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least possible value of |23 - 5y|

This topic has 10 expert replies and 1 member reply

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rsarashi Master | Next Rank: 500 Posts Default Avatar
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least possible value of |23 - 5y|

Post Sun Feb 05, 2017 9:35 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post Mon Feb 06, 2017 4:39 am
    Quote:
    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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    Post Mon Feb 06, 2017 7:07 am
    Quote:
    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

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

    Thanked by: rsarashi
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    Post Mon Feb 06, 2017 9:28 am
    Quote:
    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:

    Quote:
    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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    Post Mon Feb 06, 2017 9:38 am
    GMATGuruNY wrote:
    Quote:
    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:

    Quote:
    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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    Post 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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    Post 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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    Post 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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    Post 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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    Post 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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    Post 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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    Post 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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