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.)
(25, 49, 81)
(169, 225, 289)
Option 1: (441, 529, 676)
Option 2: (100, 144, 256)
Option 3: (289, 361, 441)
Option 4: (121, 169, 289)
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Correct Answer: (289, 361, 441)
Solution :
Given:
(25, 49, 81); (169, 225, 289)
Here, the numbers of the given sets are the perfect squares of the consecutive odd numbers.
(25, 49, 81)→$\sqrt25$ = 5; $\sqrt49$ = 7; $\sqrt81$ = 9
(169, 225, 289)→$\sqrt169$ = 13; $\sqrt225$ = 15; $\sqrt289$ = 17
Let's check the options –
First option:
(441, 529, 676)→$\sqrt441$ = 21; $\sqrt529$ = 23; $\sqrt676$ = 26; 26 is not an odd number.
Second option:
(100, 144, 256)→$\sqrt100$ = 10; $\sqrt144$ = 12; $\sqrt256$ = 16; 10, 12, and 16 are even numbers.
Third option:
(289, 361, 441)→$\sqrt289$ = 17; $\sqrt361$ = 19; $\sqrt441$ = 21
Fourth option:
(121, 169, 289)→$\sqrt121$ = 11; $\sqrt169$ = 13; $\sqrt289$ = 17; Here, the square root of numbers are not consecutive odd numbers.
So, only the third option follows the same pattern as followed by the given set of numbers. Hence, the third option is correct.
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