Latest CAT Aptitude Question SOLUTION: If a,b,c,d are in continued proportion then (a-d)/(b-c) >=x. What is the value of x. a)2 b)3 c)0 d)1

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(#M40034248) CAT Numerical Ability question Keep an EYE

If a,b,c,d are in continued proportion then (a-d)/(b-c) >=x. What is the value of x.

a)2
b)3
c)0
d)1

Asked In CAT Ish Mishra (10 years ago)

Unsolved Read Solution (3)

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Read Solution (3) :

RAKESH  (10 years ago)

let a,b,c,d are a,ar,ar^2,ar^3 respectively such that a,b,c,d are continued proportion then

(a-d)/(b-c)= (a-ar^3)/(ar-ar^2)=(1-r^3)/(r-r^2)= (1+r+r^2)/r = (1/r +r +1)

since (r+ 1/r) is always greater or equal to 2
so, (a-d)/(b-c)= (1/r +r +1) is always greater or equal to 3

so, x=3

b)3

Is this solution Helpfull? Yes (13) | No (6)  

Chitranshi Gupta  (7 years ago)

What if more than one choice was greater than 4

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HARSH PAL  (5 years ago)

If a,b, c,d are in continued proportion, a/b = b/c = c/d i.e a,b,c and d are in GP.

We can say that:

a = p, b=pr, c=pr^2 and d=pr^3 (p is the first term and r is the common ration of a GP series )

(a-d)/(b-c) = p(1-r^3)/pr(1-r) => (1+r+r^2)/r => (1+r + 1/r)

Minimum( 1+r + 1/r ) = 1 + Minimum( r + 1/r ) = 3. Hence value of x is 3.

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