GATE ECE 2016 Set 3 | GA | Question: 4

Question

The number that least fits this set$:(324,441,97$ and $64)$ is

• A. $324$
• B. $441$
• C. $97$
• D. $64$

Answer 1

Let’s analyse each of the given options

• A. $324$

Sum of every digit $=3+2+4 = 9 =3^2$

• A. $441$

Sum of every digit $=4+4+1 = 9 =3^2$

100. $97$

Sum of every digit $=9+7 = 16 =4^2$

500. $64$

Sum of every digit $=6+4 = 10$

The sum of every digit in each these numbers $324,441,97$ is a perfect square whereas $64$ doesn’t produce sum as a perfect square.

By this logic, option D is the correct answer.

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• A. $324=(18)^2 $

• A. $441=(21)^2$

100. $97$ is not a perfect square of any number.

500. $64=(8)^2$

By this logic, option C is the correct answer.

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Hence both options C and D are correct.

As per Official answer key, both options C and D are correct.

Comments

can we choose option based on two different criteria?

Answer 2

Ans. (C)

$324 = (18)^2$ 

$441 = (21)^2$

$64 = (8)^2$

Where as $97$ is not perfect square of any number.

Therefore, ans is (c)

Answer 3

97 is not a perfect square

Answer 4

97 as it is not perfect square no.

Answer 5

Sum of digits in a number is not 9 in 97

Comments

@Ritik Jain RJ 

Your method doesn't work for $64?$

Sum of digit$=6+4=10$

Answer 6

97 is the only prime no among all of them.

so option C is correct.

but when we give a little more effort then we get that the D option is also correct as the sum of the digit of every number is a perfect square except 64. so C, and D is the correct option but if in an exam this type of question comes in MCQ  then they give marks to all.