sufficient.

(2) Sue's monthly installment was 4 times John's monthly installment --> $$\frac{m_j}{m_j+m_s}=\frac{m_j}{m_j+4m_j}=0.2$$. Sufficient.

Bunuel,

[ m(j)/m(s) ] * 100?
and thats 25%.

Yes, that's true. Though the solution would be almost the same.
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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11 Oct 2013, 19:39
1
Bunuel wrote:
Yes, that's true. Though the solution would be almost the same.

But the percentage value differs right ?
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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26 Oct 2014, 18:20
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1
Hi Bunuel,

Please could you explain how we deduced to mj/(mj + ms)? Although, I understand that it would essentially mean Mj's percentage contribution thereby giving Ms percent. But I wanted to understand the thought process/approach of coming to that.

Here's how I solved it. Let me know if there's any flaw:

Given: r and n are same. Therefore, the only value which may cause a difference in Mj and Ms is P (the loan amounts)

Questn stem: Mj is what percent of Ms? i.e. Mj/Ms=?

So I'm looking for either Pj and Ps or Mj and Ms itself.

St 1: Ps= 4Pj----> Will give me the ratio Mj:Ms--- SUFFICIENT

St 2: Ms= 4Mj----> Answers the questn stem directly---- SUFFICIENT

Thanks,
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If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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18 Jul 2015, 11:36
Correct me if i am wrong, but since it is asking for percent and it uses the same formula and states that the monthly installments are the same for both, you dont have to make any calculation. If you have the monthy installments relation you have the loan amount relation and vice-versa.

it does not matter here if it is compound or simple interest, you have the same interest formula and the same number of monthly installments for both John and Sue.

You have (in both 1 and 2) that Sue is 4 times John, so 1/4 = 25%, done...next question...
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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15 Sep 2015, 02:57
3
This question is made really confusing. It took me some time to figure out what they really were asking and what is given.

Once you figure it out, it's more a Sub-600 Level question. Basically everything is the same but amount or monthly installment is 4 times bigger -> which both make the monthly installment 4 times bigger.

I had some time pressure during the mock-test so I was just one click away of guessing this question because it seemed like some Level 800 question. Could see lot of people doing it to save some time. -> Note to myself: If GMAT tries to word the question harder, the calculus itself is mostly realtively easy. A easy looking, short, few words question, however, is likely to have a trap.
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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21 Sep 2015, 15:26
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Mascarfi wrote:
Correct me if i am wrong, but since it is asking for percent and it uses the same formula and states that the monthly installments are the same for both, you dont have to make any calculation. If you have the monthy installments relation you have the loan amount relation and vice-versa.

it does not matter here if it is compound or simple interest, you have the same interest formula and the same number of monthly installments for both John and Sue.

You have (in both 1 and 2) that Sue is 4 times John, so 1/4 = 25%, done...next question...

Hi Mascarfi,
Yes, you are correct. The interest rate and the number of monthly installments are the same for both John and Sue. The only difference is the principal of each person. Therefore, if the principal is different but the formula is the same, we can conclude that the monthly installment dollar amount will also be different for each person.
- Statement 1 gives you the answer in terms of principal
- Statement 2 gives you the answer in terms of monthly installment dollar amount.

The wording is unnecessarily cumbersome and the question stem displays an ugly formula just to scare you.
Once you understand what the question is really asking, I´d say this becomes a 600-level question that can be clearly solved under 2 minutes.

Cheers,
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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30 May 2016, 05:40
Does anyone have any tips for simplifying questions such as this? I look at this question, with so much going on, and it takes me well over 2 minutes of re-reading to even start to understand what is going on. Should i just register guesses on these types of questions on the GMAT, and move on?

Thanks
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If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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10 Aug 2016, 08:14
4
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The question is much much simpler then it looks like. It took me less then 10 seconds to solve it.

If you look at the question and the formula there are
- p with p1=Sue's loan, p2=John's loan
- Interest r
- Monthly installment n
- Installment m, m1 for Sue, m2 for John

The questions states explicitely that r and n are exactly the same, so f(p) = m depends solely on p in a linear way

=> f(p) = A * p with A = all the small details you really do not need to care about

(1) P1 = 4P2 => f(P1) = f(4*P2) = m1 = 4m2, sufficient to calculate 1/4=25% （not 20% as wrongly calculated above, but that doesn't really matter, as it is not asked)
(2) m1 of Sue = 4*m2 of John => Already the answer! Sufficent to calculate 1/4=25%

Answer is D, both are sufficient alone
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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20 Oct 2016, 23:30
The question is much much simpler then it looks like. It took me less then 10 seconds to solve it.

If you look at the question and the formula there are
- p with p1=Sue's loan, p2=John's loan
- Interest r
- Monthly installment n
- Installment m, m1 for Sue, m2 for John

The questions states explicitely that r and n are exactly the same, so f(p) = m depends solely on p in a linear way

=> f(p) = A * p with A = all the small details you really do not need to care about

(1) P1 = 4P2 => f(P1) = f(4*P2) = m1 = 4m2, sufficient to calculate 1/4=25% （not 20% as wrongly calculated above, but that doesn't really matter, as it is not asked)
(2) m1 of Sue = 4*m2 of John => Already the answer! Sufficent to calculate 1/4=25%

Answer is D, both are sufficient alone

nice explanation!! this helped
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If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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23 Mar 2017, 14:47
P is the only variable since r and n are specified as constants.

1) Tells us that Ps (P for Sue) is 4* Pj (P for John). m for Sue = 4Pj. m for John = Pj. (Pj/4Pj)*100=25%

2) ms (monthly installment for Sue) is 4*mj (monthly installment for John). (mj/4mj)*100+25%

D

Agree?
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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08 May 2017, 02:29
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Using the formula and doing lengthy calculation is a waste of time since the only thing one should be aware of is that :
the first statement ables to get the answer by using the principal, while, the second allows do the same with the monthly installment amount
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Re: If a loan of P dollars, at an interest rate of r percent...  [#permalink]

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07 Jul 2018, 07:54
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