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

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Bunuel
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If |-1 - x| 3, where x is a positive integer, what is the smallest [#permalink] New post   02 Dec 2022, 11:30
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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
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C
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gmatophobia
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If |-1 - x| 3, where x is a positive integer, what is the smallest [#permalink] New post   02 Dec 2022, 12:40
Bunuel 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


x is a positive integer, so we can eliminate A and B.

Two ways in which we can solve this question 1) Substitution AND 2) Algebraic

Using Substitution

1 is the smallest number among the remaining three, substitute 1

| - 1 - 1 | ≤ 3

True, hence 1 is the smallest number

Using Algebra

Case 1: (-1 - x) is positive

-1 - x ≤ 3

- x ≤ 4

x >= -4; as x is positive, the smallest number = 1

Case 2: (-1 - x) is negative

-(-1 - x) ≤ 3

1 + x ≤ 3

x ≤ 2

as x is positive, the smallest number = 1

Option C
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luca1999
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Re: If |-1 - x| 3, where x is a positive integer, what is the smallest [#permalink] New post   02 Dec 2022, 13:50
gmatophobia wrote:
Bunuel 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


x is a positive integer, so we can eliminate A and B.

Two ways in which we can solve this question 1) Substitution AND 2) Algebraic

Using Substitution

1 is the smallest number among the remaining three, substitute 1

| - 1 - 1 | ≤ 3

True, hence 1 is the smallest number

Using Algebra

Case 1: (-1 - x) is positive

-1 - x ≤ 3

- x ≤ 4

x >= -4; as x is positive, the smallest number = 1

Case 2: (-1 - x) is negative

-(-1 - x) ≤ 3

1 + x ≤ 3

x ≤ 2

as x is positive, the smallest number = 1

Option C


if x is equal to -4 then | -1 - (-4)| ≤ 3 --> | -1 +4 | ≤ 3 --> |3|≤ 3 --> 3≤ 3 it can be option B
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gmatophobia
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Re: If |-1 - x| 3, where x is a positive integer, what is the smallest [#permalink] New post   02 Dec 2022, 13:53
luca1999 wrote:

if x is equal to -4 then | -1 - (-4)| ≤ 3 --> | -1 +4 | ≤ 3 --> |3|≤ 3 --> 3≤ 3 it can be option B


The question states "x is a positive integer". Hence, x cannot be -4.

Let me know if you think otherwise.
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If |-1 - x| 3, where x is a positive integer, what is the smallest [#permalink] New post   08 Jul 2023, 05:59
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧



Given that |-1 - x| ≤ 3, where x is a positive integer. And we need to find what is the smallest possible value of x?

|-1 - x| ≤ 3
=> |-(1+x)| ≤ 3

We know that x is positive => 1 + x is positive
=> |-(1+x)| = 1 + x ( As |A| = A for A ≥ 0 )

=> 1 + x ≤ 3
=> x ≤ 3 - 1
=> x ≤ 2

=> x = 1 or 2 (As x is a positive integer)
=> Smallest possible value of x = 1

So, Answer will be C
Hope it helps!

Watch the following video to MASTER Absolute Values

­
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gmatclubot
If |-1 - x| 3, where x is a positive integer, what is the smallest [#permalink]
08 Jul 2023, 05:59
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