Past Questions

Question 1

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?
[CAT 2003 R]

		$[ \dfrac{a}{27} , \dfrac{b}{e} ]$
		$[ \dfrac{a}{36} , \dfrac{c}{e} ]$
		$[ \dfrac{a}{12} , \dfrac{bd}{18} ]$
		$[ \dfrac{a}{6} , \dfrac{c}{d} ]$

Question 2

The Howrah-Puri express can move at $45$ km/hour without its rake, and the speed is diminished by a constant that varies as the square root of the number of wagons attached. If it is known that with $9$ wagons, the speed is $30$ km/hour, what is the greatest number of wagons with which the train can just move?
[IIFT 2012]

		$63$
		$64$
		$80$
		$81$

Question 3

If $\dfrac{m}{n} = \dfrac{4}{3}$ and $\dfrac{r}{t} = \dfrac{9}{14}$, the value of $\dfrac{3 \space mr - nt}{4 \space nt - 7 \space mr}$ is:
[FMS 2011]

		$-5 \dfrac{1}{2}$
		$- \dfrac{11}{14}$
		$-1 \dfrac{1}{4}$
		$\dfrac{11}{14}$