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Two integers x and y are in the ratio of 5:6

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Sumukh19
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Two integers x and y are in the ratio of 5:6 [#permalink] New post   01 Feb 2022, 07:52
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Two integers \(X\) and \(Y\) are the ratio of 5:6. Which of the following options are true?

A. 11 can be the highest prime factor of \(X+Y\)
B. 3 is the highest prime factor of \(XY\)
C. \(X+Y\) must be an odd number
D. \(XY\) must be an even number
E. \(X\) must be less than \(Y\)
F. \(X\) must be divisible by 10

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D
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YashZ
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Re: Two integers x and y are in the ratio of 5:6 [#permalink] New post   02 Feb 2022, 02:43
Why A is not one of the correct answer choices?
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Sumukh19
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Two integers x and y are in the ratio of 5:6 [#permalink] New post   02 Feb 2022, 05:45
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YashZ wrote:
Why A is not one of the correct answer choices?


Let's assume that \(X=5a\) and \(Y=6a\) as they are in the ratio of 5:6

Therefore,
\(X+Y=5a+6a=11a\)

Here, it seems like 11 is the highest prime factor of \(X+Y\) but what if \(a\) is another prime number greater than 11, in that case \(a\) will the highest prime factor of \(X+Y\).

For example
\(X=65\)
\(Y=78\)

Then, \(X+Y=143\)
Here, the highest prime factor will be 13.

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Re: Two integers x and y are in the ratio of 5:6 [#permalink] New post   23 Jun 2023, 07:27
Why is E not a correct answer

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Re: Two integers x and y are in the ratio of 5:6 [#permalink] New post   23 Jun 2023, 07:58
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Harsh2910 wrote:
Why is E not a correct answer

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E is true if and only if X and Y are only positive.
Consider:
x=-5, y=-6 (x>y)
but
x=5, y=6 is also valid (y>x)
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Re: Two integers x and y are in the ratio of 5:6 [#permalink] New post   23 Jun 2023, 09:20
Sumukh19 wrote:
YashZ wrote:
Why A is not one of the correct answer choices?


Let's assume that \(X=5a\) and \(Y=6a\) as they are in the ratio of 5:6

Therefore,
\(X+Y=5a+6a=11a\)

Here, it seems like 11 is the highest prime factor of \(X+Y\) but what if \(a\) is another prime number greater than 11, in that case \(a\) will the highest prime factor of \(X+Y\).

For example
\(X=65\)
\(Y=78\)

Then, \(X+Y=143\)
Here, the highest prime factor will be 13.

Posted from my mobile device


But it is written "A. 11 can be the highest prime factor of X+Y" not 11 must be...
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Re: Two integers x and y are in the ratio of 5:6 [#permalink] New post   30 Oct 2024, 17:57
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Two integers x and y are in the ratio of 5:6 [#permalink]
30 Oct 2024, 17:57
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