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CAT 2020 Slot 3 — QA Question 8

Number TheoryEasy

Let m and n be natural numbers such that n is even and 0.2 < m20,nm,n11 < 0..5. Then m – 2n equals

Answer & solution

  • A

    4

  • B

    3

  • C

    2

  • 1

Solution

We know, 0.2 <  m/20 <0.5 ⇒ 4 < m < 10

Values m can take = {5, 6, 7, 8, 9}

We know, 0.2 < n/11 <0.5 ⇒ 2.2 < n < 5.5

Values n can take = {3, 4, 5}

Since n is even, the only possible value of n is 4.

Also, 0.2 < m20,nm,n11 < 0.5 ⇒ m/5 < n < m/2

Since n = 4 ⇒ 20 > m > 8

The only possible value of m is 9.

∴ m – 2n = 9 – 2 × 4 = 1.

Hence, option (d).

CAT 2020 Slot 3 QA Q8: Let m and n be natural numbers such that n is even and 0.2 < m 20 , n m , n 11 < 0..5. Then m &ndash; 2n equal — Solution | TheCATExam