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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

\(|23-5y|\) 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: \(|23-25|=2\).

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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\(|23-5y|\) 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]

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01 Oct 2012, 19:40

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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]

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02 Oct 2012, 06:14

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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

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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If y is an integer, then the least possible value of |23-5| [#permalink]

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10 Nov 2013, 00:29

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Re: If y is an integer, then the least possible value of |23-5| [#permalink]

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24 Nov 2014, 10:22

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Re: If y is an integer, then the least possible value of |23-5| [#permalink]

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17 Feb 2015, 20:16

for this question i just asked myself, what multiple of 5 is closest to 23, which would be 25 and that is 2 digits away from 23 hence the answer is 2 . when i see an abs() question i always think in terms of distance

Re: If y is an integer, then the least possible value of |23-5| [#permalink]

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26 May 2015, 05:50

When they asked least possible value, I was thinking of the value with the lowest probability and figured it could either be 1 4 and 5. Didnt think that they were asking what is the closest value

GMAT writers are never trying to 'trick' you, so 'Probability' questions on the GMAT almost always include the word "probability" in the prompt. Here, the phrase "least possible value" means "smallest value that you can possibly end with given the restrictions in the prompt" (it does NOT mean "least likely value"). As you continue to practice with Official materials, you'll get a better sense of the 'style' that GMAT writers use (and that familiarity will lead to certain advantages on Test Day).

Re: If y is an integer, then the least possible value of |23-5| [#permalink]

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30 May 2016, 05:21

Bunuel wrote:

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

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

To solve this question, we must make sure we interpret it correctly. We are not finding the least possible value of y, but rather the least possible value of |23-5y| (the absolute value of 23 – 5y). Remember that the smallest value that can result from taking the absolute value is zero. Thus we need to make 23 - 5y as close to zero as possible.

We know that 5y is a multiple of 5, so let’s first look at the multiples of 5 closest to 23. We have “20” and “25”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 5y = 20, y is 4 and when 5y = 25, y is 5. Let’s start with letting y = 4.

|23-5(4)|

|23-20|

|3| = 3

Next, let’s let y equal 5.

|23-5(5)|

|23-25|

|-2| = 2

We see that the smallest possible value of |23-5y| is 2.

Answer B.

Another approach to solving this problem is to see what value of y makes the expression 23 – 5y equal to 0:

23 – 5y = 0

23 = 5y

y = 4.6

However, we know that y must be an integer, so we round y = 4.6 to y = 5.

We then plug the value 5 for y into the absolute value equation, as was done earlier, yielding the same answer of 2, which is answer choice B.
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