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# Is xy < 1 ? (1) x > 1 and y < 1 (2) 2x – y > 1

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Math Expert
Joined: 02 Sep 2009
Posts: 56271
Is xy < 1 ? (1) x > 1 and y < 1 (2) 2x – y > 1  [#permalink]

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10 Mar 2017, 07:00
1
4
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Difficulty:

45% (medium)

Question Stats:

64% (01:56) correct 36% (01:42) wrong based on 140 sessions

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Is xy < 1 ?

(1) x > 1 and y < 1
(2) 2x – y > 1

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Director
Joined: 05 Mar 2015
Posts: 992
Re: Is xy < 1 ? (1) x > 1 and y < 1 (2) 2x – y > 1  [#permalink]

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10 Mar 2017, 08:00
2
1
Bunuel wrote:
Is xy < 1 ?

(1) x > 1 and y < 1
(2) 2x – y > 1

(1) clearly insuff
if x=15 , y=0.5 then NO
if x =2 , y = -1 then YES....insuff

(2) 2x-(y+1)>0
if x = 2 , y = 0 then YES
if x= 10 , y = 0.9 then NO...insuff

combining again take above examples as in (2)
insuff

Ans E
Manager
Joined: 14 Oct 2015
Posts: 246
GPA: 3.57
Is xy < 1 ? (1) x > 1 and y < 1 (2) 2x – y > 1  [#permalink]

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10 Mar 2017, 08:32
rohit8865 wrote:
Bunuel wrote:
Is xy < 1 ?

(1) x > 1 and y < 1
(2) 2x – y > 1

(1) clearly insuff
if x=15 , y=0.5 then NO
if x =2 , y = -1 then YES....insuff

(2) 2x-(y+1)>0
if x = 2 , y = 0 then YES
if x= 10 , y = 0.9 then NO...insuff

combining again take above examples as in (2)
insuff

Ans E

I also reached the same answer, but not sure if we're both right. I tried it slightly differently for 2.

1- $$x > 1, y < 1$$

If $$x = 2, y = -1 , xy < 1$$
If $$x = 2, y = 0.99, xy > 1$$ -- Assuming decimal value since we don't see defined anywhere x and y have to be integers

-- clearly not sufficient.

2- $$2x - y > 1 --> 2x > y + 1 --> x > y/2 + 1/2$$

Taken alone, for $$y = 2, x > 2/2 + 1/2 --> x > 3/2$$ and thus $$xy > 1$$.
However, for $$y = -8, x > -8/2 + 1/2 --> x > -7/2$$ which could make $$xy < 1$$ in case x is a positive number, or $$xy > 1$$ for certain negative x values.

-- clearly not sufficient.

Even combined, $$x > y/2 + 1/2$$ assuming close to max value of $$y = 0.98, --> x > 0.98/2 + 1/2 --> x > 0.49 + 0.50$$ --> $$x > 0.99$$ which does not restrict $$x$$'s range from what we already know. $$y$$ could be a negative value and it would again expand the range of $$x$$ to either negative of positive thus leading to no real confirmation of the question.
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Intern
Joined: 19 Jul 2017
Posts: 7
Re: Is xy < 1 ? (1) x > 1 and y < 1 (2) 2x – y > 1  [#permalink]

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26 Dec 2018, 03:24
Hey,
Do anyone have any idea regarding the level of this questions.
Re: Is xy < 1 ? (1) x > 1 and y < 1 (2) 2x – y > 1   [#permalink] 26 Dec 2018, 03:24
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