Expected CAT Question

Expected CAT Question:

Q1: 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) 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 2.

Q2:

a1 = 1

an+1 = 4n + 3an – 2

a2 = 4 – 2 + 3(1) = 5 = 32 – 1

a3 = 4(2) + 3(5) – 2 = 21 = 33 – 6

a4 = 4(3) + 3(21) – 2 = 73 = 34 – 8

∴ an = 3n – 2(n)

∴ a100 = 3100 – 200
Hence, option 3.