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In a set of three numbers,the difference between the largest and the 26 Sep 2015, 12:03
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C
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82% (02:05) correct 18% (02:15) wrong based on 262 sessions

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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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C
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In a set of three numbers,the difference between the largest and the 26 Sep 2015, 17:18
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capsicumgirl
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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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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In a set of three numbers,the difference between the largest and the 26 Sep 2015, 23:44
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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 27 Sep 2015, 00:28
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hdwnkr
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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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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In a set of three numbers,the difference between the largest and the 22 Jan 2026, 23:28
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Instead of setting up equations, use this key principle: When you change a number in a set, the change in average equals the total change divided by the number of elements.

Here's what happens:
- Original set: L, M, S
- New set: L, M, S + (L - M)

The only change is that S becomes S + (L - M), which means we're adding (L - M) to our total sum.

Therefore:
Change in average = Total change ÷ Number of elements
5 = (L - M) ÷ 3
(L - M) = 15

Answer: 15

Time-saving tip: Whenever a problem involves changing one element and finding the new average, just focus on what's being added/removed to the total, then divide by the number of elements. This saves you from setting up and solving lengthy equations!

This concept works because averages are just totals divided by count - so any change to the total directly affects the average in a proportional way.

hdwnkr
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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