CAT Exam  >  CAT Tests  >  Quantitative Aptitude (Quant)  >  Arun Sharma Test: Number System- 2 - CAT MCQ

Arun Sharma Test: Number System- 2 - CAT MCQ


Test Description

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

Arun Sharma Test: Number System- 2 for CAT 2025 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 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Arun Sharma Test: Number System- 2 below.
Solutions of Arun Sharma Test: Number System- 2 questions in English are available as part of our Quantitative Aptitude (Quant) for CAT & Arun Sharma Test: Number System- 2 solutions in Hindi for Quantitative Aptitude (Quant) course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt Arun Sharma Test: Number System- 2 | 15 questions in 20 minutes | Mock test for CAT preparation | Free important questions MCQ to study Quantitative Aptitude (Quant) for CAT Exam | Download free PDF with solutions
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 that (1025 - 7) - (1024 + x) is divisible by 3:

  • Start with the expression: 1025 - 7 - 1024 - x.
  • Factor out 1024:
    • Resulting in: 1024(10 - x) - 7.
  • The simplified form is: 9 × 1024 - 7 - x.

For the expression to be divisible by 3, we find:

  • Setting 9 × 1024 - 7 - x equal to 0 modulo 3.
  • We can derive that the 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 = 10000x
All the digits without Bar written once = 1762.125 = 10x
Rational form = 

Arun Sharma Test: Number System- 2 - Question 3

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

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

► 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, but the question says its odd. so, the information provided is inconsistent.

Arun Sharma Test: Number System- 2 - Question 4

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

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

Therefore, the last two digits of the multiplication 122×123×125×127×129 are: 50

Arun Sharma Test: Number System- 2 - Question 5

(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 5

► 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 6

Which is the largest Even Prime number?

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

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

Arun Sharma Test: Number System- 2 - Question 7

Which of the following is a prime number?

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

► 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 8

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

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

► 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 9

Find the LCM of 5/2, 8/9, 11/14.

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

LCM of 5/2, 8/9 and 11/14 would be given by: (LCM of numerators)/(HCF of denominators) =440/1 =440

Arun Sharma Test: Number System- 2 - Question 10

Two numbers P = 23.310.5 and Q = 25.31.71 are given. Find the GCD of P and Q.

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

For the GCD, take the least powers of all common prime factors.

Arun Sharma Test: Number System- 2 - Question 11

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

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

► 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 12

Find the number of divisors of 1420.

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

1420=142 × 10=22×711×51.
Thus, the number of factors of the number would be (2+1)(1+1)(1+1)=3×2×2=12.
Option (d) is correct.

Arun Sharma Test: Number System- 2 - Question 13

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

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

► 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 14

Find the number of divisors of 720 (including 1 and 720).

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

720= 24 × 32 × 51. Number of factors = 5 × 3 × 2 = 30. Option (d) is correct.

Arun Sharma Test: Number System- 2 - Question 15

The value of the expression (153.212)/(352.34) is

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

The given expression can be written as: 53 × 33 × 32 × 72/52 × 72 × 34 = 53 × 35 × 72/52 × 7× 34 = 15.
Option (b) is correct.

183 videos|177 docs|103 tests
Information about Arun Sharma Test: Number System- 2 Page
In this test you can find the Exam questions for Arun Sharma Test: Number System- 2 solved & explained in the simplest way possible. Besides giving Questions and answers for Arun Sharma Test: Number System- 2, EduRev gives you an ample number of Online tests for practice
183 videos|177 docs|103 tests
Download as PDF