 # Problems on Numbers System: Level 01

1. Which of the following is an odd prime number?
1. 1
2. 9
3. 3
4. 15

Among the given options, 3 is an odd prime number. Therefore, the answer is option 3.
2. What least digit should come in place of # in the 9 digit number 15549#325, for which the number is divisible by 3?
1. 0
2. 1
3. 2
4. Any of these

A number if divisible by 3 if sum of digits is multiple of 3. In 15549#325,
Sum of the digits= 1 + 5 + 5 + 4 + 9 + # + 3 + 2 + 5 = 34 + # = 34 + 2 = 36 which is divisible by 3.
3. What is the product of smallest 15 whole numbers?
1. 1
2. 0
3. 25
4. 60

Smallest 15 whole numbers are 0, 1, 2, 3, 4,.....14. As these numbers contain a zero, so, product will be zero. So, answer is option 2.
4. What is the sum of first 10 perfect cubes?
1. 3025
2. 5625
3. 1225
4. None of these

Sum of 1st 10 perfect cubes :- = 13 + 23 + 33 ______ + 103 = (10(10+1)/2)2 = 3025 Hence, the correct answer is option 1
5. What is the difference between the greatest 5 digit number and the smallest 5 digit number?
1. 99998
2. 89999
3. 89990
4. 99990

The greatest 5 digit number = 99999
Smallest 5 digit number = 10000.
The required difference = 99999 – 10000 = 89999
So, the answer is option 2.
1. There are 20 people in a party. If every person shakes hand with every other person, what is the total number of handshakes?
1. 180
2. 155
3. 145
4. 190

1st person will shake hand with 19 other persons. 2nd person will shake hand with remaining 18 persons, and so on.
Therefore, total number of handshakes.
= 19 + 18 + 17+ ……………………+ 3 + 2 + 1 = Σ19 =(19(19+1)/2) =190
So, the correct answer is option 4.
2. A 107 digit number is formed by writing first 58 natural numbers next to each other. Find the remainder when number is divided by 8.
1. 6
2. 10
3. 4
4. 9

To find remainder by 8, we only divide the number formed by the last 3 digit by 8. The last 3 digits would give the number 758. The remainder when 758 is divided by 8 = 6. So, answer is option 1.
3. The five digit number 7500A8 is divisible by 4. How many values of A are possible?
1. 0
2. 3
3. 5
4. 4

To find divisibility by 4, we need to consider last two digits of the number, these should be divisible by 4. Hence, A can take values equal to 0, 2, 4, 6 and 8. Therefore 5 values are possible. So, the correct answer is option 3.
4. What is the sum of this series 1 + 1 + 2 + 8 + 3+ 27 + 4 + 64 +_______10 + 1000?
1. 308
2. 3008
3. 3800
4. 3080