Questions :
When 12, 16, 18, 20 and 25 divide the least number N, the remainder in each case is 4 but it is divisible by 7. What is the digit at the thousand’s place in x ?
Options :
- 5
- 3
- 9
- 4
correct answer: b)
First, we find the LCM of 12, 16, 18, 20 and 25.
12 → 2, 6, 3
16 → 2, 8, 4, 2
18 → 2, 9, 3
20 → 2, 10, 5
25 → 5, 5
LCM = 2 × 2 × 2 × 3 × 5 × 5 = 600
∴ Required number = 3600, such which is divisible by 7.
3600 ÷ 7 = 514 × 7 + 2
Here, 2y + 4 is divisible by 7 if y = 5.
∴ 3600 × 5 = 18000 + 4 = 18004
Thousandth digit = 8