CAT 2005 — QA Question 25
Answer the next 2 questions based on the information given below.
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
Let S be a set of positive integers such that every element n of S satisfies the conditions
a. 1000 ≤ n ≤ 1200
b. every digit in n is odd
Then how many elements of S are divisible by 3?
Answer & solution
9
- B
10
- C
11
- D
12
n will be of the form 11ab, where a and b are odd numbers.
We are looking for all n’s divisible by 3.
∴ 1 + 1 + a + b = 3 or 6 or 9 or 12 or 15 or 18
∴ a + b = 1 or 4 or 7 or 10 or 13 or 16
∴ a + b = 1 or 7 or 13 is not possible as the sum of two odd numbers cannot be odd.
∴ (a, b) = (1, 3), (3, 1), (1, 9), (3, 7), (5, 5), (7, 3), (9, 1), (7, 9), (9, 7)
∴ 9 elements of S are divisible by 3.
Hence, option (a).