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If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is

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If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is [#permalink]

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New post 04 May 2017, 03:35
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88% (00:48) correct 13% (02:04) wrong based on 61 sessions

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Re: If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is [#permalink]

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New post 04 May 2017, 06:30
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Bunuel wrote:
If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is the product xy?

A. 108
B. 84
C. 21
D. 12
E. 9


The sum of x and y is 21
So, x + y = 21

The ratio of x to y is 3 to 4
So, x/y = 3/4

Take x + y = 21 and solve for x to get x = 21 - y
Now take x/y = 3/4 and replace x with (21-y) to get: (21-y)/y = 3/4
Cross multiply: 4(21-y) = 3y
Expand: 84 - 4y = 3y
Solve: y = 12
Since x + y = 21, we can conclude that x = 9

So, xy = (9)(12) = 108
Answer:

Cheers,
Brent
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Re: If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is [#permalink]

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New post 04 May 2017, 07:11
by looking into the sum 21, the numbers are below 21, with average 3:4.. possible values could be 3,4 or 6,8(ruled out since the sum is odd, for the sum to be odd, atleast one should be odd) and 9,12.. this satisfies the condition
Hence 12*9 = 108
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Re: If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is [#permalink]

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New post 04 May 2017, 09:30
Bunuel wrote:
If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is the product xy?

A. 108
B. 84
C. 21
D. 12
E. 9


Quote:
The ratio of x to y is 3 to 4,
x : y = 3a : 4a

Aga, it is given -

Quote:
The sum of x and y is 21


So, 3a + 4a = 21

Or, 7a = 21

Or, a = 3

Thus, the product of xy is 3a*4a => (3*3)(4*3) = 108

Hence, answer must be (A) 108
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Re: If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is [#permalink]

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New post 06 May 2017, 18:01
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Bunuel wrote:
If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is the product xy?

A. 108
B. 84
C. 21
D. 12
E. 9


We can create an equation and ratio.

x + y = 21

and

x : y = 3n : 4n

Thus:

3n + 4n = 21

7n = 21

n = 3

So, x = 3(3) = 9 and y = 4(3) = 12.

Therefore, the product of x and y is xy = (9)(12) = 108.

Answer: A
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Re: If the sum of x and y is 21 and the ratio of x to y is 3 to 4, what is   [#permalink] 06 May 2017, 18:01
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