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Are a and b both integers? (1) a^2 + b^2 is an integer (2) a/b is an

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Bunuel
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Are a and b both integers? (1) a^2 + b^2 is an integer (2) a/b is an [#permalink] Are a and b both integers? (1) a^2 + b^2 is an integer (2) a/b is an   05 May 2021, 08:00
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E

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66% (01:08) correct 34% (01:22) wrong based on 67 sessions
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Are a and b both integers?

(1) \(a^2 + b^2\) is an integer.

(2) \(\frac{a}{b}\) is an integer.
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E
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TarunKumar1234
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Re: Are a and b both integers? (1) a^2 + b^2 is an integer (2) a/b is an [#permalink] Are a and b both integers? (1) a^2 + b^2 is an integer (2) a/b is an   05 May 2021, 08:12
Are a and b both integers?

Stat1: a^2+b^2 is an integer.
Not sufficient as a and b can be square root.

Stat2: a/b is an integer.
again Not sufficient as a and b can be square root, e.g. a = 8^1/2, b= 2^1/2

Combining both, Still a and b can be square root values. Not sufficient.

So, I think E :)
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Re: Are a and b both integers? (1) a^2 + b^2 is an integer (2) a/b is an [#permalink] Are a and b both integers? (1) a^2 + b^2 is an integer (2) a/b is an   26 Sep 2021, 07:07
Bunuel wrote:
Are a and b both integers?

(1) \(a^2 + b^2\) is an integer.

(2) \(\frac{a}{b}\) is an integer.


Very good question Bunuel!

S1: \(a^2 + b^2\) is an integer [Insufficient]
1. If \(a = 2\) and \(b = 3\) then \(a^2 + b^2\) is an integer, and \(a\) and \(b\) are both integers
2. If \(a =\) \(\sqrt{2}\) and \(b = 3\) then \(a^2 + b^2\) is an integer, but \(a\) and \(b\) both are not integers

S2: \(\frac{a}{b}\) is an integer [Insufficient]
1. If \(a = 4\) and \(b = 2\) then \(\frac{a}{b}\) is an integer, and \(a\) and \(b\) are both integers
2. If \(a =\) \(\sqrt{8}\) and \(b =\) \(\sqrt{2}\) then \(\frac{a}{b}\) is an integer, but \(a\) and \(b\) both are not integers

S1 + S2 [Insufficient]
1. If \(a = 4\) and \(b = 2\) then \(a^2 + b^2\) and \(\frac{a}{b}\) are integers, and \(a\) and \(b\) are both integers
2. If \(a =\) \(\sqrt{8}\) and \(b =\) \(\sqrt{2}\) then \(a^2 + b^2\) and \(\frac{a}{b}\) are integers, but \(a\) and \(b\) both are not integers

Ans. E
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Re: Are a and b both integers? (1) a^2 + b^2 is an integer (2) a/b is an [#permalink]
26 Sep 2021, 07:07
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Bunuel
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