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04 Aug 2020, 02:31
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E
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Difficulty:
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Question Stats:
64% (02:03) correct
36%
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[GMAT math practice question]
What is the value of \(\frac{2}{3·5} + \frac{2}{5·7} + \frac{2}{7·9} + \frac{2}{9·11} + \frac{2}{11·13}\)?
A. \(\frac{2}{27}\)
B. \(\frac{3}{29}\)
C. \(\frac{5}{33}\)
D. \(\frac{9}{37 }\)
E. \(\frac{10}{39} \)
What is the value of \(\frac{2}{3·5} + \frac{2}{5·7} + \frac{2}{7·9} + \frac{2}{9·11} + \frac{2}{11·13}\)?
A. \(\frac{2}{27}\)
B. \(\frac{3}{29}\)
C. \(\frac{5}{33}\)
D. \(\frac{9}{37 }\)
E. \(\frac{10}{39} \)
Thelegend2631
Posts: 371
Updated on: 07 Aug 2020, 03:24
Originally posted by Thelegend2631 on 04 Aug 2020, 05:30.
Last edited by Thelegend2631 on 07 Aug 2020, 03:24, edited 3 times in total.
Last edited by Thelegend2631 on 07 Aug 2020, 03:24, edited 3 times in total.
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Try this way
1/3-1/5 = 2/15 = 2/3.5
That means,
Y =(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)
=1/3-1/13
=(13-3)/39
= 10/39
Posted from my mobile device
1/3-1/5 = 2/15 = 2/3.5
That means,
Y =(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)
=1/3-1/13
=(13-3)/39
= 10/39
Posted from my mobile device
06 Aug 2020, 03:44
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=>
Remember that \(\frac{2}{n(n + 2)} = \frac{1}{n} – \frac{1}{n + 2}.\)
\(\frac{2}{3·5} + \frac{2}{5·7 }+ \frac{2}{7·9} + \frac{2}{9·11} + \frac{2}{11·13}\)
\(= (\frac{1}{3} – \frac{1}{5}) + (\frac{1}{5} – \frac{1}{7}) + (\frac{1}{7} – \frac{1}{9}) + (\frac{1}{9} – \frac{1}{11}) + (\frac{1}{11} – \frac{1}{13})\)
\(= \frac{1}{3} – \frac{1}{13}\)
\(= \frac{(13 - 3)}{(3·13)} = \frac{10}{39}\)
Therefore, E is the correct answer
Answer: E.
Remember that \(\frac{2}{n(n + 2)} = \frac{1}{n} – \frac{1}{n + 2}.\)
\(\frac{2}{3·5} + \frac{2}{5·7 }+ \frac{2}{7·9} + \frac{2}{9·11} + \frac{2}{11·13}\)
\(= (\frac{1}{3} – \frac{1}{5}) + (\frac{1}{5} – \frac{1}{7}) + (\frac{1}{7} – \frac{1}{9}) + (\frac{1}{9} – \frac{1}{11}) + (\frac{1}{11} – \frac{1}{13})\)
\(= \frac{1}{3} – \frac{1}{13}\)
\(= \frac{(13 - 3)}{(3·13)} = \frac{10}{39}\)
Therefore, E is the correct answer
Answer: E.
