Consider the following statements:
(A) The unit's digit in the product of (5236 × 6231) is 1.
(B) The digit in the unit's place for the product 31 × 32 × 33 × 34 × ..... × 49 is 0.
(C) The sum of the face values of 7 and 4 in 8175349 is 11.
(D) The sum of the place values of 3 in 3935 is 6.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
The unit’s digit of a product depends only on the unit’s digits of the numbers multiplied. The face value of a digit is the digit itself; its place value is the digit times the value of its place.
(A) The unit’s digit in the product of (5236 × 6231) is 1. Incorrect. The unit’s digits are 6 and 1, and \(6\times1=6\), so the product ends in 6, not 1.
(B) The digit in the unit’s place for the product 31 × 32 × 33 × 34 × ..... × 49 is 0. Correct. The product includes 40, which ends in 0 (and also 35 × 32, which gives another 0), so the whole product ends in 0.
(C) The sum of the face values of 7 and 4 in 8175349 is 11. Correct. Face values are the digits themselves, so the sum is \(7+4=11\), whatever their places.
(D) The sum of the place values of 3 in 3935 is 6. Incorrect. The first 3 is in the thousands place (3000) and the second in the tens place (30), so the sum of the place values is 3030; 6 is the sum of the face values.