M17-14

Question

A non-zero amount was deposited at bank A at a rate of $x$ percent compounded annually, while half that amount was deposited at bank B at a rate of $y$ percent compounded annually, where $x$ and $y$ are both greater than 0. In three years, will the total interest earned on the deposit in bank A be greater than the total interest earned on the deposit in bank B?

(1) $y = 0.8x$.

(2) The initial deposit at Bank A exceeded the initial deposit at Bank B by $100.

Show Answer

Official Answer

A

(1)  y = 0.8x .
 
(2) The initial deposit at Bank A exceeded the initial deposit at Bank B by $100.

Bunuel · Answer

Official Solution:

A non-zero amount was deposited at bank A at a rate of  x  percent compounded annually, while half that amount was deposited at bank B at a rate of  y  percent compounded annually, where  x  and  y  are both greater than 0. In three years, will the total interest earned on the deposit in bank A be greater than the total interest earned on the deposit in bank B? 
 
(1)  y = 0.8x . 
 
The above implies that  x > y . Therefore, at bank A, a larger amount was deposited at a higher interest rate compared to bank B. Given that all other conditions are the same, it is evident that the total interest earned on the deposit in Bank A will be greater than the total interest earned on the deposit in Bank B. Sufficient.
 
(2) The initial deposit at Bank A exceeded the initial deposit at Bank B by $100. 
 
The above implies that $200 was deposited in bank A and $100 was deposited in bank B. However, we do not have any information on the interest rates, so this statement is insufficient.

Answer: A

earnit · Answer

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

Bunuel · Answer

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.

nurba92 · Answer

Bunuel  @chetan4u  VeritasKarishma

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

KarishmaB · Answer

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.

CrackverbalGMAT · Answer

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!

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

draftpunk · Answer

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

CrackVerbalGMAT   VeritasKarishma   chetan2u

chetan2u · Answer

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.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Gemmie · Answer

Amount deposited in bank A: M
Amount deposited in bank B:  \frac{M}{2}

The amounts after 3 years for both banks:

For bank A:  M * (1 + \frac{x}{100})^3

For bank B:  \frac{M}{2} * (1 + \frac{y}{100})^3

Statement (1): y=0.8x 
(i) y < x
(ii)  \frac{M}{2} < M

=> Amount in Bank B after 3 years < Amount in Bank A after 3 years

Therefore, statement (1) is sufficient.

Statement (2): The initial deposit at Bank A exceeded the initial deposit at Bank B by $100.

This statement alone does not provide information about the interest rates x and y​.

Hence, statement (2) alone is not sufficient.

The correct answer is: Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.

chaitanyab109 · Answer

I like the solution - it’s helpful.

heyRaj · Answer

I like the solution - it’s helpful.

riaathaakur · Answer

I like the solution - it’s helpful.

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