Question
Download Solution PDFSelect the set in which the numbers are related in the same way as are the numbers of the following set.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)
(3, 14, 1)
(4, 36, 2)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLogic : (Cube of 1st number + Cube of 3rd number) / 2 = 2nd number
Given :
-
(3, 14, 1)
⇒\({(3)^3 + (1)^3 \over 2}\) = 14
⇒\({27 + 1 \over 2}\) = 14
⇒\({28 \over 2}\) = 14
⇒14 = 14 (LHS = RHS)
- (4, 36, 2)
⇒\({(4)^3 + (2)^3 \over 2}\) = 36
⇒\({64 + 8 \over 2}\) = 36
⇒\({72 \over 2}\) = 36
⇒36 = 36 (LHS = RHS)
So,
- Option - (1) : (8, 12, 2)
⇒\({(8)^3 + (2)^3 \over 2}\) = 12
⇒\({512 + 8 \over 2}\) = 12
⇒\({520 \over 2}\) = 12
⇒260 ≠ 12 (LHS ≠ RHS)
- Option - (2) : (5, 81, 4)
⇒\({(5)^3 + (4)^3 \over 2}\) = 81
⇒\({125 + 64 \over 2}\) = 81
⇒\({189 \over 2}\) = 81
⇒94.5 ≠ 81 (LHS ≠ RHS)
- Option - (3) : (7, 40, 3)
⇒\({(7)^3 + (3)^3 \over 2}\) = 40
⇒\({343 + 27 \over 2}\) = 40
⇒\({370 \over 2}\) = 40
⇒185 ≠ 40 (LHS ≠ RHS)
- Option - (4) : (8, 260, 2)
⇒\({(8)^3 + (2)^3 \over 2}\) = 260
⇒\({512 + 8 \over 2}\) = 260
⇒\({520 \over 2}\) = 260
⇒260 = 260 (LHS = RHS)
Hence, "Option - (4)" is the correct answer.
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