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![[x] denotes the greatest integer less than or equal to x.](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "[x] denotes the greatest integer less than or equal to x."){kind=icon}
22 Jun 2013, 00:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:49) correct
36%
(01:55)
wrong
based on 930
sessions
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[x] denotes the greatest integer less than or equal to x. What is the value of [x]?
(1) [3x] = 1
(2) [2x+1] = 2
(1) [3x] = 1
(2) [2x+1] = 2
22 Jun 2013, 01:22
Kudos
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First of all, the question stem means: for any X, we must round down to the nearest integer.
For example: x = 4.5 ==> [x] = 4; or x = 3.333 ==> [x] = 3
Statement 1:
[3x] = 1 ==> 1/3 < x < 2/3 because:
if x < 1/3 ==> 3x < 1 ==> [3x] = 0, not 1
if x > 2/3 ==> 3x > 2 ==> [3x] greater or equal 2, not 1
So we have: 0.333 < x < 0.666 ==> 0 < x < 1 ==> [x] = 0
Statement 1 is sufficient.
Statement 2:
[2x + 1] = 2 ==> 2 < 2x + 1 < 3 ==> 1/2 < x < 1
So we have: 0.5 < x < 1 ==> 0 < x < 1 ==> [x] = 0
Statement 2 is sufficient.
Hence, D is correct.
Hope it helps.
For example: x = 4.5 ==> [x] = 4; or x = 3.333 ==> [x] = 3
Statement 1:
[3x] = 1 ==> 1/3 < x < 2/3 because:
if x < 1/3 ==> 3x < 1 ==> [3x] = 0, not 1
if x > 2/3 ==> 3x > 2 ==> [3x] greater or equal 2, not 1
So we have: 0.333 < x < 0.666 ==> 0 < x < 1 ==> [x] = 0
Statement 1 is sufficient.
Statement 2:
[2x + 1] = 2 ==> 2 < 2x + 1 < 3 ==> 1/2 < x < 1
So we have: 0.5 < x < 1 ==> 0 < x < 1 ==> [x] = 0
Statement 2 is sufficient.
Hence, D is correct.
Hope it helps.
22 Jun 2013, 11:54
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fozzzy
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