CAT 2000 — QA Question 13

1421 ≡ 5(mod 12); 1423 ≡ 7(mod 12); 1425 ≡ 9(mod 12)

∴ N ≡ 5(mod 12) × 7(mod 12) × 9(mod 12)

    = 315(mod 12) = 3(mod 12)

∴ The remainder is 3.
 
Hence, option (c).

Alternatively,

N = 1421 × 1423 × 1425

= (1422 – 1)(1422 + 1)(1428 – 3) = (1422² – 12)(1428 – 3)  

Both 1422² and 1428 are divisible by 3 as well as 4.

N = (1422² – 1)(1428 – 3)
 
(1422² – 1) divided by 12 leaves a remainder of −1 and (1428 – 3) divided by 12 leaves a remainder of −3
 
Effective remainder = −1 × −3 = 3
 
∴ N when divided by 12 leaves a remainder of 3.
 
∴ N = X + 3; where X is divisible by 12

Thus, when N = 1421 × 1423 × 1425 is divided by 12, the remainder will be 3.

Hence, option (c).