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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what

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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what [#permalink] New post 24 Jan 2012, 08:52
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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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Re: DS If n is one of the numbers [#permalink] New post 24 Jan 2012, 10:04
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LM wrote:
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}


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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Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what [#permalink] New post 24 Jun 2013, 02:17
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Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what [#permalink] New post 25 Jun 2013, 09:36
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LM wrote:
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}



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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Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what   [#permalink] 25 Jun 2013, 09:36
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