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CAT 1991 — QA Question 36

Number TheoryEasy

Let k be a positive integer such that k + 4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k + 2n is divisible by 7 equals

Answer & solution

Correct answer: 9

  • 9

  • B

    7

  • C

    5

  • D

    3

Solution

a = k + 4 is divisible by 7

b = k + 2n is divisible by 7

⇒ b – a = 2n – 4 is divisible by 7

⇒ 2n – 4 = 0 or 7 or 14 ...

For minimum integral value of n, greater than 2

2n – 4 = 14

⇒ n = 9

Hence, option (a).

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CAT 1991 QA Q36: Let k be a positive integer such that k + 4 is divisible by 7. Then the smallest positive integer n, greater t — Solution | TheCATExam