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29 Sep 2023, 08:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:37) correct
30%
(02:03)
wrong
based on 74
sessions
History
Date
Time
Result
Not Attempted Yet
Is |s - t| > |s| - |t|?
(1) s > t
(2) st < 0
(1) s > t
(2) st < 0
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
https://gmatclub.com/forum/data-sufficiency-ds-141/
https://gmatclub.com/forum/data-sufficiency-ds-141/
29 Sep 2023, 09:28
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Is |s - t| > |s| - |t|?
s and t could be both positive or
both negative
or one negative and other positive
Both together can't be '0'.( This is a clue actually)
(1) s > t
s = 2 and t = 1
1 > 1, NO
s = -1 and t = -2
1 > -1, YES
INSUFFICIENT.
(2) st < 0
Either of them is negative.
s = -1 and t = 2
3 > -1, YES
s = 2 and t = -1
3 > 1, YES
SUFFICIENT.
Answer B.
s and t could be both positive or
both negative
or one negative and other positive
Both together can't be '0'.( This is a clue actually)
(1) s > t
s = 2 and t = 1
1 > 1, NO
s = -1 and t = -2
1 > -1, YES
INSUFFICIENT.
(2) st < 0
Either of them is negative.
s = -1 and t = 2
3 > -1, YES
s = 2 and t = -1
3 > 1, YES
SUFFICIENT.
Answer B.
04 Sep 2026, 08:45
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First things first, let's go over a few properties related to absolute values (modulus) which can be incredibly useful in solving questions on 'Mods', especially like the one we have here.
1) |x * y| = |x| * |y|
2) |x / y| = |x| / |y|
3) |x + y| ≤ |x| + |y|
4) |x – y| ≥ |x| - |y|
5) |x| = \(√(x^2 )\)
It is to be noted that, in properties 3 and 4,
Now, let’s take a look at the question, which asks us if |s – t| > |s| - |t|.
Using property number 4 discussed above, we see that this happens if s and t are of opposite signs. Therefore, the question asks if s and t are of opposite signs.
Statement 1 alone: s > t.
One number being more than the other does not tell us anything about their signs.
Statement 1 alone is insufficient.
Answer options A and D can be eliminated.
Statement 2 alone: st < 0.
This means that s and t are of opposite signs, which means that the question is answered with a definite YES, using this information.
Statement 2 alone is sufficient to answer the question with a definite YES.
Answer options C and E can be eliminated.
The correct answer option is B.
Hope that helps!
1) |x * y| = |x| * |y|
2) |x / y| = |x| / |y|
3) |x + y| ≤ |x| + |y|
4) |x – y| ≥ |x| - |y|
5) |x| = \(√(x^2 )\)
It is to be noted that, in properties 3 and 4,
- The inequality is applicable if x and y have opposite signs
- Equality holds if x and y have same signs.
Now, let’s take a look at the question, which asks us if |s – t| > |s| - |t|.
Using property number 4 discussed above, we see that this happens if s and t are of opposite signs. Therefore, the question asks if s and t are of opposite signs.
Statement 1 alone: s > t.
One number being more than the other does not tell us anything about their signs.
- s and t could have the same signs, in which case the question is answered with a NO.
- s and t could have opposite signs, in which case the question is answered with a YES.
Statement 1 alone is insufficient.
Answer options A and D can be eliminated.
Statement 2 alone: st < 0.
This means that s and t are of opposite signs, which means that the question is answered with a definite YES, using this information.
Statement 2 alone is sufficient to answer the question with a definite YES.
Answer options C and E can be eliminated.
The correct answer option is B.
Hope that helps!
