GATE EE 2018 Set 1 — Question 4
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
For what values of k given below is an integer?
Correct answer
(C) 4, 8, 28
Solution
Let the given expression be .
For to be an integer, we can simplify the expression. Let's substitute , which means . Then .The expression becomes:
For to be an integer, is an integer (since and is an integer from the options). Therefore, must also be an integer.
This implies that must be a divisor of 25.The divisors of 25 are .We can find the corresponding values of using :
(A) 4, 8, 18: 18 is not in our set of possible values.
(B) 4, 10, 16: 10 and 16 are not in our set of possible values.
(C) 4, 8, 28: All three values (4, 8, 28) are in our set of possible values.
(D) 8, 26, 28: 26 is not in our set of possible values.Therefore, the correct set of values is given in option (C).
For to be an integer, we can simplify the expression. Let's substitute , which means . Then .The expression becomes:
For to be an integer, is an integer (since and is an integer from the options). Therefore, must also be an integer.
This implies that must be a divisor of 25.The divisors of 25 are .We can find the corresponding values of using :
- If , then .
- If , then .
- If , then .
- If , then .
- If , then .
- If , then .
(A) 4, 8, 18: 18 is not in our set of possible values.
(B) 4, 10, 16: 10 and 16 are not in our set of possible values.
(C) 4, 8, 28: All three values (4, 8, 28) are in our set of possible values.
(D) 8, 26, 28: 26 is not in our set of possible values.Therefore, the correct set of values is given in option (C).
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