Last visit was: 23 Jul 2024, 02:01 It is currently 23 Jul 2024, 02:01
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Kudos
Tags:
Difficulty: 505-555 Level,   Absolute Values,   Min-Max Problems,                           
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94545
Own Kudos [?]: 643165 [231]
Given Kudos: 86728
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94545
Own Kudos [?]: 643165 [73]
Given Kudos: 86728
Send PM
User avatar
Senior Manager
Senior Manager
Joined: 31 Oct 2011
Posts: 474
Own Kudos [?]: 278 [31]
Given Kudos: 57
GMAT 1: 690 Q45 V40
WE:Asset Management (Mutual Funds and Brokerage)
Send PM
General Discussion
Senior Manager
Senior Manager
Joined: 24 Aug 2009
Posts: 388
Own Kudos [?]: 2298 [5]
Given Kudos: 275
Concentration: Finance
Schools:Harvard, Columbia, Stern, Booth, LSB,
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
3
Kudos
2
Bookmarks
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
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19176
Own Kudos [?]: 22696 [4]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
2
Kudos
2
Bookmarks
Expert Reply
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.
User avatar
Director
Director
Joined: 22 Mar 2011
Posts: 518
Own Kudos [?]: 2162 [3]
Given Kudos: 43
WE:Science (Education)
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
2
Kudos
1
Bookmarks
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


GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


\(|23-5y|\) 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.
Manager
Manager
Joined: 26 Jul 2011
Posts: 65
Own Kudos [?]: 281 [3]
Given Kudos: 20
Location: India
WE:Marketing (Manufacturing)
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
2
Kudos
1
Bookmarks
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
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11793 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
2
Kudos
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 Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30852 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
1
Bookmarks
Expert Reply
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|

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
Tutor
Joined: 26 Jun 2014
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
Posts: 450
Own Kudos [?]: 810 [1]
Given Kudos: 8
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
1
Kudos
Expert Reply
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



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
Tutor
Joined: 21 Mar 2017
Status:Professional GMAT Trainer
Affiliations: GMAT Coach
Posts: 429
Own Kudos [?]: 1200 [1]
Given Kudos: 204
Location: United States (WA)
GMAT 1: 760 Q50 V44
GMAT 2: 770 Q51 V44
GMAT 3: 770 Q50 V44
GMAT 4: 770 Q50 V45 (Online)
GMAT 5: 780 Q51 V48
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
1
Kudos
Expert Reply
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
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
2021-11-11 20_24_13-Number line diagram - OneNote.png [ 36.37 KiB | Viewed 15265 times ]

avatar
Intern
Intern
Joined: 23 May 2015
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
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
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1804
Own Kudos [?]: 2146 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
Expert Reply
Top Contributor
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

Senior Manager
Senior Manager
Joined: 11 Sep 2022
Posts: 497
Own Kudos [?]: 178 [0]
Given Kudos: 2
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
Send PM
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
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
GMAT Club Bot
Re: If y is an integer, then the least possible value of |23 - 5y| is [#permalink]
Moderator:
Math Expert
94544 posts