Question

The number 20 is multiplied either by 4 or by 5, then the product is increased either by 3 or by 5, and then the sum is divided either by 6 or by 7. What is the final quotient, if it is a natural number?

Answer 1

15

Explanation:

We try every possibility.

20 is multiplied either by 4 or by 5

20 * 4 = 80

20 * 5 = 100

then the product is increased either by 3 or by 5

80 + 3 = 83

80 + 5 = 85

100 + 3 = 103

100 + 5 = 105

the sum is divided either by 6 or by 7

None of the numbers are divisible by 6 since they are all odd.

Only 105 is divisible by 7.

105/7 = 15

Answer: 15

Answer 2

15

Explanation:

If it was 20 × 4 = 80, 80 + 3 = 83 and 80 + 5 = 85 but neither of those numbers are divisible by either 6 or 7 so we know it's not 20 × 4. If we did 20 × 5 = 100, 100 + 3 = 103 and 100 + 5 = 105. Since 105 / 7 = 15 the answer is 15.