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Is |2x − y| < 10? (1) 2x − y < 10 (2) y − 2x < 10
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Bunuel
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Is |2x − y| < 10? (1) 2x − y < 10 (2) y − 2x < 10 [#permalink] New post  19 Feb 2021, 00:15
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A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

64% (01:11) correct 36% (01:26) wrong based on 42 sessions

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Is |2x − y| < 10?

(1) 2x − y < 10

(2) y − 2x < 10



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Re: Is |2x − y| < 10? (1) 2x − y < 10 (2) y − 2x < 10 [#permalink] New post  19 Feb 2021, 02:41
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Bunuel wrote:
Is |2x − y| < 10?

(1) 2x − y < 10

(2) y − 2x < 10


CONCEPT:
- Two inequations may be added if their inequality signs are identical
- If the inequality signs of two inequalities are not identical then multiply one of the inequality and reverse the inequation sign


Question: Is |2x − y| < 10?
Question REPHRASED: Is -10 < 2x − y < 10?

Statement 1: 2x − y < 10

SInce we do NOT know the lower side limit of expressions 2x-y which may be greater than -10 or less than -10 hence

NOT SUFFICIENT

Statement 2: y − 2x < 10
Multiplying -2 both sides and reversing the inequality sign
y − 2x < 10
(-1)(y − 2x) > (-1)(10)
2x - y > -10

SInce we do NOT know the Upper side limit of expressions 2x-y which may be greater than +10 or less than +10 hence

NOT SUFFICIENT

Combining the statements

We get, -10 < 2x − y < 10 hence

SUFFICIENT

Answer: Option C

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Re: Is |2x − y| < 10? (1) 2x − y < 10 (2) y − 2x < 10 [#permalink] New post  19 Feb 2021, 23:56
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Kudos
Is |2x − y| < 10?

As we know property of mod, -10<(2x − y) < 10

Stat1:1 2x − y < 10 -> Doesn't satisfy negative condition. Not sufficient.

Stat2: y − 2x < 10 or, 2x-y >-10 ->Doesn't satisfy positive condition. Not sufficient.

Combining both, -10<(2x − y) < 10 so, Sufficient.

So, I think C. :)
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