Question : Directions: Select the option in which the numbers share the same relationship in the set as that shared by the numbers in the given set. (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.)
(8, 27, 125)
(64,1331, 1728)
Option 1: (289, 212,196)
Option 2: (200, 215, 256)
Option 3: (125, 172, 144)
Option 4: (216, 343, 512)
Correct Answer: (216, 343, 512)
Solution :
Given:
(8, 27,125); (64,1331,1728)
The first, second, and third number is a perfect cube number –
⇒ (8, 27,125)→8 = 2
3
; 27 = 3
3
;125 = 5
3
⇒ (64,1331,1728)→64 = 4
3
; 1331 = 11
3
; 1728 = 12
3
Let's check each option –
First option:
(289, 212,196)→289 = 17
2
; 212 = Not a perfect cube number; 196 = 14
2
;
Second option:
(200, 215, 256)→200 = Not a perfect cube number; 215 = Not a perfect cube number; 256 = Not a perfect cube number.
Third option:
(125,172,144)→125 = 5
3
; 172 = Not a perfect cube number; 144 = Not a perfect cube number.
Fourth option:
(216, 343, 512)→216 = 6
3
; 343 = 7
3
; 512 = 8
3
;
So, only the fourth option follows the same pattern as the given set of numbers. Hence, the fourth option is correct.
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