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This contains 15 Multiple Choice Questions for CAT Arun Sharma Test: Number System- 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

What is the Place Value and Face Value of 7 in 78654?

Solution:

Face Value of any number remains the same irrespective of the place, for 7 it is 7

Place Value = Place Multiplier x Face Value

= 10000 x 7

= 70000

QUESTION: 2

In which one of the following is the Place Value of 9 highest?

Solution:

**Option A:**Place value of 9 = 9 x 1000 = 9000**Option B:**Place value of 9 = 9 x 100 = 900**Option C:**Place value of 9 = 9 x 1 = 9**Option D:**Place value of 9 = 9 x 10 = 90

QUESTION: 3

What is the Base of Hexadecimal Number System?

Solution:

**(a)** 8 is the Base of Octal Number System

**(b)** 16 is the Base of **Hexadecimal Number System**

**(c)** 2 is the Base of Binary Number System

**(d)** 10 is the Base of Decimal Number System

QUESTION: 4

Which of the following is a Real Number but not a Rational Number?

Solution:

**(a)** −√4 = −2 is a Real Number as well as a Rational Number

**(b)** −√3 is a **Real number **and an **irrational number**

**(c)** √−4 is an imaginary number

QUESTION: 5

Convert in p/q form

Solution:

► All the digits written once = 2116

► All the digits without Bar written once = 21

► Number of digits with bar after decimal = 2

► Number of digits without bar after decimal = 0

► Rational form =

QUESTION: 6

√16 will not fall under which of the following categories?

Solution:

► √16 = 4, which is a **natural number**, **rational number **as well as a **real number**.

QUESTION: 7

(16a + 6) will fall under which of the following categories, a is an Integer

Solution:

(16a + 6) will always be even, whether the a is odd or even.

**For a = 1 (odd)**

(16 * 1) + 6 = 16 + 6 = 22 (even)**For a = 2 (even)**

(16* 2) + 6 = 32 + 6 = 38 (even)

QUESTION: 8

If (7a - 3) is odd then 'a' would be, a is an Integer

Solution:

As it is given, 7a - 3 is odd

⇒ 7a = odd +3 **i.e. **even (say, x)

∵ a is an integer

⇒ For 7a = x, x should be completely divisble by 7

⇒ a = x/7 **i.e.** even/odd = even

QUESTION: 9

What is the smallest possible positive Integer?

Solution:

**Option A:**0 is an integer but not positive(it is neutral).**Option B:**1 is an**integer**also**positive**and the**smallest**.**Option C:**0.5 is not even an integer.**Option D:**2 is an integer as well as positive but not the smallest.

QUESTION: 10

Which of the following is a prime number?

Solution:

**Option A:**93 is divisible by 3**Option B:**97 is**not perfectly divisible**by any number.**Option C:**95 is divisible by 5**Option D:**91 is divisible by 7

QUESTION: 11

1837 × 1712 × 1839 will be

Solution:

We do not need to do the multiplication in this question.

► 1837 is Odd

► 1712 is Even

► 1839 is Odd

**Odd x Even x Odd = Even**

Only option 1 is Even rest all are Odd.

QUESTION: 12

Largest 3 digit composite number is

Solution:

► 999 is the Largest composite number, it is divisible by 1, 3, 9, 111, 333, 999.

QUESTION: 13

What is the difference between 517^{th} Whole number and 516^{th} Natural Number?

Solution:

► 517^{th} Whole number = 516

► 516^{th} Natural Number = 516

- 516 - 516 = 0

QUESTION: 14

Smallest Composite numbers is______.

Solution:

► Prime and Composite are properties of Natural numbers.

► 0 is not a natural number.

► 1 is neither prime nor composite.

► 2 is a prime number divisible by 1 and 2 only.

► 4 is a composite number divisible by 1,2 and 4. Smallest among all.

QUESTION: 15

How many pairs of consecutive prime numbers are there?

Solution:

► Only pair of consecutive prime numbers is (2, 3)

Consecutive (difference is 1) ==> only pair possible is (2,3), no other pair possible since 2 is the only even prime, any other 2 consecutive numbers will have an even number, which is not prime.

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