Official Solution:


Statement (1) by itself is sufficient. It means that \(y \lt x\). A smaller amount deposited at a smaller rate will grow to a smaller figure than a larger amount deposited at a higher rate.

Statement (2) by itself is insufficient. We don't know how the interest paid on the deposits compares with the initial difference of $100.


Answer: A
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Hi Bunuel,

I have noticed that especially in DS, whenever I am facing a question with regard to SIMPLE INTEREST, AMOUNT, Compounded annually and so on, i get stumped given the limited time frame during a test so I would be grateful if you could suggest me some questions on similar topic that would enable me to understand its most common types and tricky areas.

Placing the values in a given formula is easy. It is getting the synopsis of the qs in a read that would matter.

Thanks in advance

Check Compound Interest Problems in our Special Questions Directory.

Theory on Percent and Interest Problems: math-number-theory-percents-91708.html

All DS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=33
All PS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=54

Hope this helps.
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x>y only when x and y are greater than 1.

x=0.2 y=0.16 as per statement 1.Therefore,x <y. If the amount is really small this may affect the answer.

Bunuel @chetan4u VeritasKarishma

experts, please, clarify why the rates cannot be 0 in this case?

Thanx in advance)

If the rate were 0, depositing in a bank at x% compounded annually just doesn't make sense. If there is no interest, what will you compound.

It is similar to saying that if Alex bought A apples, A can be 0. He didn't buy in that case but we are given that he bought. So it doesn't really make sense.
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Compound Interest questions test your ability to apply percentage values and exponents. But, they also test your ability to apply logic in inferring certain hidden clues.

This question is actually easy because, interest is compounded annually on the amounts deposited at both the banks. Had one of them been calculated annually and the other half-yearly/quarterly/monthly, this question would have become much more difficult to tackle.

In questions on CI, taking a slightly larger number is advisable because it reduces the possibility of having to deal with vulgar fractions. In this question, let’s assume that $1000 was deposited at bank A and $500 was deposited at bank B. Bank A offers x% interest which is compounded annually, while B offers y% interest which is compounded annually as well.

At this stage, you need to ask yourself this question –> if x = y, where will I get a higher total interest? Your answer to this question would be ‘from bank A’. That’s because the amount that you have invested in A is so much larger (double) than the one you have invested in B that, if the interest rates were same, then, naturally bank A would give you more total interest.

This is when you understand that your answer depends more on knowing what the interest rates are than knowing what was the investment. This should naturally point you in the direction of statement I, but, let’s analyse it and see what it gives us.

Statement I alone says that y = 0.8x or y = (\(\frac{4}{5}\)) x.

Let’s assume the principal invested in bank A as 2P and that in bank B as P. Then,

Amount from bank A = \(2P (1+ \frac{x}{100})^3\) and

Amount from bank B = \(P (1+ \frac{4x}{500})^3\) = \(P(1+\frac{x}{125})^3\).

Clearly, in the second case, the term inside the bracket will be much smaller than the one in the first case. And when you raise it to an integral power, you’ll obtain a smaller value in the second case as compared to the first case.

We can infer that the person obtained a higher total profit from bank A than from bank B.

An alternative approach (and one that’s close to my heart) in analyzing statement I would be to take simple values for the variables and evaluate. I’d pick the investment in A as $1000 and in B as $500. I’d pick x = 10% pa and consequently y = 8% pa. Applying these values, we get,

Amount from bank A = 1000 \((1.1)^3\) = 1000 * 1.331 = 1331 and
Amount from bank B = 1000 \((1.08)^3\) = 1000 * 1.26 (approximately) = 1260.

Statement I alone is sufficient. Possible answer options are A or D. Answer options B, C and E can be eliminated.

From statement II alone, we can understand that the investments in bank A and bank B are $200 and $100 respectively. However, since the values of x and y can be anything, we cannot conclusively say about which bank will give us a higher interest.

If x is more than y, bank A is naturally going to give you more than bank B.
But, if x is infinitely small when compared to y, bank B can still give more than bank A.

Statement II alone is insufficient, answer option D can be eliminated.
The correct answer option is A.

Hope that helps!
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I think this is a high-quality question and I agree with explanation.

IF the question was revised such that (1) x = 0.8y , would the answer be D?


CrackVerbalGMAT VeritasKarishma chetan2u

Of course the answer cannot be D, because changing statement I does not change the way we deal with statement II because we do not deal with information of statement I.

Say you meant C or E, then we can work on the question further.

With all due respect, you are wrong. It would not be correct to say "it does not make sense". The correct sentence should be "YOU WOULD BE INDIFFERENT". "it does not make sense" is when the interest rate is NEGATIVE, NOT ZERO.

Additionally, Bunuel I think this question might be also wrong, because you can get compound on 0% interest, which is zero. You simply get zero interest on your money. At first, it may not make sense logically, but technically and theoratically it is possible.