Question: What is \(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+\frac{1}{5*6}+\frac{1}{6*7}+\frac{1}{7*8}+\frac{1}{8*9}+\frac{1}{9*10}\)?

1. \(\frac{2}{5}\)
2. \(\frac{3}{5}\)
3. \(\frac{7}{10}\)
4. \(\frac{46}{55}\)
5. \(\frac{9}{10}\)

Correct Answer: E

Approach Solution (1):

\(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+\frac{1}{5*6}+\frac{1}{6*7}+\frac{1}{7*8}+\frac{1}{8*9}+\frac{1}{9*10}\)

This can be rewritten as:

\([\frac{1}{1}-\frac{1}{2}]+[\frac{1}{2}-\frac{1}{3}]+[\frac{1}{3}-\frac{1}{4}]+[\frac{1}{4}-\frac{1}{5}]+[\frac{1}{5}-\frac{1}{6}]+[\frac{1}{6}-\frac{1}{7}]+[\frac{1}{7}-\frac{1}{8}]+[\frac{1}{8}-\frac{1}{9}]+[\frac{1}{9}-\frac{1}{10}]\)

Every term cancels out except

\([\frac{1}{1}-\frac{1}{10}]=\frac{9}{10}\)

Approach Solution (2):

\(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+\frac{1}{5*6}+\frac{1}{6*7}+\frac{1}{7*8}+\frac{1}{8*9}+\frac{1}{9*10}\)

Can be rewritten as:

0.5 + 0.166 + 0.083 + 0.05 + 0.03 + 0.023 + … ans so on (other values are too small)

Add them up

Sum = approximately 0.85 and a little more

Check option:

(A) \(\frac{2}{5}\)= 0.4
(B) \(\frac{3}{5}\)= 0.6
(C) \(\frac{7}{10}\)= 0.7
(D) \(\frac{46}{55}\)= 0.83
(E) \(\frac{9}{10}\)= 0.9 = Correct

“What is \(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+\frac{1}{5*6}+\frac{1}{6*7}+\frac{1}{7*8}+\frac{1}{8*9}+\frac{1}{9*10}\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills.

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