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Source: — Data Sufficiency |
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by neoreaves » Sun Apr 25, 2010 1:26 am
IMO A

1) 9x > 10x

x >10/9x

x > 1.1x

if x > 0 then divide both sides by x 1 > 1.1 which is not true

if x <0 then to divide both sides we have to flip the inequality 1< 1.1 which is true

Thus sufficient


2) x = -2 satisfies this so does x = 100 so Insufficient

Ans: A
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by Testluv » Sun Apr 25, 2010 1:40 am
We can also just use reasoning/picking numbers.

(1) 9x>10x

If x were positive, say positive 2, would the inequality be satisfied? That is, is 9(2) > 10(2)? Clearly not. Thus, x cannot be positive.

If x were zero, would the inequality be satisifed? That is, is 9(0) > 10(0)? Clearly not. Thus, x cannot be zero.

Thus, x must be negative.

As neoreaves points out, the information in (2) allows for x to be either positive or negative. Thus, the answer to the question "is x negative?" is "we don't know for sure".

(1) is sufficient by itself but (2) is not. Choose A.
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by Scott@TargetTestPrep » Sun Jul 22, 2018 5:12 pm
pradeepkaushal9518 wrote:is x a negative number ?

1. 9x> 10x
2.x+3 is positive
We need to determine whether x is a negative number.

Statement One Alone:

9x > 10x

Simplifying we have:

9x – 9x > 10x – 9x

0 > x

Since 0 is greater than x, x is less than 0. In other words, x must be negative.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

x + 3 is positive.

From statement two we see that x itself could be either positive or negative.

If x is positive

Let x = 1:

1 + 3 = 4, which is positive.

If x is negative

Let x = -1:

-1 + 3 = 2, which is also positive.

Statement two alone is not sufficient to answer the question.

Answer: A

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