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If y is an integer, then the least possible value of |23-5|

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If y is an integer, then the least possible value of |23-5| [#permalink] New post 01 Oct 2012, 03:58
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A
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Difficulty:

  25% (low)

Question Stats:

62% (01:28) correct 37% (00:28) wrong based on 438 sessions
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 01 Oct 2012, 03:58
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SOLUTION

If y is an integer, then the least possible value of |23 - 5y| is

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

|23-5y| represents the distance between 23 and 5y on the number line. Now, the distance will be minimized when 5y, which is multiple of 5, is closest to 23. Multiple of 5 which is closest to 23 is 25 (for y=5), so the least distance is 2: |23-25|=2.

Answer: B.
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 01 Oct 2012, 04:10
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To find the value of y that yields that minimum for |23 - 5y|, I tested numbers (integers).

1: |23-5(1)| = 18
2: |23-5(2)| = 13
3: |23-5(3)| = 8
4: |23-5(4)| = 3
5: |23-5(5)| = 2
6: |23-5(6|| = 7
7: |23-5(7)| = 12

[Reveal] Spoiler:
The correct answer is B, 2.


This is a rather simple problem that can be figured out well under the 2 minute allowance - that said, it is a bit of a trap if you're not paying attention, and mark 5 instead of 2, as 5 is the value of y that yields the answer of 2.
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 01 Oct 2012, 07:10
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If y is an integer, then the least possible value of |23 - 5y| is

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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Page: 159
Difficulty: 600


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|23-5y| is the distance between 23 and the integer multiple of 5, 5y.
So, the question is asking for the smallest distance between a multiple of 5 and 23.
Since 20=4\cdot5<23<5\cdot5=25 and 23 is closer to 25 than to 20, the answer is |23-25|=2.

Answer B.
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 01 Oct 2012, 18:40
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If y is an integer, then the least possible value of |23 - 5y| is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

The integers which are multiple of 5 & closest to 23 on the number line are either 20 or 25.
Thus the minimum distance possible is 2 units
Answer B
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 02 Oct 2012, 05:14
Since absolute value stands for the distance on the number line. The question asks for a shortest distance between 23 and a multiple of 5. 25 is the multilple of 5 that is closest to 23 with a shortest distance of 2. 5 is the value of y that shall yield 25 and hence the answer is E
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 02 Oct 2012, 05:18
oops!! the question asks for value of Mod and not y...sorry my bad!! the answer should be B
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 02 Oct 2012, 11:31
ratinarace wrote:
oops!! the question asks for value of Mod and not y...sorry my bad!! the answer should be B


Haha! see my post above about avoiding the fact this this question can be a trap depending on how you approach it.
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 03 Oct 2012, 23:59
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The two closest multiples of 5 that are closest to 23 are 20 and 25.

23 - 20 = -3 .....and |-3| = 3

23 - 25 = 2 ......and |2| = 2

Thus answer is B (2)
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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 04 Oct 2012, 12:55
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SOLUTION

If y is an integer, then the least possible value of |23 - 5y| is

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

|23-5y| represents the distance between 23 and 5y on the number line. Now, the distance will be minimized when 5y, which is multiple of 5, is closest to 23. Multiple of 5 which is closest to 23 is 25 (for y=5), so the least distance is 2: |23-25|=2.

Answer: B.

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Re: If y is an integer, then the least possible value of |23-5| [#permalink] New post 09 Nov 2013, 23:29
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Re: If y is an integer, then the least possible value of |23-5|   [#permalink] 09 Nov 2013, 23:29
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