Which number should be subtracted from 24, 31, 58 and 79 so that the ratio of the remainders of the first two numbers is proportion to the ratio of the remainders of the other two numbers?

5
7
8
None of the above

The correct answer is (d).

To solve this question, we can first find the remainders of each number when divided by 10:

  • 24 ÷ 10 = 2, remainder 4
  • 31 ÷ 10 = 3, remainder 1
  • 58 ÷ 10 = 5, remainder 8
  • 79 ÷ 10 = 7, remainder 9

We can then subtract 4 from each number:

  • 24 – 4 = 20
  • 31 – 4 = 27
  • 58 – 4 = 54
  • 79 – 4 = 75

The ratio of the remainders of the first two numbers is now 20:27, and the ratio of the remainders of the other two numbers is 54:75. These ratios are not equal, so we need to subtract another number from the first two numbers.

We can continue subtracting 4 from each number until the ratio of the remainders of the first two numbers is equal to the ratio of the remainders of the other two numbers. However, we will never reach a point where the ratios are equal, because the remainders of the first two numbers are always odd, while the remainders of the other two numbers are always even.

Therefore, the answer is (d).

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