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If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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24 Jun 2014, 06:47
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If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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SOLUTIONIf \(m^2 < 225\) and \(n  m = 10\), what is the difference between the smallest possible integer value of \(3m + 2n\) and the greatest possible integer value of \(3m + 2n\)?A. 190 B. 188 C. 150 D. 148 E. 40 This question is about algebraic manipulations with inequalities. From \(n  m = 10\) it follows that \(n=m10\). Thus, \(3m + 2n=3m+2(m10)=5m20\). So, we need to find the difference between the smallest possible integer value of \(5m20\) and the greatest possible integer value of \(5m20\). 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 \(5m20\) is 94 and the greatest possible integer value of \(5m20\) is 54. Therefore, the difference is 94  54= 148. Answer: D. Try NEW inequalities DS question.
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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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24 Jun 2014, 10:22
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Hi, i am getting 140 as the answer(none of the options:(). My calculations are as below: min value of m=14,thus n=24 max value of m=14,thus n=4
Smallest 3m+2n=3(14)+2(24)=4248=90 Largest 3m+2n=3(14)+2(4)=50
Diff between smallest and largest=9050=140
Can you please help ,what is wrong in my calculations.



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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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24 Jun 2014, 11:00
Not sure about the answer, but wanna try.
m^2<225 => m<15
nm=10 => m=n+10
As far as it is not mentioned that "m" and "n" should be integers => m=14,5
Calculating max value: 14,5=n+10 => n=4,5 3m+2n = 43,5+9=52,5 =>52 (as the smallest integer value)
Calculating min value: 14,5=n+10 => n=24,5 3m+2n = 43,549=92,5 => 93 (as the smallest integer value)
Difference "minmax" = 9352=145
Hence "C"



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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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24 Jun 2014, 11:36



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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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25 Jun 2014, 02:51



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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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25 Jun 2014, 10:47
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I get 148.
15 < m <15 Also, 3m+2n= 5m20, since n=m10 For m=15, which isn't an option, we get 5m20= 95. But the exact previous number 94 is an option since m doesn't have to be an intenger. So that is our minimum Similarly, for m=+15, which is not an option, 5m20= +55. But the exact previous number +54 is an option. So this is our maximum.
So minmax = 94 54= 148.



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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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25 Jun 2014, 21:27
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Answer = D = 14894  54 = 148 \(m^2 < 225\) m can be anything from 14.9 to + 14.9 Kindly refer chart below for detailed calculation:
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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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29 Jun 2014, 12:15
SOLUTIONIf \(m^2 < 225\) and \(n  m = 10\), what is the difference between the smallest possible integer value of \(3m + 2n\) and the greatest possible integer value of \(3m + 2n\)?A. 190 B. 188 C. 150 D. 148 E. 40 This question is about algebraic manipulations with inequalities. From \(n  m = 10\) it follows that \(n=m10\). Thus, \(3m + 2n=3m+2(m10)=5m20\). So, we need to find the difference between the smallest possible integer value of \(5m20\) and the greatest possible integer value of \(5m20\). 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 \(5m20\) is 94 and the greatest possible integer value of \(5m20\) is 54. Therefore, the difference is 94  54= 148. Answer: D. Kudos points given to correct solutions above.Try NEW inequalities DS question.
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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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10 Jul 2014, 11:16
Bunuel wrote: ankushbassi wrote: Hi, i am getting 140 as the answer(none of the options:(). My calculations are as below: min value of m=14,thus n=24 max value of m=14,thus n=4
Smallest 3m+2n=3(14)+2(24)=4248=90 Largest 3m+2n=3(14)+2(4)=50
Diff between smallest and largest=9050=140
Can you please help ,what is wrong in my calculations. Solution for this question will be published by the end of the week. By the way this question is a part of our NEW PROJECT. Hi Bunuel.. I did also the same way above mentioned and got 140. However I did understand the method which you have explained in the discussion but still want to clarify about the method which has been explained above... Can you pls explain...whats wrong with above method??? Thanks in advance



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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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10 Jul 2014, 11:21
GGMAT760 wrote: Bunuel wrote: ankushbassi wrote: Hi, i am getting 140 as the answer(none of the options:(). My calculations are as below: min value of m=14,thus n=24 max value of m=14,thus n=4
Smallest 3m+2n=3(14)+2(24)=4248=90 Largest 3m+2n=3(14)+2(4)=50
Diff between smallest and largest=9050=140
Can you please help ,what is wrong in my calculations. Solution for this question will be published by the end of the week. By the way this question is a part of our NEW PROJECT. Hi Bunuel.. I did also the same way above mentioned and got 140. However I did understand the method which you have explained in the discussion but still want to clarify about the method which has been explained above... Can you pls explain...whats wrong with above method??? Thanks in advance We are NOT told that m is an integer, hence from 15<m<15 saying that the minimum value of m is 14 and the maximum value of m is 14 is wrong.
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Re: If m^2 < 225 and n  m = 10, what is the sum f the smallest [#permalink]
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14 Aug 2014, 23:30
its D 148
I did it in a following way
here n  m = 10
m = n+10
then 3m +2n = 3(n+10)+2n = 5n+30
so we need to findout max and minimum values of 5n+30
m^2 <225
put m= n+10 (n+10)^2 <225
solving this equation becomes n^2 +20n 125 <0
(n+25)(n5) <0
so here we have three ranges
n <25 25 <n <5 n>5
taking n>5 it becomes >0 so sequence will be ++
now n will be between 25 <n<5
taking n= 4.9 . 5n+30 will have value 54.5 so integer value is 54 taking n = 24.9. 5n+30 will become 124.5+30 = 94.5 = 94(integer value)
so difference is 54  (94) = 148



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