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# Are a and b both integers?

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Tuck School Moderator
Status: Valar Dohaeris
Joined: 31 Aug 2016
Posts: 301
GMAT 1: 700 Q49 V37
Are a and b both integers?  [#permalink]

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18 Feb 2019, 08:17
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Difficulty:

45% (medium)

Question Stats:

58% (01:29) correct 42% (01:22) wrong based on 38 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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Re: Are a and b both integers?  [#permalink]

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18 Feb 2019, 08:35
PeepalTree wrote:
Are a and b both integers?

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

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

IMO E

so we have a and b, which can be equal, +ive, -ive, irrational numbers, rational numbers.

from 1) a = b =$$\sqrt{2}$$
or a = b = 2

Now 2 + 2 = I, question is answered with a No

Now 4+4 = I, question is answered with a Yes

We can use the same test cases to negate B

Even when we combine both the statements, we can get 2 values

Therefore answer

E
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Are a and b both integers?  [#permalink]

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18 Feb 2019, 17:57
St 1:
$$(\sqrt{2})^2 + (\sqrt{3})^2 = 5$$; a & b are non integers
$$(2)^2 + (3)^2 = 5$$; a & b are integers
NOT SUFFICIENT

St 2:
$$2.5/2.5 = 1$$; a & b are non integers
$$6/3 = 2$$; a & b are integers
NOT SUFFICIENT

St 1 & St 2:
Same as above

(E)
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Are a and b both integers?   [#permalink] 18 Feb 2019, 17:57
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# Are a and b both integers?

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