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LM
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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what 24 Jan 2012, 09:52
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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) \(\frac{7}{13}<n<\frac{19}{33}\)
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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what 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?

1. \(\frac{5}{16}<n<\frac{7}{12}\)

2. \(\frac{7}{13}<n<\frac{19}{33}\)
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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?

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.
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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what 24 Jun 2013, 03:17
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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what 25 Jun 2013, 10:36
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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?

(1) \(\frac{5}{16}<n<\frac{7}{12}\)

(2) \(\frac{7}{13}<n<\frac{19}{33}\)
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I find it easier to convert the fractions into decimal form
1/3= 0.3333
3/16= 0.1875 ( Easier way to do this will be, we know 1/8 = 0.125 and so 1/16 = 0.0625 ----> 0.0625*3= 0.1875)
4/7 = 0.568 ( 1/7 = 0.142857...consider only 0.142 as the given options are not so close)
3/5 = 0.6

From st 1 we have 5/16< n< 7/12 can be converted to 0.3125 < n < 0.583...

we see that 2 values are possible ie 1/3 or 4/7 and hence st 1 ruled out

st 2 7/13< n< 19/33 -----> 0.49<n< 0.577

Another way to look at it will be , Since the largest fraction is 3/5 which is 0.6,we can calculate 60% of 33 which is 19.8 but since the numerator in the fraction (19/33) is 19 which is less than 19.8 and thus we will have only one value in the range Only 1 value that is 4/7 is in this range
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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what 05 Jan 2023, 09:16
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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?

(1) \(\frac{5}{16}<n<\frac{7}{12}\)

(2) \(\frac{7}{13}<n<\frac{19}{33}\)
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From Question stem 1/3, 3/16, 4/7,3/5 are the given numbers

Option 1) \(\frac{5}{16}<n<\frac{7}{12}\)

LCM of 16, 12 is 48
\(\frac{5}{16}*48 <n*48 <\frac{7}{12}*48\)
Implies,
15 <n*48 < 28

\(\frac{1}{3}\)*48 = 16 -- lies in range

\(\frac{3}{16}\)*48 = 9 -- doesn't lie in the range

\(\frac{4}{7}\)*48 = 27.42 -- lies in the range

\(\frac{3}{5}\)*48 = 28.8 -- doesn't lie in the range

Option 2) \(\frac{7}{13}<n<\frac{19}{33}\)
LCM of 13, 33 is 429
\(\frac{7}{13}*429 <n*429 <\frac{19}{33}*429\)
Implies,
231 <n*429 < 247

\(\frac{1}{3}\)*429 = 143 -- doesn't lie in the range

\(\frac{3}{16}\)*429 = approx. 90 -- doesn't lie in the range

\(\frac{4}{7}\)*429 = approx. 244 -- lies in the range

\(\frac{3}{5}\)*429 = approx. 255 -- doesn't lie in the range

therefore answer is B
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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what 05 Aug 2024, 19:21
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