leonswati wrote:If Tom's age is 5 years less than the combined ages of Dick and Harry, what is the sum of the ages of Tom, Dick, and Harry?

1) Two of the people are the same age.
2) Dick is 2 years older than Harry

As per given info: T = ( D + H ) - 5 and we need T + D + H = ?

using statement 1: two of the people have same age: i..e say T = H, => D = 5 but still you can't find the actual age of T or H. if you try T = D or D = H, .. still it's not sufficient.

using statement 2: D = H + 2, that leads to T = 2H - 3 ..here you'll have many possibilities like T = 1 , H =2 or T = 3 , H = 3...etc which will endup different sum for T + D + H!

Hence not sufficient.

combine 1 and 2:

T = D or D = H or H = T, and D = H + 2...using equation: T = ( D + H ) - 5
you endup with different suitable values like : T = D = 7 and H = 5 ; T = H = 3 and D = 5...
still no fixed sum, hence it's not sufficient.

Option : E!

The questions tells you that T = D + H -5

Statement 1 - if you know that 2 of the numbers are the same you still don't know which two are the same, nor do you know what the sum is - if D=h then the sum could be anything.

BCE

Statement #2 - if we know that D = h+2 we can still have any sum becuase H can be any number, then we can calculate D and T from that and can get almost any sum.

CE

Together we know that

T = D + H -5, two of the numbers are the same and D = H +2 - thus we know that D and H can't be the same numbers. Either T = D or T = H

put those in algebraically

D = D + H - 5 - solve to find h = 5
or
H = D + H - 5 to find that D = 5

These numbers would achieve different sums - therefore insufficient and the answer is E.

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IMO E