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Bunuel
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If x and y are positive integers such that (3x + 7y) is a multiple of 21 Apr 2021, 04:15
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If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will also be divisible by 11?

(A) 4x + 6y
(B) x + y + 4
(C) 9x + 4y
(D) 4x – 9y
(E) 4x – 8y
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D
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If x and y are positive integers such that (3x + 7y) is a multiple of 21 Apr 2021, 05:04
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If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will also be divisible by 11?

3x +7 y= 11*m
so, x = 5 and y =1 one of the solution.

Only D satisfies values of x and y. So, I think D. :)
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If x and y are positive integers such that (3x + 7y) is a multiple of 21 Apr 2021, 05:10
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I made (3x + 7y) equal to 22 and found which values for x and y solved the equation.

x = 5 and y = 1 giving me that (15+7) = 22

Plugging those values into the answer choices yielded:

(A) 26 not divisible by 11
(B) 9 not divisible by 11
(C) 49 not divisible by 11
(D) 11 DIVISIBLE BY 11
(E) 12 not divisible by 11


Answer choice D.
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If x and y are positive integers such that (3x + 7y) is a multiple of 16 May 2021, 07:42
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If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will also be divisible by 11?

(A) 4x + 6y
(B) x + y + 4
(C) 9x + 4y
(D) 4x – 9y
(E) 4x – 8y
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Solution:

We can let x be 5 and y be 1 (notice that 3(5) + 7(1) = 22). Now let’s check the answer choices:

A) 4x + 6y = 20 + 6 = 26 → This is not divisible 11.

B) x + y + 4 = 5 + 1 + 4 = 10 → This is not divisible 11.

C) 9x + 4y = 9(5) + 4(1) = 45 + 4 = 49 → This is not divisible by 11.

D) 4x - 9y = 4(5) - 9(1) = 20 - 9 = 11 → This is divisible by 11.

E) 4x - 8y = 4(5) - 8(1) = 20 - 8 = 12 → This is not divisible 11.

Answer: D
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If x and y are positive integers such that (3x + 7y) is a multiple of 29 Jun 2021, 06:25
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TarunKumar1234
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will also be divisible by 11?

3x +7 y= 11*m
so, x = 5 and y =1 one of the solution.

Only D satisfies values of x and y. So, I think D. :)
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X=4 and y=3 also satisfies the condition. Why cannot that be used? Could you explain that please?
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If x and y are positive integers such that (3x + 7y) is a multiple of 29 Jun 2021, 13:55
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KavyaVijay
TarunKumar1234
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will also be divisible by 11?

3x +7 y= 11*m
so, x = 5 and y =1 one of the solution.

Only D satisfies values of x and y. So, I think D. :)


X=4 and y=3 also satisfies the condition. Why cannot that be used? Could you explain that please?
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Without pluging numbers:
3x+7y=11k -> y=(11k-3x)/7
sustituting in D we have
4x-9y = 4x-9(11k-3x)/7 = (28x-99k+27x)/7 = (55x-99k)/7 = 11(5x-9k)/7 which is divisible by 11
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If x and y are positive integers such that (3x + 7y) is a multiple of 10 Sep 2024, 04:17
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­ScottTargetTestPrep - why cant we take x = 4 and y = 3 in this question?
if we do we have 4+3+4 = 11 ( option B : x+y+4 ) divisible by 11 as well. Please let me know if i made any mistake here
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If x and y are positive integers such that (3x + 7y) is a multiple of 10 Sep 2024, 06:04
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­ScottTargetTestPrep - why cant we take x = 4 and y = 3 in this question?
if we do we have 4+3+4 = 11 ( option B : x+y+4 ) divisible by 11 as well. Please let me know if i made any mistake here
Show more
­
The correct option must be divisible by 11 for all values of x and y that satisfy the condition that 3x + 7y is a multiple of 11. Option D will be divisible by 11 for all such x and y, while the other options might only be divisible for specific values of x and y.
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If x and y are positive integers such that (3x + 7y) is a multiple of 10 Sep 2024, 06:25
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Bunuel

msaree1
­ScottTargetTestPrep - why cant we take x = 4 and y = 3 in this question?
if we do we have 4+3+4 = 11 ( option B : x+y+4 ) divisible by 11 as well. Please let me know if i made any mistake here
­
The correct option must be divisible by 11 for all values of x and y that satisfy the condition that 3x + 7y is a multiple of 11. Option D will be divisible by 11 for all such x and y, while the other options might only be divisible for specific values of x and y.
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­Thanks for your response. In that case is there a better way than to plug in numbers and check? One would need to check multiple cases to see which options are in sync otherwise
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If x and y are positive integers such that (3x + 7y) is a multiple of 10 Sep 2024, 06:27
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msaree1
­ScottTargetTestPrep - why cant we take x = 4 and y = 3 in this question?
if we do we have 4+3+4 = 11 ( option B : x+y+4 ) divisible by 11 as well. Please let me know if i made any mistake here
­
The correct option must be divisible by 11 for all values of x and y that satisfy the condition that 3x + 7y is a multiple of 11. Option D will be divisible by 11 for all such x and y, while the other options might only be divisible for specific values of x and y.
­Thanks for your response. In that case is there a better way than to plug in numbers and check? One would need to check multiple cases to see which options are in sync otherwise
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­
Algebrai way is given here:

https://gmatclub.com/forum/if-x-and-y-a ... l#p2814373

Hope this helps.
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If x and y are positive integers such that (3x + 7y) is a multiple of 22 Sep 2025, 04:19
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