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Is x+y < 1? 1. x < 8/9 2. y < 1/8

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Source: — Data Sufficiency |
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by GMATGuruNY » Thu May 18, 2017 3:35 pm
ziyuenlau wrote:Is x+y < 1?

1. x < 8/9
2. y < 1/8
Clearly, neither statement is sufficient on its own.

Statements combined:
Inequalities in which the <> faces the same direction can be ADDED TOGETHER.
Adding together x < 8/9 and y < 1/8, we get:
x+y < 8/9 + 1/8
x+y < 64/72 + 9/72
x+y < 73/72.

If x+y = 71/72, then the answer to the question stem is YES.
If x+y = (72.5)/72, then the answer to the question stem is NO.
INSUFFICIENT.

The correct answer is E.
Last edited by GMATGuruNY on Fri May 19, 2017 6:36 am, edited 1 time in total.
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by Jay@ManhattanReview » Thu May 18, 2017 4:35 pm
ziyuenlau wrote:Is x+y < 1?

1. x < 8/9
2. y < 1/8

Source : GMATPrep
OA=E
We see that each statement by itself is not sufficient as each lacks the information about the other variable.

Let's combine both the statements.

From statement 1, we have x < 8/9 => x < 1 - 1/9

From statement 2, we have y < 1/8

Thus, x + y < 1 - 1/9 + 1/8

Since 1/8 > 1/9, (1 - 1/9 + 1/8) > 1

OR, x + y < (A little greater than 1)

So, if 1 < x + y < (A little greater than 1), the answer is NO.

And, if x + y < 1, the answer is YES. Insufficient.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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by [email protected] » Fri May 19, 2017 11:03 am
Hi ziyuenlau,

When dealing with fractions in GMAT Quant questions, it's sometimes helpful to convert from fraction-to-decimal (doing so might make the requisite math faster or easier).

We're asked if (X+Y) is less than 1. This is a YES/NO question.

1) X < 8/9

This FACT tells us that X is LESS than .88888...., but we don't know anything about Y.
Fact 1 is INSUFFICIENT

2) Y < 1/8

This FACT tells us that Y is LESS than .125, but we don't know anything about X.
Fact 2 is INSUFFICIENT

Combined, we know that (X+Y) must be LESS than .8888.... + .125 = 1.01388888....

IF... the sum = 1, then the answer to the question is NO.
IF... the sum = 0, then the answer to the question is YES.

Combined, INSUFFICIENT

Final Answer: E

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