CA Foundation · Quantitative Aptitude · Sequence and Series
Three positive numbers are in geometric progression. Their sum is 39 and their product is 729. What is the sum of the squares of the three numbers?
The sum of squares is 819. Taking the numbers as a/r, a, ar, the product gives a = 9. The sum condition then gives r = 3 or 1/3, so the numbers are 3, 9 and 27. Their squares 9, 81 and 729 add up to 819.
- A1521
- B729
- C819Correct
- D891
Explanation
Let the numbers be a/r, a, ar. The product is a³ = 729, so a = 9. The sum gives 9(r + 1/r) + 9 = 39, so r + 1/r = 10/3, which gives r = 3 or 1/3. The numbers are 3, 9, 27, and the sum of squares is 9 + 81 + 729 = 819. The option 1521 is 39², the square of the sum.
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