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# If |-1-x| ≤ 3, where x is a positive integer, what is the smallest pos

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If |-1-x| ≤ 3, where x is a positive integer, what is the smallest pos  [#permalink]

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27 Nov 2018, 15:46
5
00:00

Difficulty:

55% (hard)

Question Stats:

47% (01:09) correct 53% (00:57) wrong based on 83 sessions

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If |-1-x| ≤ 3, where x is a positive integer, what is the smallest possible value of x?

A. -5
B. -4
C. 1
D. 3
E. 4
Math Expert
Joined: 02 Aug 2009
Posts: 7765
Re: If |-1-x| ≤ 3, where x is a positive integer, what is the smallest pos  [#permalink]

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27 Nov 2018, 22:38
rencsee wrote:
If |-1-x| ≤ 3, where x is a positive integer, what is the smallest possible value of x?

A. -5
B. -4
C. 1
D. 3
E. 4

Use the choices to your advantage, and this becomes sub 600 level question.

|-1-x| ≤ 3..
Now x cannot be a negative number and we are looking for least value of x...
In the choices, 1 is the least integer.

substitute this value in |-1-x| ≤ 3..
|-1-(1)|≤ 3.........2 ≤ 3.. YES
So, 1 is a valid value....

C

Otherwise..
|-1-x| ≤ 3..
two cases..
(I) MODULUS is positive.
-1-x≤ 3.........-4 ≤ x
(II) MODULUS is negative.
1+x≤ 3.........x ≤ 2
but x is positive, so x is 1

C
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Re: If |-1-x| ≤ 3, where x is a positive integer, what is the smallest pos   [#permalink] 27 Nov 2018, 22:38
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