# Aptitude - Number System

### MCQ

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Q 41.

If the sum of 4 consecutive even number is 268 then what is the smallest number?

Options:

• 62

• 64

• 68

• 60

Let the 4 consecutive even number be x, x+2, x+4, x+6.

Given, x + (x+2) + (x+4) + (x+6) = 268

Or, x = 64

Q 42.

What least number must be added to 2270 to get a number exactly divisible by 23?

Options:

• 5

• 6

• 7

• 8

2270/23 gives remainder 16.

Required least number = 23 - 16 = 7

Q 43.

How many rational numbers are there between 100 and 1000?

Options:

• 100

• 900

• Infinite

• 1000

There are infinite number of rational numbers between any to given numbers.

Q 44.

The sum of 5 consecutive even numbers is 70. What is the product of the first and the last number?

Options:

• 160

• 170

• 180

• 190

Let the 5 consecutive even numbers be x, x+2, x+4, x+6 and x+8.

Given, x + (x+2) + (x+4) + (x+6) + (x+8) = 70

Or, x = 10

So, first number = x = 10

And the last number = x+8 = 18

Product = 10x18 = 180

Q 45.

Find the unit digit in (987)754

Options:

• 6

• 7

• 8

• 9

(987)754

Consider only the unit digit

= (7)754

= (74)188 x (7)2

= (2401)188 x 49

= (1)188 x 9

= 9

Q 46.

Find the unit digit in the product of 123x456x789.

Options:

• 1

• 2

• 3

• 4

123x456x789

= 3x6x9 (taking only the unit digit)

= 162

= 2 (Unit digit)

Q 47.

On Salman's birthday Aamir gifted a golden box that was locked with a secret password. Salman can only open the box if he enters the correct password. Aamir loves to play with numbers so he locked the box with a natural number and wrote a riddle on a piece of paper and gifted it along with the golden box. Salman being busy that day asked you to solve the riddle and unlock the box for him.

Riddle: If 1/4 of a number is subtracted from the number itself, it will give a value which is equal to the sum of all the angles of the Bermuda Triangle.

Options:

• 210

• 220

• 230

• 240

Sum of all the angles of a triangle = 180

Let the required number be P.

As per the riddle, P - 1/4P = 180

Or, P = 240

Q 48.

Sum of first 10 natural numbers is?

Options:

• 55

• 100

• 45

• 10

n = 10

Sum = n(n+1)/2 = 55

Q 49.

What is the product of 3rd natural, 2nd prime, 1st whole number?

Options:

• 9

• 6

• 0

• Infinite

3rd natural number = 3

2nd prime number = 3

1st whole number = 0

Product = 3x3x0 = 0

Q 50.

What is the sum of 1st and 2nd prime numbers?

Options:

• 1

• 2

• 3

• 5

1st prime number = 2

2nd prime number = 3

Sum = 2+3 = 5

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