Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the given sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(9, 11, 404)
(4, 13, 370)
Option 1: (8, 12, 416)
Option 2: (7, 11, 380)
Option 3: (8, 9, 300)
Option 4: (8, 10, 326)
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Correct Answer: (8, 12, 416)
Solution :
Given:
(9, 11, 404); (4, 13, 370)
Here, (9, 11, 404)→((9)
2
+ (11)
2
) × 2 = (81 + 121) × 2 = 202 × 2 = 404
(4, 13, 370)→((4)
2
+ (13)
2
) × 2 = (16 + 169) × 2 = 185 × 2 = 370
Let's check each option –
First option:
(8, 12, 416)→((8)
2
+ (12)
2
) × 2 = (64 + 144) × 2 = 208 × 2 = 416
Second option:
(7, 11, 380)→((7)
2
+ (11)
2
) × 2 = (49 + 121) × 2 = 170 × 2 = 340 ≠ 380
Third option:
(8, 9, 300)→((8)
2
+ (9)
2
) × 2 = (64 + 81) × 2 = 145 × 2 = 290 ≠ 300
Fourth option:
(8, 10, 326)→((8)
2
+ (10)
2
) × 2 = (64 + 100) × 2 = 164 × 2 = 328 ≠ 326
So, only the first option follows the same pattern as followed by the given set of numbers. Hence, the first option is correct.
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