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If y is a positive integer, and |x| < 5 − y, then what is the least po

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If y is a positive integer, and |x| < 5 − y, then what is the least po [#permalink]

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New post Updated on: 20 Mar 2018, 09:55
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If y is a positive integer, and |x| < 5 − y, then what is the least possible value of x ?

A. 4
B. 1
C. 0
D. -1
E. -4

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[Reveal] Spoiler: OA

Originally posted by Ayush1692 on 20 Mar 2018, 09:44.
Last edited by Bunuel on 20 Mar 2018, 09:55, edited 1 time in total.
Renamed the topic and edited the question.
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If y is a positive integer, and |x| < 5 − y, then what is the least po [#permalink]

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New post 20 Mar 2018, 10:25
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Ayush1692 wrote:
If y is a positive integer, and |x| < 5 − y, then what is the least possible value of x ?

A. 4
B. 1
C. 0
D. -1
E. -4

Don't remove brackets and solve. The question asks for the logic behind absolute value.

\(y\) is a positive integer

\(|x| < 5 − y\)

LHS is nonnegative - it is positive or 0.
Least value for x is ZERO

Does RHS work?
For LHS to be less than RHS:
RHS cannot be negative
RHS cannot be 0
RHS must be positive
RHS = (5 - pos. integer)
y could = 4, 3, 2, or 1, and
RHS can = (5 - y) = 1, 2, 3, 4
That works.

The least possible value of |x| = 0
The absolute value of 0 is 0
Or: the distance of 0 from 0 is 0
Least possible value: x = 0

Answer C

--== Message from GMAT Club Team ==--

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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If y is a positive integer, and |x| < 5 − y, then what is the least po   [#permalink] 20 Mar 2018, 10:25
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