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Two integers x and y are in the ratio of 5:6
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01 Feb 2022, 07:52
01 Feb 2022, 07:52
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Question Stats:
18% (01:36) correct
81% (01:33) wrong based on 33 sessions
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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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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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Re: Two integers x and y are in the ratio of 5:6
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02 Feb 2022, 02:43
02 Feb 2022, 02:43
Why A is not one of the correct answer choices?
Two integers x and y are in the ratio of 5:6
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02 Feb 2022, 05:45
02 Feb 2022, 05:45
2
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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