Given that (1/x) > -3, which of the following cannot . .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

Given that (1/x) > -3, which of the following cannot . .

by VJesus12 » Thu Jan 18, 2018 4:06 am

Given that (1/x) > -3, which of the following cannot be the value of x?

A. 3
B. -1
C. -1/2
D. -1/3
E. -3

The OA is the option D.

The only way to solve this PS question is trying number by number? Experts, can you show me how to solve it fast?

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Source: Beat The GMAT — Problem Solving | Thu Jan 18, 2018 4:06 am

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 am; Thanked: 86 times; Followed by:15 members; GMAT Score:770

by ErikaPrepScholar » Thu Jan 18, 2018 6:11 am

Thinking through the problem logically is going to be faster than building equations on this one: we know that 1/x > -3. This means that any positive answers will definitely work (since any positive number is going to be greater than negative three) and any negative whole number answers will definitely work (since a negative fraction is going to be greater than negative three). This gets us down to C and D - we know that 1 over a fraction will equal the reciprocal of the fraction, so we'll end up with -2 > -3 and -3 > -3, of which only the first works. So the correct answer is D.