CAT Progressions

Question
Second term of a GP is 1000 and the common ratio is   where n is a natural number. Pn is the product of n terms of this GP. P6 > P5 and P6 > P7, what is the sum of all possible values of n?
A.            5
B.            9
C.            8
D.            11

Correct Answer
Choice B

Explanatory Answer
Common ratio is positive, and one of the terms is positive => All terms are positive
P6 = P5 * t6 => If P6 > P5, t6 > 1
P7 = P6 * t7 => If P6 > P7, t7 < 1
T6 = t2 * r4 = 1000r4;
T7 = t2 * r5 = 1000r5
1000r4 > 1 and 1000r5 < 1
1/r^4 < 1000 and 1/r^5 > 1000
1/r = n
n4 < 1000 and n5 > 1000, where n is a natural number
n4 < 1000 => n < 6
n5 > 1000 => n > 4
n could be 4 or 5. Sum of possible values = 9

Answer Choice (B)

Labels: , , , , ,

IIM CAT Preparation Tips: CAT Progressions

May 31, 2013

CAT Progressions

Question
Second term of a GP is 1000 and the common ratio is   where n is a natural number. Pn is the product of n terms of this GP. P6 > P5 and P6 > P7, what is the sum of all possible values of n?
A.            5
B.            9
C.            8
D.            11

Correct Answer
Choice B

Explanatory Answer
Common ratio is positive, and one of the terms is positive => All terms are positive
P6 = P5 * t6 => If P6 > P5, t6 > 1
P7 = P6 * t7 => If P6 > P7, t7 < 1
T6 = t2 * r4 = 1000r4;
T7 = t2 * r5 = 1000r5
1000r4 > 1 and 1000r5 < 1
1/r^4 < 1000 and 1/r^5 > 1000
1/r = n
n4 < 1000 and n5 > 1000, where n is a natural number
n4 < 1000 => n < 6
n5 > 1000 => n > 4
n could be 4 or 5. Sum of possible values = 9

Answer Choice (B)

Labels: , , , , ,

0 Comments:

Post a Comment

Subscribe to Post Comments [Atom]

<< Home