CAT 2005 — QA Question 13
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.
The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B − A is perfectly divisible by 7, then which of the following is necessarily true?
Answer & solution
- A
100 < A < 299
106 < A < 305
- C
112 < A < 311
- D
118 < A < 317
Let A = 100x + 10y + z (x ≠ 0, x, y, z are single-digit numbers)
∴ B = 100z + 10y + x
∴ B – A = 99(z – x)
As (B – A) is divisible by 7 and 99 is not, (z – x) is divisible by 7.
∴ z and x can have values (8, 1) or (9, 2).
[Since B > A, z > x]
y can have any value from 0 to 9.
A = 1y8 or 2y9
∴ Lowest possible value of A is 108 and the highest possible value of A is 299.
Hence, option (b).