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11 Apr 2020, 19:08
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:35) correct
36%
(02:39)
wrong
based on 125
sessions
History
Date
Time
Result
Not Attempted Yet
GMATBusters’ Quant Quiz Question -2
The sum of 5 numbers in the geometric progression is 24. The sum of their reciprocals is 6. The product of the terms of the geometric progression is
(a) 36
(b) 32
(c) 24
(d) 18
(e) 16
A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
11 Apr 2020, 19:09
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Official Solution:
Let the terms in geometric progression are a/r^2, a/r, a, ar & ar^2.
The sum of 5 numbers in the geometric progression is 24.
a/r^2 + a/r + a + ar + ar^2 = 24 ... Eq (1)
The sum of their reciprocals is 6.
1/ar^2 + 1/ar + 1/a + r/a + r^2/a = 6 ... Eq(2)
Multiplying Eq (2) by a^2
ar^2 + ar + a + a/r + a/r^2 = 6a^2 = 24
a^2 = 4; a= +/-2
The product of the terms of the geometric progression is =a^5 = 32 or -32
out of the given answer options. We can select 32
Hence, Answer = B
(PS: in Probalem Solving type Question: even if the answer can be more than one value, we must select the answer from the available answer options.)
Updated on: 11 Apr 2020, 20:15
Originally posted by Kinshook on 11 Apr 2020, 19:16.
Last edited by GMATBusters on 11 Apr 2020, 20:15, edited 2 times in total.
Last edited by GMATBusters on 11 Apr 2020, 20:15, edited 2 times in total.
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In Problem solving question, we need to select the answer out of the given options.
Given:
1. The sum of 5 numbers in the geometric progression is 24.
2. The sum of their reciprocals is 6.
Asked: The product of the terms of the geometric progression is
(a) 36
(b) 32
(c) 24
(d) 18
(e) 16
Let the 5 numbers in geometric progression be ar^2, ar, a, a/r & a/r^2.
1. The sum of 5 numbers in the geometric progression is 24.
ar^2 + ar + a + a/r + a/r^2 = 24 (1)
2. The sum of their reciprocals is 6.
1/ar^2 + 1/ar + 1/a + r/a + r^2/a = 6. (2)
Multiplying (2) by a^2
ar^2 + ar + a + a/r + a/r^2 = 6a^2 = 24
a^2 = 4; a= 2 or a = -2
The product of the terms of the geometric progression is = ar^2*ar*a*a/r*a/r^2 = a^5 = 2^5 = 32
IMO B
Hi GMATBusters
If a = - 2; a^5 = -32
Therefore, -32 is also a solution to the above problem
Given:
1. The sum of 5 numbers in the geometric progression is 24.
2. The sum of their reciprocals is 6.
Asked: The product of the terms of the geometric progression is
(a) 36
(b) 32
(c) 24
(d) 18
(e) 16
Let the 5 numbers in geometric progression be ar^2, ar, a, a/r & a/r^2.
1. The sum of 5 numbers in the geometric progression is 24.
ar^2 + ar + a + a/r + a/r^2 = 24 (1)
2. The sum of their reciprocals is 6.
1/ar^2 + 1/ar + 1/a + r/a + r^2/a = 6. (2)
Multiplying (2) by a^2
ar^2 + ar + a + a/r + a/r^2 = 6a^2 = 24
a^2 = 4; a= 2 or a = -2
The product of the terms of the geometric progression is = ar^2*ar*a*a/r*a/r^2 = a^5 = 2^5 = 32
IMO B
Hi GMATBusters
If a = - 2; a^5 = -32
Therefore, -32 is also a solution to the above problem
