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# Is xy > 5? (1) 1 <= x <= 3 and 2 <= y <= 4

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Is xy > 5? (1) 1 <= x <= 3 and 2 <= y <= 4 [#permalink]  29 Mar 2005, 18:28
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Is xy > 5?

(1) 1 <= x <= 3 and 2 <= y <= 4
(2) x + y = 5

I am having a rough time with ineqalities so explanation would be highly appreciated. Thanks
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
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1) x is between 1 and 3. y is between 2 and 4.
So xy will lie between 2 and 12. So 1) is not sufficient since xy can be <5 or >5.

2) x+y=5
Possible values:
Question does not state that x and y must be positive, so x=0 or y=0 is possible. If that is the case, xy could be 0. So 2 is insufficient.

1) and 2)
x+y = 5 and 1 <= x <= 3 and 2 <= y <= 4

Possible values:
x=1,y=4 --> xy < 5
x=2,y=3 --> xy >5
x=3,y=2 --> xy >5

So 1) and 2) together are insufficient as well.

E it is.
Senior Manager
Joined: 15 Mar 2005
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YWilfred did it very well.

I agree with (E).
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Re: DS - Inequality 1 [#permalink]  05 Apr 2005, 17:45
Folaa3 wrote:
Is xy > 5?

(1) 1 <= x <= 3 and 2 <= y <= 4
(2) x + y = 5

I am having a rough time with ineqalities so explanation would be highly appreciated. Thanks

Stmt 1:
If x=1, y=2 then xy <5
If x=3, y=4, xy >5
Hence, Stmt 1 not suff

Stmt 2:
Not suff as x & y cld take any value that satisfies x+y = 5

stmt 1 & 2 taken together:
To satisfy x+y = 5,
values for x & y can be
x=1, y=4=> xy <5
x=2, y=3 => xy >5
Hence Stmt 1 & 2 are insuffiecient

Ans is 'E'
VP
Joined: 13 Jun 2004
Posts: 1122
Location: London, UK
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If you're not confortable with those kind of questions, you should always try to find what the problem is aksking you to find and then try to find the contrary. When the statement is good and when it is false, always try the extreme possibilities.

Answer E for this one. Just take examples :

Statement 1 : 1 <= x <= 3 and 2 <= y <= 4
if x=1 and y=2 ; xy=2 so xy<5
if x=3 and y=4 ; xy=12 so xy>5
so statement 1 is insuff

Statement 2 : x + y = 5
if x=2 and y=3 ; xy=6 so xy>5
if x=-5 and y=10 ; xy=-50 so xy<5

together 1 and 2 :
if x=1 and y=4 ; xy=4 so xy<5
if x=2 and y=3 ; xy=6 so xy>5
insuff
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