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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]

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01 Oct 2012, 04:58
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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

Practice Questions
Question: 51
Page: 159
Difficulty: 600
[Reveal] Spoiler: OA

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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, 04:58
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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: $$|23-25|=2$$.

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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, 05:10
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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]

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01 Oct 2012, 08:10
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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

Practice Questions
Question: 51
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 $$|23-25|=2$$.

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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
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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

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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, 06:18
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]

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02 Oct 2012, 12:31
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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]

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04 Oct 2012, 00:59
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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 $$|2| = 2$$

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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

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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

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

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26 May 2015, 10:21
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Hi Psy881212,

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).

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

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30 May 2016, 05:21
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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.

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

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30 May 2016, 09:35
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

Practice Questions
Question: 51
Page: 159
Difficulty: 600

Plug in values of y

1. If y = 1 |23 - 5y| = 18

2. If y = 2 |23 - 5y| = 13

3. If y = 3 |23 - 5y| = 8

4. If y = 4 |23 - 5y| = 3

5. If y = 6 |23 - 5y| = 7

6. If y = 7 |23 - 5y| = 12

Thus you find the least value of |23 - 5y| comes as 3 only when y = 4

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

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02 Jun 2016, 00:42
Abhishek009 wrote:
Plug in values of y

1. If y = 1 |23 - 5y| = 18

2. If y = 2 |23 - 5y| = 13

3. If y = 3 |23 - 5y| = 8

4. If y = 4 |23 - 5y| = 3

5. If y = 6 |23 - 5y| = 7

6. If y = 7 |23 - 5y| = 12

Thus you find the least value of |23 - 5y| comes as 3 only when y = 4

Hi Abhishek, I think you missed checking the value of the expression when y = 5

If y = 5, then

|23 - 5y| = |23 - 25| = |-2| = 2

So, 2 seems to be the least value (when y = 5)

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

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02 Jun 2016, 09:55
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

Practice Questions
Question: 51
Page: 159
Difficulty: 600

The value will be positive.

l23- 5*5l = 2

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04 Sep 2016, 08:56
Manonamission 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

Plug in some values to test answer will be (B)

Let y = 6

|23-5y| => |23-30| = 7

Let y = 5

|23-5y| => |23-25| = 2

Let y = 4

|23-5y| => |23-25| = 3
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Re: If y is an integer, then the least possible value of |23-5| [#permalink]

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07 Feb 2017, 09:38
Top Contributor
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

Another approach is to check each answer choice to see if it COULD be the smallest possible value of |23 - 5y|

A) 1
Is it possible that |23 - 5y| = 1 if y MUST BE AN INTEGER?
Let's solve it.
If |23 - 5y| = 1, then 23 - 5y = 1 or 23 - 5y = -1

Take 23 - 5y = 1 and subtract 23 from both sides to get: -5y = -22
Solve to get: y = 4.4 NOT an integer

Take 23 - 5y = -1 and subtract 23 from both sides to get: -5y = -24
Solve to get: y = 4.8 NOT an integer

So, if y is an INTEGER, it's IMPOSSIBLE for |23 - 5y| to equal 1
ELIMINATE A

B) 2
Is it possible that |23 - 5y| = 2 if y MUST BE AN INTEGER?
Let's solve it.
If |23 - 5y| = 2, then 23 - 5y = 2 or 23 - 5y = -2

Take 23 - 5y = 2 and subtract 23 from both sides to get: -5y = -21
Solve to get: y = 4.2 NOT an integer

Take 23 - 5y = -2 and subtract 23 from both sides to get: -5y = -25
Solve to get: y = 5 AN INTEGER

AHA! It IS POSSIBLE for |23 - 5y| to equal 2

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

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31 Aug 2017, 17:59
hi Bunuel Engr2012

I understood post of calculating distance from number line for |x-a|
But I wanted to know flaw in below approach:

when some expression≤0 then |some expression|=−(some expression). For example: |−5|=−(−5) = 5

Based on this understanding , I approached the problem that if I need to find least possible value of |23-5y|
I need to find least negative value. In other words 5y should be as high as possible so that 23-5y in still lower.
Meaning if y is maximum say 5 among given choices then 23-5y = -2 which is lowest among answer choices available.

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

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14 Sep 2017, 22:41
5 multiples always ends with 0 or 5, so difference with 3( last digit of 23) will
0-3 = 3
5-3 = 2
since there is MOD||
so here least value should be 2
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Re: If y is an integer, then the least possible value of |23-5|   [#permalink] 14 Sep 2017, 22:41
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