**Which of the following is an odd prime number?**1. 12. 93. 34. 15**Suggested Action**Answer : Option 3

Among the given options, 3 is an odd prime number. Therefore, the answer is option 3.**What least digit should come in place of # in the 9 digit number 15549#325, for which the number is divisible by 3?**1. 02. 13. 24. Any of theseAnswer : Option 3

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.**What is the product of smallest 15 whole numbers?**1. 12. 03. 254. 60Answer : Option 2

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.**What is the sum of first 10 perfect cubes?**1. 30252. 56253. 12254. None of theseAnswer : Option 1

Sum of 1^{st}10 perfect cubes :- = 1^{3}+ 2^{3}+ 3^{3}______ + 10^{3}= (10(10+1)/2)^{2}= 3025 Hence, the correct answer is option 1**What is the difference between the greatest 5 digit number and the smallest 5 digit number?**1. 999982. 899993. 899904. 99990Answer : Option 2

The greatest 5 digit number = 99999

Smallest 5 digit number = 10000.

The required difference = 99999 – 10000 = 89999

So, the answer is option 2.

Must Read Problems on Numbers System Articles

- Problems on Numbers System: Level 01
- Problems on Numbers System : Level 02

**There are 20 people in a party. If every person shakes hand with every other person, what is the total number of handshakes?**1. 1802. 1553. 1454. 190Answer : Option 4

1^{st}person will shake hand with 19 other persons. 2^{nd}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.**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. 62. 103. 44. 9Answer : Option 1

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.**The five digit number 7500A8 is divisible by 4. How many values of A are possible?**1. 02. 33. 54. 4Suggested Action:Answer : Option 3

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.**What is the sum of this series 1 + 1 + 2 + 8 + 3+ 27 + 4 + 64 +_______10 + 1000?**1. 3082. 30083. 38004. 3080Answer : Option 4

Here, we are given a combination of two series

(1 + 2 + 3 + 4 +.....................+10) + (1 + 8 + 27 + 64 +............+1000)

= (1 + 2 + 3 + 4 +.....................+10) + (1^{3}+2^{3}+3^{3}+4^{3}+.................+10^{3})

(10(10+1)/2) + ((10 × 11)/2)^{2}= 3080. So, correct answer is option 4.**Which one of the following is not a rational number?**1. 0.23332. 0.566663. √34. 7Answer : Option 3

Here, 0.2333, 0.56666 and 7 are rational numbers as these can be represented in the form p/q.√3 is not a rational number, therefore answer is option 3.