MensaNumber wrote:

which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

a) 1/24

b) 7/30

c) 1/45

d) 13/56

e) 1/72

Let the 2 consecutive integers be "a" and "a+1"

So we have \(\frac{1}{a}\)

- \(\frac{1}{(a+1)}\)

Simplify and we get \(\frac{1}{a(a+1)}\)....So the answer needs to have 1 in numerator and denominator should be product of consecutive integers...

Option B and D can be ruled out

24=6*4 (Not consecutive)

45= 9*5 (not consecutive)

72=8*9 (Consecutive) and hence your answer.

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