Question

Find the smallest coefficient of 4 which is divided by 5, 11 and 13 and get successive remainders 1, 7 and 9.
1. 2856
2. 1744
3. 2800
4. 711

Answer 1

Correct Answer - Option 1 : 2856

Calculation:

L.C.M. of 5, 11 and 13 is 715.

⇒ 5 – 1 = 4

⇒ 11 – 7 = 4

⇒ 13 – 9 = 4

⇒ 715x – 4 (The smallest coefficient of 4)

Let x = 1,

⇒ 715 – 4 = 711 (It’s not a coefficient of 4)

Let x = 2,

⇒ 715  ×  2 – 4 = 1430 – 4 = 1426 (It’s not a coefficient of 4)

Let x = 3,

⇒ 715  ×  3 – 4 = 2145 – 4 = 2141 (It’s not a coefficient of 4)

Let x = 4,

⇒ 715  ×  4 – 4 = 2860 – 4 = 2856 (It’s a coefficient of 4)

∴ Required answer is 2856.