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This mock test of Arun Sharma Test: Number System- 2 for CAT helps you for every CAT entrance exam.
This contains 15 Multiple Choice Questions for CAT Arun Sharma Test: Number System- 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

What is the difference between the Place Value and Face Value of 9 in 798652?

Solution:

► Face Value of any number remains the Same irrespective of the place, for 9 it is 9

► Place Value = Place Multiplier x Face Value

⇒ 10000 x 9

⇒ 90000

► Place Value - Face Value = 90000 - 9 = 89991

QUESTION: 2

Convert in p/q form

Solution:

► All the digits written once = 1762125

► All the digits without Bar written once = 1762

► No. of digits with bar after decimal = 3

► No. of digits without bar after decimal = 1

Rational form =

QUESTION: 3

(a^{2} + 2ab + b^{2}) will fall under which of the categories, a and b are Integers

Solution:

► There are 4 case in the same

► __Case 1__ : a and b both are odd

⇒ a^{2} + 2ab + b^{2}

⇒ Odd^{2} + 2 x Odd x Odd +Odd^{2}

⇒ Odd + Even + Odd

⇒ Even

►__Case 2__ : a and b both are even

⇒ a^{2 }+ 2ab + b^{2}

⇒ Even^{2} + 2 × Even × Even + Even^{2}

⇒ Even + Even + Even

⇒ Even

► __Case 3__ : a is odd and b is even

⇒ a^{2} + 2ab + b^{2}

⇒ Odd^{2} + 2 x Odd x Even + Even^{2}

⇒ Odd + Even + Even

⇒ Odd

► __Case 4__ : a is even and b is odd

⇒ a^{2} + 2ab + b^{2}

⇒ Even^{2} + 2 × Even × Odd + Odd^{2}

⇒ Even + Even + Odd

⇒ Odd

► In 2 Cases its Odd and in other 2 it is Even, so we cannot say anything about the answer.

QUESTION: 4

If (6a + 12) is odd then 'a' would be, a is an Integer

Solution:

► There are two possibilities for a

► __Case 1:__ a is even

⇒ 6a = Even x Even = Even

⇒ 6a + 12 = Even + Even = Even

► __Case 2:__ a is odd

⇒ 6a = Even x Odd = Even

⇒ 6a + 12 = Even + Even = Even

► In both the cases the answer is even, so the information provided is inconsistent.

QUESTION: 5

(abc) is odd what would (a^{2} + b^{2} + c^{2}) be, a, b and c are Integers.

Solution:

► For abc to be Odd the only case possible is none of them being Even i.e. a, b and c all three are Odd

⇒ a^{2} + b^{2} + c^{2}

⇒ Odd^{2} + Odd^{2} + Odd^{2}

⇒ Odd + Odd + Odd

⇒ Odd

Vice versa can also be true

QUESTION: 6

What is the smallest positive Even Rational Number?

Solution:

► Option A : 0, It is even and rational but not positive

► Option B : 1, it is positive and rational but odd

► Option C : 2, it is even positive and rational. Also the smallest

► Option D : 4, it is even, positive and rational but not the smallest

QUESTION: 7

How many prime numbers are there between 25 and 75?

Solution:

► There are 12 prime numbers between 25 and 75 as listed below:

QUESTION: 8

Which is the largest Even Prime number?

Solution:

► There is only one Even prime number i.e. 2.

QUESTION: 9

Which of the following is a prime number?

Solution:

► We know the property that a prime number when divided by 6 gives a remainder of 1 or 5.

► Option A : 8831 divided by 6 gives a remainder of 5

► Option B : 8829 divided by 6 gives a remainder of 3

► Option C : 8833 divided by 6 gives a remainder of 1, but is divisible by 11

► Option D : 8835 divided by 6 gives a remainder of 3

QUESTION: 10

If a and b are odd numbers, which of the following is surely even?

Solution:

► Option A : a^{2} + b^{2} = Odd^{2} + Odd^{2} = Odd + Odd = Even

► Option B : a^{2} + 2b^{2} = Odd^{2 }+ Even × Odd^{2 }= Odd + Even = Odd

► Option C ∶ 2a^{2} + b^{2} = Even × Odd^{2} + Odd^{2} = Even + odd = Odd

► Option D ∶ a^{2} + b^{2} + ab = Odd^{2} + Odd^{2} + Odd × Odd = Odd + Odd + Odd = Odd

QUESTION: 11

Sum of any 50 consecutive 4 digit Whole numbers would always be:

Solution:

► Sum of Any Consecutive 50 Whole Numbers

⇒ Sum of 25 Even Numbers + Sum of 25 Odd Numbers

⇒ Even + Odd

⇒ Odd

QUESTION: 12

The sum of first 10 Prime numbers is

Solution:

► First 10 Prime numbers are listed Below :

► Their sum = 129

QUESTION: 13

How many Prime numbers less than 1000 are divisible by 17?

Solution:

► Being Prime numbers any number would be divisible by 1 or itself.

► Since 17 is a prime number. It will be the only prime number less than 1000 which will be divisible by 17.

QUESTION: 14

How many Prime numbers less than 1000 are divisible by 16?

Solution:

► Being Prime numbers any number would be divisible by 1 or itself.

► Since 16 is not a prime number. There would be no other prime number divisible by 16.

QUESTION: 15

How many pairs of consecutive odd prime numbers are there less than 200?

Solution:

► The List of such pairs is listed below:

(3,5); (5,7); (11,13); (17,19); (29,31); (41,43); (59,61); (71,73), (101,103); (107,109); (137,139); (149,151); (179,181); (191,193); (197,199)

► 15 Such pairs exist.

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