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16 Sep 2014, 01:46
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Official Solution:If \(m^2 < 225\) 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
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Re: M3019 [#permalink]
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25 May 2015, 00:02
Hello,
For the below solution is it also possible to directly put the least possible value of m(14) and the greatest possible value of m(14) in the equation( 5m20)?
Regards, Mahuya
If \(m^2 < 225\) 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[/quote]



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25 May 2015, 01:53



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Re: M3019 [#permalink]
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28 Sep 2016, 08:52
Bunuel wrote: mahuya78 wrote: Hello,
For the below solution is it also possible to directly put the least possible value of m(14) and the greatest possible value of m(14) in the equation( 5m20)?
Regards, Mahuya 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. That is exactly where I got stuck and ended up guessing the answer to be the closest number I got with max = 14 min = 14. Gotta read the question more carefully!



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Re M3019 [#permalink]
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02 Oct 2016, 03:13
I think this is a highquality question and I agree with explanation.



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Re: M3019 [#permalink]
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16 Oct 2016, 19:15
Hi, I am a little bit confused as for the meaning of "the difference between x and y". In this question, the wording has not effect on the solution since all the answers are negative. However, it may cause trouble in future problems. That being said, does "the difference between x and y" get translated to "xy" or to "yx"? Thanks for your help!  Need Kudos
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Re: M3019 [#permalink]
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02 Nov 2016, 00:04
is there any other way to do this



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02 Nov 2016, 02:15



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Re M3019 [#permalink]
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05 Nov 2016, 19:05
I think this is a highquality question and I agree with explanation.



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Re: M3019 [#permalink]
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16 Apr 2017, 00:34
Hi Experts,
I have a question on this. The mentioned answer will work only when m =+15, which is not possible as m2 has to be lass that 225. Also this question does mention that 3m+2n should be greatest and minimum INTEGER. Should it make any difference in the answer?



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16 Apr 2017, 01:32



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Re: M3019 [#permalink]
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02 May 2017, 12:18
phanikrishna wrote: is there any other way to do this I solved the equation for \(m=15\) and \(m=15\) and just used the next smaller/larger integer. \(m=15 > 5m20=55 > value=54\) \(m=15 > 5m20=95 > value=94\) \(difference=148\)



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Re: M3019 [#permalink]
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16 Jun 2017, 21:47
I solved it like this:
Given information : Square(m) < 225 => 15<m<15  (1) & nm=10 (2)
Manipulation starts : We will fit n in the inequality using (1) & (2) as that is the demand of the question. Replace m in (1) with n10 from (2), new equation will be 25<n<5  (3)
Now, simply make (1) & (3) in the form of equation as asked in the question i.e. 3m+2n 45<3m<45 (Multiplying (1) by 3) 50<2n<10 (Multiplying (3) by 2)
Add above two equations , we will get 95<3m+2n<55
Remember integer criteria is applicable on 3m+2n & not on m & n separately.
From above equation, Min integer = 94 & Max integer is 54 Difference = 9454 = 148



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Re M3019 [#permalink]
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05 Sep 2017, 04:29
What if we take m = 14 , n = 24 and m = 14 , n = 4 and try to find the answer?



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05 Sep 2017, 04:36



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30 Oct 2017, 23:59
I think this is a highquality question and I agree with explanation.



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Re: M3019 [#permalink]
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13 Feb 2018, 07:07
I agree with the solution. But, what's wrong with the following:
15<m<15 45<3m<45 add 2n on all sides 2n45<3m+2n<2n+45
the least number will be 2n44 and the greatest number will be 2n+44. When you subtract greatest from the least, you will get 88. What is the role of n in this? Am I missing something?



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Re: M3019 [#permalink]
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13 Feb 2018, 07:09
Thanks for explaining so nicely










