# CAT 2018 LRDI Questions

Question No. 1:
Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is
Options:
1. 3/6
2. 3/2
3. 5/2
4. 1/6

Question No. 2:
A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

Question No. 3:
Given that x2018y2017 = 1/2 and x2016y2019 = 8, the value of x2 + y3 is
Options:
1. 35/4
2. 37/4
3. 31/4
4. 33/4

Question No. 4:
Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

Explanation:

Since x, y ,and z are in G.P.  and x<y<z, let x = a, y=ar and z=ar2, where a>0 and r>1.

It is also given that, 15x, 16y and 12z are in A.P.

Therefore, 2×16y=5x+12z

Substituting the values of x, y and z we get,

$32ar=5a + 12ar^2$

$\Rightarrow 32 r=5+12 r^{2}$

$\Rightarrow 12 r^{2}-32 r+5=0$

On solving the above quadratic equation we get r=1/6 or 5/2.

Since r>1, therefore r=5/2.

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