CAT 2007 — QA Question 21
Number TheoryEasy
Passage / Data
Answer the next 2 questions based on the information given below.
Let a1 = p and b1 = q, where p and q are positive quantities.
Define:
an = pbn−1 bn = qbn−1, for even n > 1 and
an = pan − 1 bn = qan − 1, for odd n > 1.
How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?
Answer & solution
- A
6
- B
4
- C
7
- D
5
3
Solution
1/m + 4/n = 1/12
∴ 1/m = 1/12 – 4/n
∴ m = 12n/(n – 48)
As, m is a positive integer, n should be greater than 48 and moreover since n is a positive odd integer lesser than 60, n can take values 49, 51, 53, 55, 57 and 59.
If n = 49, 51, 57 then m is a positive integer.
If n = 53, 55, 59 then m is not an integer.
∴ 3 pairs of values of m and n satisfy the given equation.
Hence, option (e).