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Director  Joined: 03 Sep 2006
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If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what  [#permalink]

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Question Stats: 59% (02:51) correct 41% (02:34) wrong based on 236 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) $$\frac{7}{13}<n<\frac{19}{33}$$
Math Expert V
Joined: 02 Sep 2009
Posts: 59147
Re: DS If n is one of the numbers  [#permalink]

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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.

Hope it's clear.
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Math Expert V
Joined: 02 Sep 2009
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Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what  [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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

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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]

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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_________________ Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what   [#permalink] 26 Mar 2019, 14:51
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