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

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.

Answer: D.
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Bunuel,

Isnt the question asking for

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

Please correct me if wrong

Yes, that's true. Though the solution would be almost the same.
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But the percentage value differs right ?

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

Answer D.

Thanks,
Chandni

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...

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.

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,

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

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

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?

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

This question is just asking about ratios. The key point is that everything is the same except the total amount P, and the subsequent monthly (P/12). The ratio of both is the same.

1) Gives us the ratio of S total to J total as 4:1. S monthly to J monthly is thus also 4:1
2) Gives us the ratio of monthly to monthly, which is the reverse of 1)

I think this question is a good example of when doing any kind of calculation or manipulation is actually counterproductive... or doing much writing at all instead of just thinking about it.

----Correct me if I am wrong-----
The formula looks a bit complicated and our focus will be shifted easily to this complication. Let's break down the the problem.
We have the same interest rate (r), the number of monthly installments (n)
-->The differences will be Principal (P) and values of monthly installments (m)
Question: mj/ms (John's values of monthly installments and Sue's values of monthly installments)

St1: Sue's principal is 4 times John's principal (Ps=4Pj)-->Suff
Because both m&P are in the same side of the ratio, so if P increase then m will increase.
St2: ms=4mj
The given info answer the question directly-->Suff

So the answer is D: both A&B are correct.

VeritasKarishma, MentorTutoring

Can you pls clarify what Bunuel meant here in saying that solution would be almost same

Though, this is a DS question where we just need to look for sufficiency, if it were a PS question then 25% would be the answer

Kindly help with this
Thanks in advance!

Hello, GDT. I cannot speak for Bunuel, but the math checks out just fine. It appears as if the solution offered answers the question, John's monthly installment was what percent of the combined monthly installment? John pays 1 part in 5, since Sue's payment is 4 times John's, so the J:S payment ratio is 1:4. Yes, the answer would be 25% in a PS question, although I will be honest and say that I was not worried about calculating an exact answer here. That is, if r and n are both constant, since they would represent the same values for John and Sue, that leaves only P or m as variables to consider, or those that can be manipulated. Statement (1) tells us about P, allowing us to potentially solve the equation for m, while statement (2) tells us about m instead. This was a pretty quick (D) (although I cannot boast a speed read and sub-10-second answer, as someone claimed above).

Thank you for tagging me, and good luck with your studies.

- Andrew

I believe the best (and fast) way is to just write the formula on the pad and look at what values are changing, of course the constants in the formula won't change in either of the two, John and Sue, cases. so, the catch is to find what will change between in either of the two cases.

the rate for both is given to be the same, and the number of months for which they paid their premium or whatever are equal as well. so, the only "variable" changing are 'm" (installed paid each month in dollars) and "P" (amount of loan taken) once you have that this becomes a 10 sec question.

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