Arun Sharma Test: Number System- 2 - CAT MCQ

# Arun Sharma Test: Number System- 2 - CAT MCQ

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## 15 Questions MCQ Test Quantitative Aptitude (Quant) - Arun Sharma Test: Number System- 2

Arun Sharma Test: Number System- 2 for CAT 2024 is part of Quantitative Aptitude (Quant) preparation. The Arun Sharma Test: Number System- 2 questions and answers have been prepared according to the CAT exam syllabus.The Arun Sharma Test: Number System- 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Arun Sharma Test: Number System- 2 below.
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Arun Sharma Test: Number System- 2 - Question 1

### If the difference of (1025−7) and (1024+x) is divisible by 3 then x is equal to :

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 1

Given (1025−7)−(1024+x) is divisible by 3
1025−7−1024−x
1024(10−1)−7−x
9.1924−7−x
If divisible by 3 value of x=2

Therefore, the correct option is B

Arun Sharma Test: Number System- 2 - Question 2

### Convert  in p/q form

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 2

=x
► All the digits written once = 1762125.125=1000x
► All the digits without Bar written once = 1762.125=10x
► No. of digits with bar after decimal = 3
► No. of digits without bar after decimal = 1
Rational form =

Arun Sharma Test: Number System- 2 - Question 3

### (a2 + 2ab + b2) will fall under which of the categories, a and b are Integers

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 3

► There are 4 case in the same
► Case 1 : a and b both are odd

⇒ a2 + 2ab + b2
⇒ Odd2 + 2 x Odd x Odd +Odd2
⇒ Odd + Even + Odd
⇒ Even

Case 2 : a and b both are even

⇒ a2 + 2ab + b2
⇒ Even2 + 2 × Even × Even + Even2
⇒ Even + Even + Even
⇒ Even

► Case 3 : a is odd and b is even

⇒ a2 + 2ab + b2
⇒ Odd2 + 2 x Odd x Even + Even2
⇒ Odd + Even + Even
⇒ Odd

Case 4 : a is even and b is odd

⇒ a2 + 2ab + b2
⇒ Even2 + 2 × Even × Odd + Odd2
⇒ Even + Even + Odd
⇒ Odd

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

Arun Sharma Test: Number System- 2 - Question 4

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

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 4

► 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.

Arun Sharma Test: Number System- 2 - Question 5

The last two digits in the multiplication of 122×123×125×127×129 is

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 5

Divide the given expression by 100 and the expression gets reduced to 22×23×25×27×29 . 50 would be the last two digits here.

SO, the correct option is B

Arun Sharma Test: Number System- 2 - Question 6

(abc) is odd what would (a2 + b2 + c2) be, a, b and c are Integers.

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 6

► 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

⇒ a2 + b2 + c2
⇒ Odd2 + Odd2 + Odd2
⇒ Odd + Odd + Odd
⇒ Odd

Vice versa can also be true

Arun Sharma Test: Number System- 2 - Question 7

How many prime numbers are there between 25 and 75?

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 7

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

Arun Sharma Test: Number System- 2 - Question 8

Which is the largest Even Prime number?

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 8

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

Arun Sharma Test: Number System- 2 - Question 9

Which of the following is a prime number?

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 9

► 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

Arun Sharma Test: Number System- 2 - Question 10

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

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 10

► Option A : a2 + b2 = Odd2 + Odd2 = Odd + Odd = Even
► Option B  : a2 + 2b2 = Odd2 + Even × Odd2 = Odd + Even = Odd
► Option C ∶ 2a2 + b2 = Even × Odd2 + Odd2 = Even + odd = Odd
► Option D ∶ a2 + b2 + ab = Odd2 + Odd2 + Odd × Odd = Odd + Odd + Odd = Odd

Arun Sharma Test: Number System- 2 - Question 11

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

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 11

► Sum of Any Consecutive 50 Whole Numbers

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

Arun Sharma Test: Number System- 2 - Question 12

The sum of first 10 Prime numbers is

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 12

► First 10 Prime numbers are listed Below :

► Their sum = 129

Arun Sharma Test: Number System- 2 - Question 13

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

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 13

► 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.

Arun Sharma Test: Number System- 2 - Question 14

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

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 14

► 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.

Arun Sharma Test: Number System- 2 - Question 15

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

Detailed Solution for Arun Sharma Test: Number System- 2 - Question 15

► 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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