If a person makes a row of toys of 20 each, there would be 15 toys left. If they made to stand in rows of 25 each, there would be 20 toys left, if they made to stand in rows of 38 each, there would be 33 toys left and if they are made to stand in rows of 40 each, there would be 35 toys left. What is the minimum number of toys the person have?

Answer: D The product of 4 consecutive 4 numbers is always divisible by 4!. Since, we have 4 even numbers, we have an additional 2 available with each number. It is always divisible by (2^{4})4! = 16(24) = 384.

Answer: A when we take successive powers of 2 and find their remainders, we get the following cyclic patterns of cycle length 11. viz 2,4,8,16,32,64,39,78,67,45, 1 i.e 2^{11} leaves a remainder 1.Thus 2^{89} = (2^{11})^{8} (2) leaves a remainder of 2.

Q. No. 5:

In a meet, persons from five different places have assembled in Bangalore High School. From the five places the persons come to represent are 42,60,210,90 and 84. What is the minimum number of rooms that would be required to accommodate so that each room has the same number of occupants and occupants are all from the same places?

Answer: C All the students from each have to be accommodated in a certain number of rooms. there should be no person left over(remainder) from any places who can be clubbed together with the persons left over from other places. To have the minimum number of rooms, the capacity of each rooms is HCF of all the numbers. HCF(42,60,210,90,84) = 6 Thus Min number of rooms = (42+60+210+90+84)/6 = 81.

Q. No. 6:

When writing numbers from 1 to 10,000, how many times is the digit 9 written?

Answer: C The digits 9 occurs in the thousands place in 1000 numbers. It occurs in the hundreds place in 1000 numbers and so on The digit occurs 4000 times.