Discussion
Which of the following statements is/are correct?
1. If the sum of the digits of a two digit number is 10 and product of digits is 24, then the number can be 63.
2. If the difference of digits of a two digit number is 4 and the product of two digits is 45, then number can be 95.
Select the answer using the codes given below:
Answer: B
2 only is correct.
Statement 1: two digits with sum 10 and product 24 are 6 and 4, so the number is 64 or 46. The digits of 63 add to 9 and multiply to 18, so it does not qualify.
Statement 2: two digits with difference 4 and product 45 are 9 and 5 (\(9 - 5 = 4\), \(9 \times 5 = 45\)), so the number can be 95 (or 59). Correct.
A quick way to solve such pairs: list the factor pairs of the product (24: 3 × 8, 4 × 6; 45: 5 × 9) and test the other condition.
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