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24 Jan 2012, 09:52
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (02:47) correct
44%
(02:31)
wrong
based on 380
sessions
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If n is one of the numbers in \(\frac{1}{3}\), \(\frac{3}{16}\), \(\frac{4}{7}\), \(\frac{3}{5}\) then what is the value of n?
(1) \(\frac{5}{16}<n<\frac{7}{12}\)
(2) \(\frac{7}{13}<n<\frac{19}{33}\)
(1) \(\frac{5}{16}<n<\frac{7}{12}\)
(2) \(\frac{7}{13}<n<\frac{19}{33}\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
24 Jan 2012, 11:04
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LM
If n is one of the numbers in \(\frac{1}{3}\), \(\frac{3}{16}\), \(\frac{4}{7}\), \(\frac{3}{5}\) then what is the value of n?
The method of cross multiplication:
Suppose we want to know which positive fraction is greater \(\frac{4}{7}\) or \(\frac{7}{12}\). Cross-multiply --> \(4*12=48\) and \(7*7=49\) --> \(48<49\). Now, ask yourself, which fraction contributed nominator for the larger value? \(\frac{7}{12}\)! Thus \(\frac{4}{7}<\frac{7}{12}\).
(1) \(\frac{5}{16}<n<\frac{7}{12}\) --> \(\frac{5}{16}<(\frac{1}{3}=\frac{5}{15})<\frac{7}{12}\), hence \(\frac{1}{3}\) is obviously in the given range (notice also that \(\frac{1}{2}<\frac{7}{12}\)). Next, from our example above we know that \(\frac{4}{7}<\frac{7}{12}\) so \(\frac{4}{7}\) is also in the given range. Not sufficient.
(2) \(\frac{7}{13}<n<\frac{19}{33}\) --> only two values might be in this range: \(\frac{4}{7}\approx{5.7}\) and \(\frac{3}{5}=0.6\) (other possible values of n are less than 1/2 and are clearly out of the range). As the second one is larger, then let's compare it with \(\frac{19}{33}\) (the upper limit of the range). So we are comparing \(\frac{19}{33}\) and \(\frac{3}{5}\): cross-multiply --> \(3*33=99\) and \(19*5=95\) --> \(99>95\). Which fraction contributed nominator for the larger value? \(\frac{3}{5}\)! Thus \(\frac{3}{5}>\frac{19}{33}\), which means that \(\frac{3}{5}\) is out of the range. \(n\) can only be \(\frac{4}{7}\). Sufficient.
Answer: B.
Hope it's clear.
24 Jun 2013, 03:17
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!
*New project from GMAT Club!!! Check HERE
*New project from GMAT Club!!! Check HERE
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All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57
