# CAT 2003 | Question: 2-53

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Let $a, b, c, d$ and $e$ be integers such that $a = 6b = 12c,$ and $2b = 9d = 12e.$ Then which of the following pairs contains a number that is not an integer?

1. $\left[ \frac{a}{27}, \frac{b}{e} \right]$
2. $\left[ \frac{a}{36}, \frac{c}{e} \right]$
3. $\left[ \frac{a}{12}, \frac{bd}{18} \right]$
4. $\left[ \frac{a}{6}, \frac{c}{d} \right]$

Answer (D)  :- Here $\frac{c}{d}$ could not be an integer

Given a = 6b = 12c

Let  $\frac{a}{12}$ = $\frac{b}{2}$ = c = k

a=12k

b=2k

c=k...............................i

Similarly,

2b = 9d = 12e

Let $\frac{b}{18}$ = $\frac{d}{4}$ =$\frac{c}{3}$ =k

b=18k

d=4k

e=3k..............................ii

from i and ii we get

a=108k

b=18k

c=9k

d=4k

e=3k

Now, putting in option we get D) as ans.

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