The Sum of 5 Numbers in the Geometric Progression is 24 GMAT Problem Solving

Question: 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

1. 36
2. 32
3. 24
4. 18
5. 16

‘The sum of 5 numbers in the geometric progression is 24?’ –  is the topic from the GMAT Quantitative problem set. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

There is only one way to solve this problem.
This is a GP problem. To solve this problem, we can consider the terms be:
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
Taking the positive answer from the answer, we get 32.
Hence, the required solution is B
Note: 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.
Correct Answer: B

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