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inequalities 08 Jul 2011, 21:42
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35% (medium)

Question Stats:

75% (01:00) correct 25% (02:54) wrong based on 12 sessions

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\(\frac{2}{n} \frac{2}{n}\)

\(\frac{2}{4} > \frac{4}{n}\)

\(n > 4\)

4 0, so we can multiply by n

\(2 < \frac{1}{2}n < 3\)

Divide by 1/2

\(\frac{2}{1/2} < n < \frac{3}{1/2}\)

\(4 < n < 6\)



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inequalities 04 Sep 2011, 06:28
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2/n < 1/2 < 3/n

make two equations and cross multiply
2/n < 1/2
4 < n

AND
1/2 < 3/n
n < 6

4 < n < 6

D .... ans
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inequalities 04 Sep 2011, 13:18
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ssarkar
Which of the following is equivalent to the statement that 0.5 is between 2/n and 3/n？
(A) 1<n<6
(B) 2<n<3
(C) 2<n<5
(D) 4<n<6
(E) n>10
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They should have mentioned that n is +ve.
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inequalities 04 Sep 2011, 21:33
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ssarkar
Which of the following is equivalent to the statement that 0.5 is between 2/n and 3/n？
(A) 1<n<6
(B) 2<n<3
(C) 2<n<5
(D) 4<n<6
(E) n>10
Show more

An alternative non-mathematical intuitive but difficult to explain approach:

2/n < 1/2 < 3/n
My first instinct is to find out what n can be... n has to lie in a range. The moment I put n = 4 I am out of that range because I get 2/4 which is equal to 1/2, not less than 1/2.
That made me think that n = 6 will also put me out of range because 3/6 will be equal to n, not greater than n.

This gave me the two points where my range ended. So between those points, the values of n should work. If n = 5, 2/5 < 1/2 < 3/5 satisfies. My desired range must be 4 < n < 6
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inequalities 04 Sep 2011, 21:56
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2/n < 0.5 < 3/n

0.5 or 1/2 can be written as (n/2) / n
=> 2/n < (n/2)/n <3/n

=> 2<n/2<3 therefore

4<n<6. therefore ans D, n lies between 4 and 6
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inequalities 05 Sep 2011, 15:34
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ssarkar
Which of the following is equivalent to the statement that 0.5 is between 2/n and 3/n？
(A) 1<n<6
(B) 2<n<3
(C) 2<n<5
(D) 4<n<6
(E) n>10
Show more
0.5 is between 2/n and 3/n
So, 2/n < 1/2 < 3/n
First I think about multiplying by n^2, but it will not serve my purpose.So abandoned the approach.
Now, I just think of substituting to select the correct values
(A) 1<n<6 ==> 2/1 < 1/2 --OUT
(B) 2<n<3 ==> 2/2 < 1/2 -- OUT
(C) 2<n<5 ==> OUT for the same reason
(D) 4<n<6 ==> 2/4 < 1/2 < 3/6 ==> .5 < .5 < .5
(E) n>10 ==> 2/11 < 1/2 < 3/11 ==> .18 < .5 < .27 ==> OUT
So, (D)
Actually, I just solved E and D. Rest all no need of writing because they are pretty obvious without substitution.

Choose the approach that suites you best
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inequalities 04 Apr 2017, 10:39
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