What is the remainder when 51 x 27 x 35 x 62 x 75 is divided by 100?

When a number is divided by 100, last two digits of that number will always be remainder. For example 312/100 will give 12 as remainder or 5759 will give 59 as remainder. So our question is basically reduced to find last two digits of 51 × 27 × 35 × 62 × 75. However, present question can be solved by looking at only unit digit of the above multiplication. In the multiplication of two numbers, the unit’s place of the resultant number always be the product of the unit’s place digits of the number which are multiplying. For example, the unit’s digit of 51 × 27 will 1 × 7 = 7. In above we will get unit digit as 1 × 7 × 5 × 2 × 5 = ..0. Only matching option is (a).