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1. How many keystrokes are needed to type numbers from 1 to 1000?

A. 3001

B. 2893

C. 1608

D. 4890

**Answer : ****2893**

While typing numbers from 1 to 1000, you have 9 single digit numbers from 1 to 9. Each of them require one keystroke. That is 9 key strokes.

There are 90 two-digit numbers, from 10 to 99. Each of these numbers require 2 keystrokes. Therefore, you require 180 keystrokes to type the 2 digit numbers.

There are 900 three-digit numbers, from 100 to 999. Each of these numbers require 3 keystrokes. Therefore, you require 2700 keystrokes to type these 3 digit numbers.

Then 1000 is a four-digit number which requires 4 keystrokes.

Totally, therefore, one requires 9 + 180 + 2700 + 4 = 2893 keystrokes.

2. If a number is divided by 84, the remainder is 37. What will be the remainder if it is divided by 21 ?

A. 18

B. 16

C. 63

D. 58

**Answer : ****16**

If the number is divided by 84 and 37 is the remainder then that number will be the addition of those two numbers.

Hence the number is 84+37 = 121. If 121 is divided by 21, we will get the remainder 16.

Tip: Finding the number which is being divided.

3. The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 less than the original number. Find the original number.

A. 45

B. 36

C. 54

D. 63

**Answer : ****54**

All the given options satisfy the first condition. (The sum of digits is 9). But 54 can only be the actual number which satisfies the second condition also.

Reversing 54 --> 45 (Which is 9 less than 54)

So, the actual number must be 54.

Tip: It is better to find the solution from the options rather than trying for all the possibilities.

4. Division of a natural number by another natural number gives

A. a natural number

B. an integer

C. a rational number

D. an irrational number

**Answer : ****a rational number**

Division of a natural number with another natural number will give us an integer or a fraction. These outcomes are specified as rational numbers.

Information: In mathematics, A rational number is a number that can be written as a simple fraction (i.e. as a ratio).

Example: 1.5 is a rational number because 1.5 = 3/2 (it can be written as a fraction) The square root of 2 cannot be written as a simple fraction. So, it is irrational number.

5. A prime number greater than 11 will never end with

A. 5

B. 7

C. 9

D. 1

**Answer : ****5**

The Number ends with 5 will be always divisible by 5. So, it can not be a prime number ever.

Whereas there are possibilities for another options to be prime numbers,

For 9 --> 19, For 7 --> 17, For 1 --> 31

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