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Difference between the smallest and greatest possible integer value of

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KarunMendiratta

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Difference between the smallest and greatest possible integer value of [#permalink]

Updated on: 22 Aug 2024, 22:33

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A

B

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D

Question Stats:

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$m^2 < 225$ and

$n − m= −10$

Quantity A	Quantity B
Absolute difference between the smallest and greatest possible integer value of $3m + 2n$	140

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Official Answer

A

Originally posted by KarunMendiratta on 19 Aug 2021, 05:41.
Last edited by Carcass on 22 Aug 2024, 22:33, edited 1 time in total.

Fixed OA

motion2020

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

19 Aug 2021, 08:42

2

$|m|<15$ and

$m=n+10$

$|n+10|<15$

$m<15$ and

$m>-15$

$n+10<15$ and

$n+10>-15$

$n<5$ and

$n>-25$ --->

$-25<n<5$ ALSO

$-15<m<15$

$-45-50<3m+2n<45+10$ --->

$-95<3m+2n<55$

the required is

$|-95-55|=150$

IMO, answer is A

KarunMendiratta wrote:

$m^2 < 225$ and

$n − m= −10$

Quantity A	Quantity B
Absolute difference between the smallest and greatest possible integer value of $3m + 2n$	140

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

KarunMendiratta

Retired Moderator

Joined: 16 Apr 2020

Status:Founder & Quant Trainer

Affiliations: Prepster Education

Posts: 1546

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Location: India

WE:Education (Education)

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

19 Aug 2021, 09:29

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motion2020 wrote:

$|m|<15$ and

$m=n+10$

$|n+10|<15$

$m<15$ and

$m>-15$

$n+10<15$ and

$n+10>-15$

$n<5$ and

$n>-25$ --->

$-25<n<5$ ALSO

$-15<m<15$

$-45-50<3m+2n<45+10$ ---> \(-95<3m+2n<55\)

the required is

$|-95-55|=150$

IMO, answer is A

KarunMendiratta wrote:

$m^2 < 225$ and

$n − m= −10$

Quantity A	Quantity B
Absolute difference between the smallest and greatest possible integer value of $3m + 2n$	140

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Good Explanation but we cannot use 55 and -95 as per the inequality
So, The difference has to be |-94 - (54)| = |-148| = 148

motion2020

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

19 Aug 2021, 09:43

1

ah, yes
I forgot to return values for the range extremes

KarunMendiratta wrote:

motion2020 wrote:

$|m|<15$ and

$m=n+10$

$|n+10|<15$

$m<15$ and

$m>-15$

$n+10<15$ and

$n+10>-15$

$n<5$ and

$n>-25$ --->

$-25<n<5$ ALSO

$-15<m<15$

$-45-50<3m+2n<45+10$ ---> \(-95<3m+2n<55\)

the required is

$|-95-55|=150$

IMO, answer is A

KarunMendiratta wrote:

$m^2 < 225$ and

$n − m= −10$

Quantity A	Quantity B
Absolute difference between the smallest and greatest possible integer value of $3m + 2n$	140

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Good Explanation but we cannot use 55 and -95 as per the inequality
So, The difference has to be |-94 - (54)| = |-148| = 148

test01

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

18 Oct 2023, 07:56

KarunMendiratta wrote:

motion2020 wrote:

$|m|<15$ and

$m=n+10$

$|n+10|<15$

$m<15$ and

$m>-15$

$n+10<15$ and

$n+10>-15$

$n<5$ and

$n>-25$ --->

$-25<n<5$ ALSO

$-15<m<15$

$-45-50<3m+2n<45+10$ ---> \(-95<3m+2n<55\)

the required is

$|-95-55|=150$

IMO, answer is A

KarunMendiratta wrote:

$m^2 < 225$ and

$n − m= −10$

Quantity A	Quantity B
Absolute difference between the smallest and greatest possible integer value of $3m + 2n$	140

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Good Explanation but we cannot use 55 and -95 as per the inequality
So, The difference has to be |-94 - (54)| = |-148| = 148

does this mean that the answer is A?

Carcass

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

18 Oct 2023, 09:01

1

Expert Reply

ah, yes
I forgot to return values for the range extremes

By motion above

The answer is B

shrvan7h

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

22 Aug 2024, 15:36

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Carcass, please change the ans to A.

Carcass

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

22 Aug 2024, 22:34

Expert Reply

Fixed sir.

Thank you

sub24

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

23 Oct 2024, 08:55

Pls explain why not C.
if i proceed like n=m-10

and |m|<15

so 3m+2n = 3m+2(m-10)=5m-20
when m=-14 least negative=> 5m-20=-90
m=14 most positive=>5m-20=50
abs diffrnc 140.

what am i missing here? pls guide

Carcass

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

23 Oct 2024, 10:45

1

Expert Reply

This question is about algebraic manipulations with inequalities.

From

$n - m = -10$ it follows that

$n=m-10$ . Thus,

$3m + 2n=3m+2(m-10)=5m-20$ . So, we need to find the difference between the smallest possible integer value of

$5m-20$ and the greatest possible integer value of

$5m-20$ .

Now, lets' work on

$m^2 < 225$ :

Take the square root from both sides:

$|m|<15$ ;

Get rid of the modulus sign:

$-15<m < 15$ ;
Multiply all three parts by 5:

$-75< 5m < 75$ ;
Subtract 20 from all three parts:

$-95< 5m -20< 55$ ;
From

$-95< 5m -20< 55$ it follows that the smallest possible integer value of

$5m-20$ is -94 and the greatest possible integer value of

$5m-20$ is 54.
Therefore, the difference is -94 - 54= -148.

A is the answer

sub24

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Re: Difference between the smallest and greatest possible integer value of [#permalink]

25 Oct 2024, 21:47

Carcass wrote:

This question is about algebraic manipulations with inequalities.

From

$n - m = -10$ it follows that

$n=m-10$ . Thus,

$3m + 2n=3m+2(m-10)=5m-20$ . So, we need to find the difference between the smallest possible integer value of

$5m-20$ and the greatest possible integer value of

$5m-20$ .

Now, lets' work on

$m^2 < 225$ :

Take the square root from both sides:

$|m|<15$ ;

Get rid of the modulus sign:

$-15<m < 15$ ;
Multiply all three parts by 5:

$-75< 5m < 75$ ;
Subtract 20 from all three parts:

$-95< 5m -20< 55$ ;
From

$-95< 5m -20< 55$ it follows that the smallest possible integer value of

$5m-20$ is -94 and the greatest possible integer value of

$5m-20$ is 54.
Therefore, the difference is -94 - 54= -148.

A is the answer

Thank you for the explanation. So i understood i was implicitly considering m as an integer. thats where i went wrong. thank you for explaining like this.

gmatclubot

Re: Difference between the smallest and greatest possible integer value of [#permalink]

25 Oct 2024, 21:47

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