Bank account A contains exactly x dollars, an amount that will decreas

Bank account A contains exactly x dollars, an amount that will decrease by 10% each month for the next two months. Bank account B contains exactly y dollars, an amount that will increase by 20% each month for the next two months. If A and B contain the same amount at the end of two months, what is the ratio of x√ to y√?

(A) 4 : 3 (B) 3 : 2 (C) 16 : 9 (D) 2 : 1 (E) 9 : 4

Explanation:
Account A has amount after 2 months = 0.9*0.9*x = 0.81*x
Account B has amount after 2 months = 1.2*1.2*y = 1.44*y
0.81*x=1.44*y --> √(x/y)=√(1.44/0.81) = 12/9 = 4/3.

Ans A

Thanks

Please give me Kudos

Hello,

using smart numbers - applied the percentage discount or premium for each bank.

Starting with the ratio in A calculate the % increase after 2 months and so forth until you get a ratio where both banks end with the same dollar amount

use a multiplier of 10 so we're working with numbers easily multiplied by 10%

(A) 4:3 => 40:30 = 40*.9=36*.9=$32.40 @ end of 2 months
30*1.20=36 you can stop and cross this off because the amount increase will exceed the end amount for bank A
(B) 3:2 => 30:20 = 30*.9=27*.9=$24.30 @ end of 2 months
20*1.20=24 as with answer (A) you can stop and cross this off because the amount is close to the end amount for bank A
(c) 16:9 => 160:90 = 160*.9 =144*.9=$129.60 @ end of 2 months
90*1.20=108*1.20=$129.60 match!

the answer is (C) 16:9

Hi AnniK,

Your approach to TEST VALUES would absolutely work on this question. However, there is an error in your work:

Since the question asks for the ratio of √X to √Y, but the prompt asks us to 'manipulate' X and Y, you actually have to SQUARE the answer choices BEFORE you TEST VALUES. Your TESTs assume that the given answer choices are referring to X and Y, when they actually refer to √X and √Y.

GMAT assassins aren't born, they're made,
Rich

Hi EMPOWERgmatRichC/Rich,

Thank you for the explanation, I was thinking about that after submitting the response, guess the 'gut feeling' was correct.

Much appreciated

A

Yep, I also found 4:3, working the problem like this:
.........................................A..........................................B
Now..................................x...........................................y
+1 month.....................x-(0.1x).....................................y+(0.2y)
+2 months...............x-(0.1x) - 0.1 [x-(0.1x)]..........y+(0.2y) + 0.2[y+(0.2y)]

Now we equate the 2 final amounts, as they need to be equal:
x-(0.1x) - 0.1 [x-(0.1x)] = y+(0.2y) + 0.2[y+(0.2y)]
0.81x = 1.44y
81x=144y
x/y = 144/81 and their √ are x/y = 4/3. So, ANS A

account A after 2 months = 0.9x0.9xx = 0.81x
account B after 2 months = 1.2x1.2xy = 1.44y
0.81x=1.44y = root(x/y)=root(1.44/0.81) = 12/9 = 4/3.

Answer A

MANHATTAN GMAT OFFICIAL SOLUTION:

First, note the answer pairs (A)&(C) and (B)&(E), in which one ratio is the square of the other. This represents a likely trap in a problem that asks for the ratio of \(\sqrt{x}\) to \(\sqrt{y}\) to rather than the more typical ratio of x to y. We can eliminate (D), as it is not paired with a trap answer and therefore probably not the correct answer. We should also suspect that the correct answer is (A) or (B), the “square root” answer choice in their respective pairs.

For problems involving successive changes in amounts — such as population-growth problems, or compound interest problems — it is helpful to make a table:
If the accounts have the same amount of money after two months, then:

81/100*x = 144/100*y;

x/y = 144/81;

\(\frac{\sqrt{x}}{\sqrt{y}} = \frac{12}{9}\).

The correct answer is A.

Thanks Bunuel! I liked the strategy to eliminate wrong answers. I usually start solving problem without looking at answers. Does paying attention to answer choices reduce time required to solve question?

Yes, on the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Since the amount in A is decreasing 10% per month, the balance after two months = 0.9*0.9x = 0.81x

Similarly, the balance of B after two months = 1.2*1.2y = 1.44y

Since both are equal, 0.81x = 1.44y
x/y = 16/9
Also, √x : √y = 4 : 3

Thus, the correct answer is A.

Bank account A contains exactly x dollars, an amount that will decrease by 10% each month for the next two months. Bank account B contains exactly y dollars, an amount that will increase by 20% each month for the next two months. If A and B contain the same amount at the end of two months, what is the ratio of x√x to y√y?

(A) 4 : 3
(B) 3 : 2
(C) 16 : 9
(D) 2 : 1
(E) 9 : 4

Decrease by 10% each month for 2 months implies the X dollars deposited multiply by 9/10 each month = X *(\(9/10\))^2
Increase by 20% each month for 2 months implies Y dollars deposited multiply 1+20/100 = 6/5 each month = Y *(\(6/5\))^2
Equate both
X *(\(9/10\))^2 = Y *(\(6/5\))^2
X/Y = \(36/25\) * \(100/81\) =\( 144/81\)
A
\sqrt{X} = 12 \sqrt{Y} = 9
X : Y = 4 : 3

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