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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
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(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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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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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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hamm0
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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
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.
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
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.
General Discussion
Bunuel
\(|23-5y|\) 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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Love GMAT Quant questions and running.
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
(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
Posts: 62
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
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
EMPOWERgmatRichC
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Expert reply
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).
GMAT assassins aren't born, they're made,
Rich
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).
GMAT assassins aren't born, they're made,
Rich
ScottTargetTestPrep
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Joined: 14 Oct 2015
Last visit: 16 Sep 2026
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Expert reply
Posts: 22,742
Bunuel
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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Bunuel
Another approach is to check each answer choice to see if it COULD be the smallest possible value of |23 - 5y|
Let's start with answer choice A, since it is the smallest answer.
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
Answer: B
sujoykrdatta
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Tutor
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Last visit: 23 Aug 2026
Posts: 598
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 750 Q51 V39
Expert reply
GMAT 1: 750 Q51 V39
Posts: 598
Bunuel
We need to make (23 - 5y) as close to '0' as possible
23 - 5y = 0
=> y = 4.6
However, y is an integer
Thus, we need to work with y = 4 or 5, whichever makes 23 - 5y closer to '0'
For y = 4: 23 - 5y = 3 => |23 - 5y| = 3
For y = 5: 23 - 5y = -2 => |23 - 5y| = 2
Thus, the minimum value of |23 - 5y| = 2
Answer B
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GMATCoachBen
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Expert reply
Bunuel
First, make sure we understand what it's asking for — "the least possible value of |23 - 5y|"
In general, it can be helpful to visualize |A - B| as "the distance between A and B on a number line". Therefore, our next step is to figure out the value of "5y" that is closest to "23" (see below for illustration).
Also, note that the absolute value cannot be negative. So, we are looking for the value of |23 - 5y| that is closest to zero.
We could make a full table, but the easiest way is to think of multiples of 5 that are closest to 23 ("5y" must be a multiple of 5, since y is an integer).
What happens if we plug in "20" and "25" for the "5y"?
|23 - 20| = 3
|23 - 25| = |-2| = 2
Key Habit for Trap Avoidance: We must always read carefully and double-check what it's asking for before confirming our answer.
18% of people get trapped by "E" on this question, because the correct value for "y" is indeed "5". However, the question asks for "the least possible value of |23 - 5y|".
Attachments
2021-11-11 20_24_13-Number line diagram - OneNote.png [ 36.37 KiB | Viewed 34075 times ]
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Given that y is an integer and we need to find the least possible value of |23 - 5y|
Now, |23 - 5y| is Absolute Value/Modulus of a number and we know that Absolute Value of any number is always ≥ 0
=> Minimum value of |23 - 5y| will be close to zero
=> 23 - 5y should be close to 0
Since, y is an integer so let's take value of y in such a way that 23 - 5y is closer to 0
For y = 4
=> 23 - 5y = 23 - 5*4 = 3
For y = 5
=> 23 - 5y = 23 - 5*5 = -2
-2 is closer to 0 than 3
=> Minimum value of |23 - 5y| = |-2| = 2 (when y = 5)
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
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Now, |23 - 5y| is Absolute Value/Modulus of a number and we know that Absolute Value of any number is always ≥ 0
=> Minimum value of |23 - 5y| will be close to zero
=> 23 - 5y should be close to 0
Since, y is an integer so let's take value of y in such a way that 23 - 5y is closer to 0
For y = 4
=> 23 - 5y = 23 - 5*4 = 3
For y = 5
=> 23 - 5y = 23 - 5*5 = -2
-2 is closer to 0 than 3
=> Minimum value of |23 - 5y| = |-2| = 2 (when y = 5)
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
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GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
If y is an integer, then the least possible value of |23 - 5y| is
Let x = |23 - 5y|, we know that due to the modulus operator, the minimum value of x could be zero
=> x= 0
=> |23-5y| = 0
=> 23-5y=0
=> y= 23/5 or 4.6 but because y is any integer, it can not take the value of 4.6.
Therefore, we will do hit and trial for the minimum value of x with keeping y=4 and y=5
Case I y=4
=> x = |23 - 5*4| = |23 - 20| = 3
Case II y=5
=> x = |23 - 5*5| = |23 - 25| = 2
Hence the minimum value is 2
Answer B
Let x = |23 - 5y|, we know that due to the modulus operator, the minimum value of x could be zero
=> x= 0
=> |23-5y| = 0
=> 23-5y=0
=> y= 23/5 or 4.6 but because y is any integer, it can not take the value of 4.6.
Therefore, we will do hit and trial for the minimum value of x with keeping y=4 and y=5
Case I y=4
=> x = |23 - 5*4| = |23 - 20| = 3
Case II y=5
=> x = |23 - 5*5| = |23 - 25| = 2
Hence the minimum value is 2
Answer B
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