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least possible value of |23 - 5y|

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rsarashi: Master | Next Rank: 500 Posts; Posts: 186; Joined: Sat Dec 24, 2016 12:38 amFollowed by: 3 members; Thanked: 5 times

by rsarashi » Sun Feb 05, 2017 9:35 pm

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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

OAB

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Feb 06, 2017 4:39 am

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

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

|a-b| = the DISTANCE between a and b.
Thus, |23-5y| = the distance between 23 and 5y.
To minimize this distance, the value of 5y must be AS CLOSE AS POSSIBLE to 23.
Options:
If y=4, then 5y = 20.
If y=5, then 5y = 25.
If y=6, then 5y = 30.
The LEAST possible distance between 23 and 5y will be yielded by the option in red.
If y=5, then |23-5y| = |23-25| = 2.

The correct answer is B.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Feb 06, 2017 7:07 am

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 minimize |23-5y|, we need to find the value of y such that 23-5y is as close to zero as possible.

Try some values.
y=3: |23-5y| = |23-15| = |8| = 8
y=4: |23-5y| = |23-20| = |3| = 3
y=5: |23-5y| = |23-25| = |-2| = 2
y=6: |23-5y| = |23-30| = |-7| = 7

The least possible value of |23-5y| is 2.
Answer: B

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Mon Feb 06, 2017 9:38 am, edited 1 time in total.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Feb 06, 2017 9:28 am

We can just test each answer choice:

A) 1. So, |23 - 5y| = |23 - 5(1)| = 18
B) 2. So, |23 - 5y| = |23 - 5(2)| = 13
C) 3. So, |23 - 5y| = |23 - 5(3)| = 8
D) 4. So, |23 - 5y| = |23 - 5(4)| = 3
E) 5. So, |23 - 5y| = |23 - 5(5)| = 2

So, when y = 5, |23 - 5y| = |23 - 5(5)| = |-2| = 2 (and 2 is the smallest possible value of |23 - 5y|)

The question asks, "What is the least possible value of |23 - 5y|?
So, the least possible value of |23 - 5y| is 2 (and this occurs when y = 5)

Can you please clarify the line of reasoning?
The answer choices represent the value of |23-5y|, but in the solution above they are being substituted for y.
If the answer choices were 0, 1, 2, 3, 4, this approach would seem to proceed as follows:

A) 0, So, |23 - 5y| = |23 - 5(0)| = 23
B) 1. So, |23 - 5y| = |23 - 5(1)| = 18
C) 2. So, |23 - 5y| = |23 - 5(2)| = 13
D) 3. So, |23 - 5y| = |23 - 5(3)| = 8
E) 4. So, |23 - 5y| = |23 - 5(4)| = 3

So, when y = 4, |23 - 5y| = |23 - 5(4)| = |3| = 3 (and 3 is the smallest possible value of |23 - 5y|).

However the least possible value of |23-5y| is not 3 but 2.

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by Brent@GMATPrepNow » Mon Feb 06, 2017 9:38 am

GMATGuruNY wrote:
We can just test each answer choice:

A) 1. So, |23 - 5y| = |23 - 5(1)| = 18
B) 2. So, |23 - 5y| = |23 - 5(2)| = 13
C) 3. So, |23 - 5y| = |23 - 5(3)| = 8
D) 4. So, |23 - 5y| = |23 - 5(4)| = 3
E) 5. So, |23 - 5y| = |23 - 5(5)| = 2

So, when y = 5, |23 - 5y| = |23 - 5(5)| = |-2| = 2 (and 2 is the smallest possible value of |23 - 5y|)

The question asks, "What is the least possible value of |23 - 5y|?
So, the least possible value of |23 - 5y| is 2 (and this occurs when y = 5)
Can you please clarify the line of reasoning?
The answer choices represent the value of |23-5y|, but in the solution above they are being substituted for y.
If the answer choices were 0, 1, 2, 3, 4, this approach would seem to proceed as follows:

A) 0, So, |23 - 5y| = |23 - 5(0)| = 23
B) 1. So, |23 - 5y| = |23 - 5(1)| = 18
C) 2. So, |23 - 5y| = |23 - 5(2)| = 13
D) 3. So, |23 - 5y| = |23 - 5(3)| = 8
E) 4. So, |23 - 5y| = |23 - 5(4)| = 3

So, when y = 4, |23 - 5y| = |23 - 5(4)| = |3| = 3 (and 3 is the smallest possible value of |23 - 5y|).
However the least possible value of |23-5y| is not 3 but 2.

YIKES!
I was plugging in the answer choices as though they were the y-values!
Dumb, dumb, dumb!

I have edited my answer and am going back to bed!

Cheers,
Brent

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by Brent@GMATPrepNow » Mon Feb 06, 2017 9:48 am

rsarashi 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

OAB

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

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Feb 09, 2017 4:27 pm

rsarashi 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

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Fri Feb 10, 2017 3:08 am

rsarashi 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

OAB

|23-5y| is always greater than or equal to 0
-> hence 23-5y = 0 -> y = 23/5 = 4+3/5
so we can have minimum value at either y = 4 or 5 since 4<4+3/5 <5
At y = 4, |23-5y| = 3
At y = 5, |23-5y| = 2
So least possible value of |23-5y| = 2. Answer B

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by Jay@ManhattanReview » Fri Feb 10, 2017 8:59 pm

rsarashi 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

OAB

The least possible value of a number in modulus is 0.

Thus, the least possible value of |23 - 5y| = 0 => y = 23/5 = 4.6.

y = 4.6 is not possible since y is an integer, thus y can be either 4 or 5. Since '4.6' is relatively closer to '5' than to '4', |23 - 5y| would be least @y=5.

@y=4, |23 - 5y| = |23 - 5*4| = 3
@y=5, |23 - 5y| = |23 - 5*5| = 2 (Least possible value).

The correct answer: B

Relevant book: Manhattan Review GMAT Number Properties Guide

Hope this helps!

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Feb 17, 2017 1:27 am

One approach is to try to make each answer.

|23 - 5y| = 1

Won't work if 23 - 5y = 1, since y isn't an integer, and won't work if 23 - 5y = -1, since y isn't an integer.

|23 - 5y| = 2

Won't work if 23 - 5y = 2. Will work if 23 - 5y = -2, since this gives us a solution of y = 5.

Since 2 is the smallest answer left, it must be right, and we're done!

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Feb 17, 2017 1:33 am

Another approach is solving conceptually.

|23 - 5y| =

|25 - 5y + 2| =

|5(5 - y) + 2|

5(5 - y) must be some multiple of 5, so we've got (some multiple of 5) + 2. The | |s force the answer to be positive, so our smallest multiple of 5 here will be 0. (If we use a negative multiple of 5, it will become positive due to the absolute value.) That gives us 5(5 - y) = 0, y = 5, and a minimum of |23 - 5*5| or |-2| or 2.

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by [email protected] » Sun Feb 19, 2017 8:33 pm

Hi rsarashi,

When a question involves basic arithmetic, sometimes the fastest way to get to the correct answer is just to use 'brute force' (and it's important to think in those terms - however you choose to approach a question, was "your way" the "fast way?") If you have a pacing issue, then you need to consider how you're handling ALL the questions - including the ones that you answered correctly.

Here, we're told that Y is an INTEGER and we're asked for the LEAST possible value of |23 - 5Y|. Be honest - how long would it really take you to plug in increasing integer values of Y until you found the LEAST value for that inequality? 15 seconds? 20 seconds? So put the pen on the pad and get to work...

Y = 1.... |23 - 5| = 18
Y = 2.... |23 - 10| = 13
Y = 3.... |23 - 15| = 8
Y = 4.... |23 - 20| = 3
Y = 5.... |23 - 25| = 2
Y = 6.... |23 - 30| = 7

Once you increase Y past Y = 5, the value of the absolute value increases, so we can stop working. The least value is 2.

Final Answer: B

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rishab0507: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Tue Jul 16, 2019 4:10 am

by rishab0507 » Sat Sep 07, 2019 8:56 am

Simple fact,
For making something least , make other one as max ,and vice versa.
to get max answer make Y max : It can be 4 or 5 : So let us test 4

|23-5*4| = 3,
|23-5*5 | = |-2| =2

B is answer

although on first go you may seem to get with 3 as an option but do always check 1 factor above and below it, as Mode ques are likely to trick in this.

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