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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] New post   Updated on: 22 Aug 2024, 22:33
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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
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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
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motion2020
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   19 Aug 2021, 08:42
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\(|m|<15\) 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
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KarunMendiratta
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   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
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motion2020
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   19 Aug 2021, 09:43
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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
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   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?
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   18 Oct 2023, 09:01
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ah, yes
I forgot to return values for the range extremes

By motion above

The answer is B
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   22 Aug 2024, 15:36
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Carcass, please change the ans to A.
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   22 Aug 2024, 22:34
Expert Reply
Fixed sir.

Thank you
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   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
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   23 Oct 2024, 10:45
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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
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   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.
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Re: Difference between the smallest and greatest possible integer value of [#permalink] New post   23 Feb 2026, 10:34
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