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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## is x/3 < x ? tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## is x/3 < x ? $$Is\ \ \frac{x}{3}$$\left(1\right)\ \ x<\ 0(2)\ \ x\ \ does\ \ not\ \ equal\ -1.$$The OA is A. I need help to solve this DS question. Please, can any expert explain it for me? Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 LUANDATO wrote:$$Is\ \ \frac{x}{3} $$\left(1\right)\ \ x<\ 0$$ $$(2)\ \ x\ \ does\ \ not\ \ equal\ -1.$$ The OA is A. I need help to solve this DS question. Please, can any expert explain it for me? Thanks. A rephrase is helpful here. Start by multiplying both sides of the inequality in question by 3. " Is x/3 < x?", becomes Is x < 3x? Subtract 'x' from both sides Is 0 < 2x? Divide both sides by 2 Is 0 < x? Statement 1: Well if x < 0, we know it's not greater than 0, so this statement alone is sufficient. Statement 2: Clearly not sufficient. x could be -10 or 10, etc. The answer is A _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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Hi LUANDATO,

We're asked if X/3 is less than X. This is a YES/NO question and we can solve it with a mix of Number Property Rules and by TESTing VALUES.

1) X < 0

Fact 1 tells us that X is NEGATIVE. When dividing a negative number by 3, the result is ALWAYS CLOSER to 0 than X is. For example:
IF...
X = -3, then (-3)/3 = -1 and -1 is closer to zero than -3 is... so the answer to the question is NO.
This pattern exists with ANY negative number, so the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

2) X does NOT equal -1

IF...
X = -3, then (-3)/3 = -1 and -1 is closer to 0 than -3 is... so the answer to the question is NO.
X = 3, then 3/3 = 1... so the answer to the question is YES.
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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