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OG 18, question-364

This topic has 3 expert replies and 0 member replies

OG 18, question-364

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If ⌈x⌉ denotes the least integer greater than or equal to x, is ⌈x⌉=0 ?

1. -1 < x < 1
2. x < 0

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vaibhav101 wrote:
If ⌈x⌉ denotes the least integer greater than or equal to x, is ⌈x⌉=0 ?

1. -1 < x < 1
2. x < 0
S1: pick some numbers in the range
Case 1: x = -1/2; If {-1/2] denotes the least integer greater than or equal to -1/2, then {-1/2] would be 0. So we get a YES. (Effectively, if x isn't an integer, we're just rounding up to the closest integer.)
Case 2: x = 1/2; If {1/2] denotes the least integer greater than or equal to 1/2, then {1/2] would be 1. So we get a NO. Not sufficient.

S2: Clearly not sufficient. x could be -1/2. Or x could be -100.

Together: Now we know that -1 < x < 0. No matter what value we pick for x, the smallest integer greater than x will be 0. (If x = -1/2 we round up to 0. If x = -1/8 we round up to 0, etc.) The answer is definitely YES, so together the statements are sufficient. The answer is C

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Here are a couple of related questions to practice with:

- http://www.beatthegmat.com/clarity-needed-on-the-concept-t267353.html
- http://www.beatthegmat.com/ds-t276593.html

Cheers,
Brent

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Another tip: reformat the stem into something familiar so that your mind doesn't keep wandering back to the unfamiliar symbol. If we grapple with the prompt for a bit, then rephrase this as

Quote:
Is -1 < x ≤ 0 ?
the statements are a cinch, but if we don't, it's easy to keep staring at that ceiling function and doubting ourselves.

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