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# If xy < 10, is y < 1? (1) y < 7 (2) x > 10

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
If xy < 10, is y < 1? (1) y < 7 (2) x > 10  [#permalink]

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12 Apr 2018, 20:49
00:00

Difficulty:

25% (medium)

Question Stats:

90% (01:04) correct 10% (00:57) wrong based on 25 sessions

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If xy < 10, is y < 1?

(1) y < 7
(2) x > 10

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Location: India
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Re: If xy < 10, is y < 1? (1) y < 7 (2) x > 10  [#permalink]

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12 Apr 2018, 20:58
(1) y < 7
We can have (x,y) = (-1,6) or (1,0) as per given conditions. Hence NOT sufficient.

(2) x > 10
Since xy<10.
This means y<1.

Sufficient.

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Re: If xy < 10, is y < 1? (1) y < 7 (2) x > 10  [#permalink]

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12 Apr 2018, 22:34
Bunuel wrote:
If xy < 10, is y < 1?

(1) y < 7
(2) x > 10

we are asked to determine whether y is less than 1.

statement 1: y<7
clearly not sufficient. we can logically conclude that y could be positive or y could be negative.

statement 2: it states that x> 10. In this case the minimum value of x will be 11. it is also given that xy<0. In order to make xy<0 one of x or y will be negative. As x is positive y must be negative. so, we can conclude that x<1. Sufficient.

Thus, the correct answer is B.
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Re: If xy < 10, is y < 1? (1) y < 7 (2) x > 10  [#permalink]

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27 Apr 2018, 08:33
I) y can have any value less than 1 or greater than 1
So not sufficient

II)x>10
When y=1 then xy=10
But xy<10 so certaintly y<1

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Re: If xy < 10, is y < 1? (1) y < 7 (2) x > 10 &nbs [#permalink] 27 Apr 2018, 08:33
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