Let P = 5^5 \times 15^{15} \times 25^{25} \times 35^{35} and Q = 10^{10} \times 20^{20} \times 30^{30} \times 40^{40}. What is the number of consecutive zeros at the end of the sum (P + Q) ?

Explanation

P is a product of odd multiples of 5, thus it has no factor of 2 and ends in the digit 5. Q is a multiple of 10 and ends in 0. The sum P+Q ends in 5+0=5, hence there are zero consecutive zeros at the end.

Related questions on Arithmetic

• What is the remainder when (17^{25} + 19^{25}) is divided by 18?
• A bottle contains spirit and water in the ratio 1:4 and another identical bottle contains spirit and water in the ratio 4:1. In what rat...
• Two students X and Y appeared in a test. The score of X is 20 more than that of Y. If the score of X is 75% of the sum of the scores of X an...
• Question: The product of a natural number N and the number M written by the same digits of N in the reverse order is 252. What is the number...
• Question: The last digit in the expansion of the number (54D)^{100} is 1. What is the value of the digit D? Statement I : D > 5 Statement ...