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by GmatKiss » Mon May 21, 2012 5:34 am
Is x + y < 1 ?
(1) x < 8/9
(2) y < 1/8

IMO: E
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon May 21, 2012 7:16 am
GmatKiss wrote:Is x + y < 1 ?
(1) x < 8/9
(2) y < 1/8

IMO: E
We know that 8/9 + 1/9 = 1
Since 1/8 > 1/9, we can see that 8/9 + 1/8 > 1
So, if x and y are just slightly less than 8/9 and 1/8 respectively, their sum will be greater than 1.
Conversely, x and y could both equal 0, in which case their sum will be less than 1.
So, the answer must be E

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by Brent@GMATPrepNow » Mon May 21, 2012 7:23 am
GmatKiss wrote:Is x + y < 1 ?
(1) x < 8/9
(2) y < 1/8

IMO: E
We can also answer the question, by showing two contradicting cases.

Aside: 8/9 = 640/720 and 1/8 = 90/720

If x < 8/9 and y < 1/8 then we could have the following two cases:

case a: x = 639/720 and y = 89/720
In this case, x+y > 1

case b: x = 0 and y = 0
In this case, x+y < 1

Since we cannot answer the target question with certainty, the answer is E

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by GMATGuruNY » Mon May 21, 2012 8:50 am
GmatKiss wrote:Is x + y < 1 ?
(1) x < 8/9
(2) y < 1/8

IMO: E

Statement 1: x < 8/9.
No information about y.
INSUFFICIENT.

Statement 2: y < 1/8.
No information about x.
INSUFFICIENT.

Statements 1 and 2 combined:
Adding together the two inequalities, we get:
x+y < 8/9 + 1/8
x+y < 64/72 + 9/72
x+y < 73/72.
If x+y = 72/72, then x+y=1.
If x+y = 1/72, then x+y<1.
INSUFFICIENT.

The correct answer is E.
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