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Math Expert V
Joined: 02 Sep 2009
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Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 75% (02:11) correct 25% (02:26) wrong based on 228 sessions

HideShow timer Statistics 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.

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Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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Bunuel wrote:
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.

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. $$\sqrt{x}/\sqrt{y} = 12/9 = 4/3$$

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Re: Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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Bunuel wrote:
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.

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) X/Y = 144/81

$$\sqrt{X}/\sqrt{Y} = \sqrt{144} / \sqrt{81}$$

$$\sqrt{X}/\sqrt{Y} = 12/9 = 4/3$$

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Re: Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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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

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Re: Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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Bunuel wrote:
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.

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!

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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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.

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Re: Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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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

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Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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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
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Re: Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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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.

Math Expert V
Joined: 02 Sep 2009
Posts: 55801
Re: Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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Bunuel wrote:
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.

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:
Attachment: 2015-06-15_1512.png [ 51.28 KiB | Viewed 2591 times ]

If the accounts have the same amount of money after two months, then:

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

x/y = 144/81;

$$\frac{\sqrt{x}}{\sqrt{y}} = \frac{12}{9}$$.

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Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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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 wrote:
Bunuel wrote:
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.

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:
Attachment:
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;

$$\frac{\sqrt{x}}{\sqrt{y}} = \frac{12}{9}$$.

Math Expert V
Joined: 02 Sep 2009
Posts: 55801
Re: Bank account A contains exactly x dollars, an amount that will decreas  [#permalink]

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123mba123 wrote:
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 wrote:
Bunuel wrote:
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.

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:
Attachment:
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;

$$\frac{\sqrt{x}}{\sqrt{y}} = \frac{12}{9}$$.

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.
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