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19 Sep 2022, 05:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
52% (01:43) correct
48%
(01:23)
wrong
based on 91
sessions
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If a and b are positive integers, is b divisible by a?
(1) 2b/a is an integer.
(2) b^2/a is an integer
(1) 2b/a is an integer.
(2) b^2/a is an integer
27 Sep 2022, 05:59
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Bunuel
so we need to know if b/a is an integer.
lets take a simple scenario where \(a = 2^Y\) and \(b=2^U\)
Rephrasing the Original Question(OQ): Is the power of 2 in \(b\) greater than or equal to power of 2 in \(a\)?
Quote:
Here, we can easily find values that will make 2b/a as well as b/a an integer. Lets see if it fails to be an integer only for b/a.
What if 2 is a factor of \(a\) but not of b? Take U=0 and Y=1. Here 2b/a is an integer but b/a is not, as b/a turns out to be 1/2, Hence not sufficient
Quote:
Again, here we can easily find values that will make b^2/a as well as b/a an integer. Lets see if it fails to be an integer only for b/a.
What if the power of \(a\) is twice the power of \(b\)? Take U=1 and Y=2. Here b^2/a is an integer but b/a is not, as b/a turns out to be 2/4, Hence not sufficient
Quote:
Rephrase: b^2/a and 2b/a is an integer.
Again, here we can easily find values that will make the combined eqs. as well as b/a an integer. Lets see if it fails to be an integer only for b/a.
Lets try U=1 and Y=2 since we already know it does not hold for (2). Putting these values in (1), 2b/a is an integer but b/a is not, as b/a turns out to be 2/4. Hence not sufficient
Hence answer E.
01 Nov 2022, 08:10
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If a and b are positive integers, is b divisible by a?
(1) 2b/a is an integer.
(2) b^2/a is an integer
We need to find out if 'b' is divisible by 'a' or not. This is a yes-no-type DS question.
Statement 1: \(\frac{2b}{a}\) is an integer.
We suggest translating the statement into equations for easy inference.
Now, this is an integer when k is an even number. But we do not know that and hence this statement is not sufficient.
We can eliminate options A, and D.
Statement 2: \(\frac{b^2}{a}\) is an integer.
We again suggest translating the statement into equations for easy inference.
'b' will be divisible by 'a' only when the right side gives us an integer. Now that may or may not be the case.
If k = a, then it will be.
If k = 1, then it will not be.
Hence, this is not sufficient either. We eliminate B as well.
Combine:
When we combine we try to see if both yes and no are possible or not.
So if k = 4a (an even number), then we get YES
If k = 1, then we get NO.
Hence, even together they are not sufficient.
Answer: E
(1) 2b/a is an integer.
(2) b^2/a is an integer
We need to find out if 'b' is divisible by 'a' or not. This is a yes-no-type DS question.
Statement 1: \(\frac{2b}{a}\) is an integer.
We suggest translating the statement into equations for easy inference.
- We can say that \(\frac{2b}{a} = k\), where 'k' is an integer
- So,\(\frac{b}{a} =\frac{k}{2}\)
Now, this is an integer when k is an even number. But we do not know that and hence this statement is not sufficient.
We can eliminate options A, and D.
Statement 2: \(\frac{b^2}{a}\) is an integer.
We again suggest translating the statement into equations for easy inference.
- \(\frac{b^2}{a} = k\), where 'k' is an integer
- \(b^2\) =k × a
- \(b = \sqrt{a × k}\)
'b' will be divisible by 'a' only when the right side gives us an integer. Now that may or may not be the case.
If k = a, then it will be.
If k = 1, then it will not be.
Hence, this is not sufficient either. We eliminate B as well.
Combine:
When we combine we try to see if both yes and no are possible or not.
So if k = 4a (an even number), then we get YES
If k = 1, then we get NO.
Hence, even together they are not sufficient.
Answer: E
