If [x] denotes the largest integer smaller than x, is [x] > [−x]?
(1) x = [x] + 1
(2) x + 1 > 0
OA:E
If [x] denotes the
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- fiza gupta
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Hi fiza gupta,
This DS question can be solved by TESTing VALUES.
We're told that [X] = the largest integer that is SMALLER than X. We're asked if [X] > [-X]. This is a YES/NO question.
1) X = [X] + 1
IF....
X = 1
[1] = 0 and 1 = 0+1
[-1] = -2 and the answer to the question is YES.
IF....
X = 0
[0] = -1 and 0 = -1+1
[-0] = -1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) X + 1 > 0
Both of the TESTs that I used in Fact 1 also 'fit' the information in Fact 2....
IF....
X = 1
[1] = 0 and 1 = 0+1
[-1] = -2 and the answer to the question is YES.
IF....
X = 0
[0] = -1 and 0 = -1+1
[-0] = -1 and the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, we already have two TESTs that fit both Facts - and we have two different answers to the given question.
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This DS question can be solved by TESTing VALUES.
We're told that [X] = the largest integer that is SMALLER than X. We're asked if [X] > [-X]. This is a YES/NO question.
1) X = [X] + 1
IF....
X = 1
[1] = 0 and 1 = 0+1
[-1] = -2 and the answer to the question is YES.
IF....
X = 0
[0] = -1 and 0 = -1+1
[-0] = -1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) X + 1 > 0
Both of the TESTs that I used in Fact 1 also 'fit' the information in Fact 2....
IF....
X = 1
[1] = 0 and 1 = 0+1
[-1] = -2 and the answer to the question is YES.
IF....
X = 0
[0] = -1 and 0 = -1+1
[-0] = -1 and the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, we already have two TESTs that fit both Facts - and we have two different answers to the given question.
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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- Brent@GMATPrepNow
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Here are two similar questions to practice with:
- https://www.beatthegmat.com/ds-t276593.html
- https://www.beatthegmat.com/number-prope ... 71768.html
Cheers,
Brent
- https://www.beatthegmat.com/ds-t276593.html
- https://www.beatthegmat.com/number-prope ... 71768.html
Cheers,
Brent
- fiza gupta
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Before testing values, it's often helpful to translate the question into words. When the GMAT says "[x] denotes the largest integer smaller than x," what they really mean is "round down (to the left on the number line) to the nearest integer."fiza gupta wrote:If [x] denotes the largest integer smaller than x, is [x] > [−x]?
(1) x = [x] + 1
(2) x + 1 > 0
OA:E
So when would [x] > [−x]? When would the rounded-down-integer from x be greater than the rounded-down-integer from -x? When x is positive, and -x is negative. (If x = 0, then both x and -x would round down to -1).
Target question: is x > 0?
(1) x = [x] + 1
If x is 1 greater than the rounded-down-integer from x, this simply tells us that x is any integer. For example,
if x = 3, [x] = 2
if x = -5, [x] = -6
This is insufficient to answer our target question.
(2) x + 1 > 0
Rearrange:
x > -1
Since our target question is "is x positive?", this is insufficient. If x = -0.5, we'd get a "no" answer to our question, but if x = 2, we'd get a "yes" answer.
1 & 2 combined
With the two statements together, we know that x is an integer greater than -1. This might seem at first to answer our question, but remember to consider 0:
if x = 0, [x] = -1 and [-x] = -1. So the answer to our question is "no."
if x = 4, [x] = 3 and [-x] = -5, so the answer is "yes."
Insufficient. The answer is E.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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And since the GMAT really loves this construction, here's another one to add to Brent's list:
https://www.beatthegmat.com/ds-t281646.html#738122
https://www.beatthegmat.com/ds-t281646.html#738122
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education