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If x is an integer, then what is the least possible value of |99 - 7x|

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Ravixxx
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If x is an integer, then what is the least possible value of |99 - 7x| [#permalink] New post   15 Apr 2020, 23:52
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If x is an integer, then what is the least possible value of \(|99-7x|\) ?

(A) 0
(B) 1
(C) 5
(D) 98
(E) 107

Source: Ready4Gmat
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B
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Re: If x is an integer, then what is the least possible value of |99 - 7x| [#permalink] New post   15 Apr 2020, 23:59
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Ravixxx wrote:
If x is an integer, then what is the least possible value of \(|99-7x|\) ?

(A) 0
(B) 1
(C) 5
(D) 98
(E) 107

Source: Ready4Gmat


For least possible value of \(|99-7x|\), 99-7x≈0

i.e. x≈ 99/7
i.e. x ≈ 14.14

Since x is an Integer so x = 14 gives \(|99-7x| = 1\)

Answer: Option B
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Re: If x is an integer, then what is the least possible value of |99 - 7x| [#permalink] New post   09 Jul 2020, 10:58
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Ravixxx wrote:
If x is an integer, then what is the least possible value of \(|99-7x|\) ?

(A) 0
(B) 1
(C) 5
(D) 98
(E) 107

Source: Ready4Gmat


Asked: If x is an integer, then what is the least possible value of \(|99-7x|\)

|99-7x|
When x=14; |99-7*14| = |99-98| = 1
When x=15; |99-7*15| = |99-105| = 6

IMO B
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Re: If x is an integer, then what is the least possible value of |99 - 7x| [#permalink] New post   16 Apr 2020, 00:37
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If x is an integer, then what is the least possible value of |99−7x| ?

|99−7x|represents the distance between 99 and 7x on the number line. Now, the distance will be minimized when 7x, which is multiple of 7, is closest to 99. Multiple of 7 which is closest to 99 is 98 (for x=14), so the least distance is 1: |99−98|=1.

Correct Answer: B.
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Re: If x is an integer, then what is the least possible value of |99 - 7x| [#permalink] New post   09 Jul 2020, 14:34
99-7x
If x=14 -> 99-98=1

Answer -> B
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Re: If x is an integer, then what is the least possible value of |99 - 7x| [#permalink] New post   12 Jul 2020, 15:20
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Ravixxx wrote:
If x is an integer, then what is the least possible value of \(|99-7x|\) ?

(A) 0
(B) 1
(C) 5
(D) 98
(E) 107




Solution:

The least possible value of |99 - 7x| occurs when the value of 7x is as close to 99 as possible. Since x is an integer, we see that if x = 14, 7x = 98 (notice that 98 is the multiple of 7 closest to 99 that is less than 99) and we have |99 - 7x| = |99 - 98| = 1, and if x = 15, 7x = 105 (notice that 105 is the multiple of 7 closest to 99 that is greater than 99) and we have |99 - 7x| = |99 - 105| = 6.

Since 1 < 6, the least possible value of |99 - 7x| is 1.

Answer: B
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Re: If x is an integer, then what is the least possible value of |99 - 7x| [#permalink] New post   01 Mar 2024, 01:41
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Re: If x is an integer, then what is the least possible value of |99 - 7x| [#permalink]
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