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

Question

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 $\sqrt{x}$ to $\sqrt{y}$?

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

Kudos for a correct solution.

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

GMATinsight · Answer

Initial Amount Bank A $x Bank B $y
Aft. 1st Month $0.9*x $1.2*y
Aft. 1st Month $0.9^2*x $1.2^2*y

Now, 0.9^2*x = 1.2^2*y
i.e. 0.81x = 1.44y
i.e. x/y = 1.44/0.81
i.e.  \sqrt{x}/\sqrt{y} = \sqrt{1.44}/\sqrt{0.81} 
i.e.  \sqrt{x}/\sqrt{y} = 12/9 = 4/3

Answer: Option  A

tarunsng · Answer

For bank account A. you get the amount 90 (1st month after 10% decrease) and then 90-9(10% of 90) in 2nd month. Total 81 For bank account B. you get 120 (1st month 20% increase) and then 120+24 (2nd month: 20% increase on 120). Total 144 both contain the same amount after 2 months so: 81X = 144Y (Keep it simple by not using X and Y in the beginning) :lol:

X/Y = 144/81 \sqrt{X}/\sqrt{Y} = \sqrt{144} / \sqrt{81} \sqrt{X}/\sqrt{Y} = 12/9 = 4/3 A

balamoon · Answer

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 $\sqrt{x}$ to $\sqrt{y}$?

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

Kudos for a correct solution.

(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

AnniK · Answer

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

EMPOWERgmatRichC · Answer

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

AnniK · Answer

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

pacifist85 · Answer

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  ..........y+(0.2y) + 0.2

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

Vaibhav21 · Answer

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

Bunuel · Answer

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: 2015-06-15_1512.png 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.

123mba123 · Answer

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?

Bunuel · Answer

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.

GmatPoint · Answer

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.

adityasuresh · Answer

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 $\sqrt{x}$ to $\sqrt{y}$?

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

Kudos for a correct solution.

(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

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards