Q) Is mod (x-y) > mod x - mod y?
1) y < x
2) xy < 0
Answer: (B)
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Please provide an approach for the DS question below:
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Kshitij Singh
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One approach is to plot the distances on a NUMBER LINE.Is |x-y| > |x| - |y| ?
1) y < x
2) xy < 0
|x|= the distance between x and 0 = the RED segment on the number lines below.
|y| = the distance between y and 0 = the BLUE segment on the number lines below.
|x-y| = the distance BETWEEN X AND Y.
Statement 1: y<x
Case 1:
|x| - |y| = RED - BLUE.
|x-y| = RED - BLUE.
Thus, |x-y| = |x| - |y|.
Case 2:
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
INSUFFICIENT.
Statement 2: xy<0
Since x and y have different signs, they are on OPPOSITE SIDES OF 0.
In each case:
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
SUFFICIENT.
The correct answer is B.
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Hi Kshitij Singh,
This DS question can be solving by TESTing Values (there are also some noteworthy Number Properties built into this question);
We're asked if |X - Y| > |X| - |Y|. This is YES/NO question.
Fact 1: Y < X
If....
X = 1
Y = 0
|1| is not greater than |1| - |0|, so the answer to the question is NO.
X = 1
Y = -1
|2| is greater than |1| - |1|, so the answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: XY < 0
This tells us that we have 1 POSITIVE value and 1 NEGATIVE value. This means....
|X - Y| will be greater than |X|
If X = positive, Y = negative, then |(pos) - (neg)| --> more positive --> bigger than |X| (regardless of the absolute value).
If X = negative, Y = positive, then |(neg) - (pos)| --> more negative --> bigger than |X| (because of the absolute value)
Since we're also subtracting |Y| from |X|, we will end up with a value that is SMALLER than |X|.
This means that |X-Y| will ALWAYS be greater than |X| - |Y|, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
This DS question can be solving by TESTing Values (there are also some noteworthy Number Properties built into this question);
We're asked if |X - Y| > |X| - |Y|. This is YES/NO question.
Fact 1: Y < X
If....
X = 1
Y = 0
|1| is not greater than |1| - |0|, so the answer to the question is NO.
X = 1
Y = -1
|2| is greater than |1| - |1|, so the answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: XY < 0
This tells us that we have 1 POSITIVE value and 1 NEGATIVE value. This means....
|X - Y| will be greater than |X|
If X = positive, Y = negative, then |(pos) - (neg)| --> more positive --> bigger than |X| (regardless of the absolute value).
If X = negative, Y = positive, then |(neg) - (pos)| --> more negative --> bigger than |X| (because of the absolute value)
Since we're also subtracting |Y| from |X|, we will end up with a value that is SMALLER than |X|.
This means that |X-Y| will ALWAYS be greater than |X| - |Y|, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
