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In a certain game, each player scores either 2 points or 5 points. If
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03 Apr 2015, 05:05
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Re: In a certain game, each player scores either 2 points or 5 points. If
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03 Apr 2015, 05:34
is it B?
multiple of 2 always even so we need multiples of 5 ending with 0.
i see only one case in which the difference can be minimizd
5*8 +2*5=50 85=3



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In a certain game, each player scores either 2 points or 5 points. If
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Updated on: 05 Apr 2015, 01:11
Bunuel wrote: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m?
A. 1 B. 3 C. 5 D. 7 E. 9
Kudos for a correct solution. We have equation 2n + 5m = 50 We have factor 2 in first number and we have factor 5 in second number. LCM(2, 5) = 10 So we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n  m = 10  6 = 4 And there is some mistake in my way of thinking because we don't have such answer ) If we change the task and will seek for difference between m and n than minimal result will be 8  5 = 3 And answer B
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Originally posted by Harley1980 on 03 Apr 2015, 05:38.
Last edited by Harley1980 on 05 Apr 2015, 01:11, edited 1 time in total.



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Re: In a certain game, each player scores either 2 points or 5 points. If
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03 Apr 2015, 05:39
hsbinfy wrote: is it B?
multiple of 2 always even so we need multiples of 5 ending with 0.
i see only one case in which the difference can be minimizd
5*8 +2*5=50 85=3 You've made final calculation as m  n But question asks about n  m
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Re: In a certain game, each player scores either 2 points or 5 points. If
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03 Apr 2015, 09:37
Bunuel wrote: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m?
A. 1 B. 3 C. 5 D. 7 E. 9
Kudos for a correct solution. 2n+5m=50 Now m will always be even. m 2 4 6 8 n 20 15 10 5 Lowest nm=3 Answer: B



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Re: In a certain game, each player scores either 2 points or 5 points. If
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04 Apr 2015, 10:27
2n+5m=50 I put some values here , i put m=6 , so n=10 .. difference is 4 so options C,D,E are out. lets increase value of m now , let m=7 , but n is noninteger , let m=8 so n =5 .. differnce is 3. also looking at equation , differnce of 1 is not possible So answer is option B =3
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Re: In a certain game, each player scores either 2 points or 5 points. If
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05 Apr 2015, 00:40
I think answer is 'A' The question is asking the difference between n and m and NOT the difference between scores of n and m. 2n+5m=50 2*5+5*4=50 54=1 I hope i am thinking right. Please suggest
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Re: In a certain game, each player scores either 2 points or 5 points. If
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05 Apr 2015, 00:58
2n+5m=50(n+m)
2n+5m=50n+50m
45m=48n so, the lowest difference will be 3 if you substitute 1 for m and n. Is it right way?
Thanks.



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In a certain game, each player scores either 2 points or 5 points. If
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05 Apr 2015, 01:02
Divyadisha wrote: I think answer is 'A'
The question is asking the difference between n and m and NOT the difference between scores of n and m.
2n+5m=50 2*5+5*4=50 54=1
I hope i am thinking right. Please suggest 2*5+5*4 is not equal to 50 2*5+5*4 = 30
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Re: In a certain game, each player scores either 2 points or 5 points. If
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05 Apr 2015, 01:07
Chimka wrote: 2n+5m=50(n+m)
2n+5m=50n+50m
45m=48n so, the lowest difference will be 3 if you substitute 1 for m and n. Is it right way?
Thanks. You make mistake in the first equation 2n+5m=50n+50m Tasks says that Quote: If n players score 2 points and m players score 5 points, and the total number of points scored is 50 so 2n + 5m = 50 points Your equation shows variant if each player score 50 points 50n + 50m scores
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Re: In a certain game, each player scores either 2 points or 5 points. If
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05 Apr 2015, 01:07
2n+3m=50; least positive nm=?
1. 2.10+5.6=>nm=4 2. 2.5+5.8=>nm=3
Hence answer is B
Thanks,



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In a certain game, each player scores either 2 points or 5 points. If
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05 Apr 2015, 01:13
Harley1980 wrote: Chimka wrote: 2n+5m=50(n+m)
2n+5m=50n+50m
45m=48n so, the lowest difference will be 3 if you substitute 1 for m and n. Is it right way?
Thanks. You make mistake in the first equation 2n+5m=50n+50m Tasks says that Quote: If n players score 2 points and m players score 5 points, and the total number of points scored is 50 so 2n + 5m = 50 points Your equation shows variant if each player score 50 points 50n + 50m scores you're right. Thanks. I got it now



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Re: In a certain game, each player scores either 2 points or 5 points. If
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05 Apr 2015, 01:52
Bunuel wrote: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m?
A. 1 B. 3 C. 5 D. 7 E. 9
Kudos for a correct solution. Required equation is 2n+5m=50 Different combinations of n and m are 0,10 25,0 5,8 10,6 15,4 20,2 Least difference =85=3. Answer=B



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Re: In a certain game, each player scores either 2 points or 5 points. If
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06 Apr 2015, 06:40
Bunuel wrote: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m?
A. 1 B. 3 C. 5 D. 7 E. 9
Kudos for a correct solution. KAPLAN OFFICIAL SOLUTION:The quickest solution is to pick numbers for n and m. Since n = 1 and m = 1 would amount to 7 points, and since we want to minimize the difference between n and m, and since 50/7 is just a bit more than 7, we'll start with values near 7. The key is to discover what values for n, when multiplied by 2 points, will leave a multiple of 5 as the remaining points. The solution turns out to be 5 for n (10 points), which allows for 8 for m (40 points). That's a total of 50 points, and the positive difference between the two values is only 3. Answer: B.
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Re: In a certain game, each player scores either 2 points or 5 points. If
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27 Apr 2015, 14:44
Harley1980 wrote: Bunuel wrote: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m?
A. 1 B. 3 C. 5 D. 7 E. 9
Kudos for a correct solution. We have equation 2n + 5m = 50 We have factor 2 in first number and we have factor 5 in second number. LCM(2, 5) = 10 So we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n  m = 10  6 = 4 And there is some mistake in my way of thinking because we don't have such answer ) If we change the task and will seek for difference between m and n than minimal result will be 8  5 = 3 And answer B Yes i agree. Does it matter if the question asks about nm or mn? If about nm then answer should be 4. If about mn then 3. Please correct if i am wrong
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Re: In a certain game, each player scores either 2 points or 5 points. If
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27 Apr 2015, 18:24
If we create an equation then it will be 2n+5m=50 . It implies n=(505m)/2 so m is a multiple of 2 . Similarly m=(502n)/5 so n is a multiple of 5 .Minimum difference can be the case when n= 5 and m=2 so difference is 52=3. Note: Number of players is a integer ,so this approach will work fine.
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Re: In a certain game, each player scores either 2 points or 5 points. If
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28 Apr 2015, 00:04
Konstantin1983 wrote: Yes i agree. Does it matter if the question asks about nm or mn? If about nm then answer should be 4. If about mn then 3. Please correct if i am wrong Hello Konstantin1983When we have such formulation "least possible positive difference between n and m" it means both variants \(m  n\) and \(n  m\) And yes, you are right: if question asks exactly about \(n  m\) than answer will be \(4\)
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Re: In a certain game, each player scores either 2 points or 5 points. If
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29 Apr 2015, 05:07
Harley1980 wrote: Konstantin1983 wrote: Yes i agree. Does it matter if the question asks about nm or mn? If about nm then answer should be 4. If about mn then 3. Please correct if i am wrong Hello Konstantin1983When we have such formulation "least possible positive difference between n and m" it means both variants \(m  n\) and \(n  m\) And yes, you are right: if question asks exactly about \(n  m\) than answer will be \(4\) Hello Harley1980! Thanks for reply. Valuable info. I didn't know that. It will help me. Дякую!=))
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Re: In a certain game, each player scores either 2 points or 5 points. If
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29 Apr 2015, 09:44
To fit the equation 2n+5m=50, 2n must be divisible by 10 and the same goes for 5m. For every 2n to be 10, it will take n=5,10,15,20 etc. For every 5m to be 10, it will take m=2,4,6,8 etc. I want to have more 5m's than 2n's and thus start trying with n=10 and m=6, giving me 4 as a difference. I try with n=5 and m=8 (and notice that at this point n is smaller than m and making n smaller further will result in a larger difference) and get the difference of 3. Which was the answer.
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Re: In a certain game, each player scores either 2 points or 5 points. If
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30 Apr 2015, 10:38
Konstantin1983 wrote: Harley1980 wrote: Konstantin1983 wrote: Yes i agree. Does it matter if the question asks about nm or mn? If about nm then answer should be 4. If about mn then 3. Please correct if i am wrong Hello Konstantin1983When we have such formulation "least possible positive difference between n and m" it means both variants \(m  n\) and \(n  m\) And yes, you are right: if question asks exactly about \(n  m\) than answer will be \(4\) Hello Harley1980! Thanks for reply. Valuable info. I didn't know that. It will help me. Дякую!=)) Hello Konstantin1983. I've found another task that exploit this trick with wording "difference between X and Y". Think it'll be interesting for you ) acertainsalesmansyearlyincomeisdeterminedbyabase126533.html
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