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In a set of three numbers,the difference between the largest and the

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In a set of three numbers,the difference between the largest and the  [#permalink]

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New post 26 Sep 2015, 12:03
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In a set of three numbers,the difference between the largest and the second largest numbers is added to the smallest number.The average of the largest,second largest and the new number formed exceeds the average of the original three numbers by 5.The largest number exceeds the second largest number by how much ?
A) 5
B) 10
C) 15
D) 30
E) 60
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In a set of three numbers,the difference between the largest and the  [#permalink]

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New post 26 Sep 2015, 17:18
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capsicumgirl wrote:
In a set of three numbers,the difference between the largest and the second largest numbers is added to the smallest number.The average of the largest,second largest and the new number formed exceeds the average of the original three numbers by 5.The largest number exceeds the second largest number by how much ?
A) 5
B) 10
C) 15
D) 30
E) 60


Let A,B and C be the three numbers where A<B<C
It is given that the difference between the largest and the second largest numbers is added to the smallest number i.e A+(C-B)
The average of the largest,second largest and the new number formed exceeds the average of the original three numbers by 5.

or \(\frac{B+C+A+(C-B)}{3}=\frac{A+B+C}{3}+5\)

or \(\frac{A+2C}{3}=\frac{A+B+C+15}{3}\)

or \(A+2C=A+B+C+15\)
or \(C=B+15\)
So, largest number exceeds the second largest number by 15

Answer:-C
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Re: In a set of three numbers,the difference between the largest and the  [#permalink]

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New post 26 Sep 2015, 23:44
Answer is 15. Apart from the usual calculation part, is there any Avergages concept that could be used here to save time on calculations
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In a set of three numbers,the difference between the largest and the  [#permalink]

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New post 27 Sep 2015, 00:28
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hdwnkr wrote:
Answer is 15. Apart from the usual calculation part, is there any Avergages concept that could be used here to save time on calculations


Hi,
Let the numbers in increasing order be A<B<C...
since the new number(N) increase the average of new set of numbers by 5 after replacing the smallest number,A,
the new number,N, exceeds the smallest,A, by 3*5=15 or N=15+A..(1)
and what is the new number,N,---- C-B (diff in the largest and second largest)+A...(2)...
from (1) & (2) C-B=15... required answer
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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Re: In a set of three numbers,the difference between the largest and the  [#permalink]

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New post 09 Mar 2019, 23:51
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Re: In a set of three numbers,the difference between the largest and the   [#permalink] 09 Mar 2019, 23:51
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