CAT Exam  >  CAT Tests  >  Test Level 2: Number System - 1 - CAT MCQ

Test Level 2: Number System - 1 - CAT MCQ


Test Description

10 Questions MCQ Test - Test Level 2: Number System - 1

Test Level 2: Number System - 1 for CAT 2024 is part of CAT preparation. The Test Level 2: Number System - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Number System - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Number System - 1 below.
Solutions of Test Level 2: Number System - 1 questions in English are available as part of our course for CAT & Test Level 2: Number System - 1 solutions in Hindi for CAT course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt Test Level 2: Number System - 1 | 10 questions in 20 minutes | Mock test for CAT preparation | Free important questions MCQ to study for CAT Exam | Download free PDF with solutions
Test Level 2: Number System - 1 - Question 1

How many digits are required to number a book containing 200 pages?

Detailed Solution for Test Level 2: Number System - 1 - Question 1

Total number of pages = 200
Number of digits required to number the book from page 1 to 9 = 9
Number of digits required to number the book from page 10 to 99 = 2 × 90 = 180
Number of digits required to number the book from page 100 to 200 = 3 × 101 = 303
Therefore, total number of digits = 303 + 180 + 9 = 492

Test Level 2: Number System - 1 - Question 2

If X381 is divisible by 11 and 381Y is divisible by 9, find the smallest values of X and Y.

Detailed Solution for Test Level 2: Number System - 1 - Question 2

(i) X381 is the number given to us. If this number is divisible by 11, then the divisibility rule for 11 must be satisfied.
i.e. (X + 8) - (3 + 1) = (X + 4) is multiple of 11 and the smallest value of X for which X + 4 is divisible by 11 is 7. Hence, X = 7
(ii) 381Y is the number given to us. If this number is divisible by 9, then the divisibility rule for 9 must be satisfied.
i.e. (3 + 8 + 1 + Y) = Y + 12 must be divisible by 9. And smallest value of Y for which Y + 12 is divisible by 9 is 6. Hence, Y = 6

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test Level 2: Number System - 1 - Question 3

If the sum of any two positive quantities is constant, then their product is maximum when the two quantities

Detailed Solution for Test Level 2: Number System - 1 - Question 3

If the sum of two quantities is constant, then their product is maximum when they are equal.
Alternative Method:
Let X + Y = K
(X + Y)2 - (X - Y)2 = 4XY
K2 - (X - Y)2 = 4XY
⇒ 4XY < K2 (except when X - Y = 0)
Or,
X = Y
⇒ 4XY is maximum when X = Y.
⇒ XY is maximum when X = Y = (K/2)
Thus, the maximum value of XY = (K2/4)

Test Level 2: Number System - 1 - Question 4

If p, q, r, s and t are integers, which of the following must be even for the expression p2{q3(r - s) + t} to be an even number?

Detailed Solution for Test Level 2: Number System - 1 - Question 4

The expression is of the form p2X, where X = {q3(r - s) + t}.
So, whenever p is even, the product will be even, irrespective of whether the second number X is odd or even. So, p must be even.

Test Level 2: Number System - 1 - Question 5

If P, Q and R are three consecutive integers, then which of the following is always true?

Detailed Solution for Test Level 2: Number System - 1 - Question 5

The sum of two extreme numbers (whether both odd/even) and twice the 3rd number is always even.
Therefore, their sum is always even.
Alternative:
If P and R are odd and Q is even, then P + R is even and 2Q is even.
P + 2Q + R is even
If P and R is even and Q is odd, then P + R is even and 2Q is even.
P + 2Q + R is even.

Test Level 2: Number System - 1 - Question 6

Two positive whole numbers are such that the sum of the first and twice the second is 8 and the difference between the numbers is 2. The numbers are:

Detailed Solution for Test Level 2: Number System - 1 - Question 6

Let the first number be x and the second number be y.
Then, x + 2y = 8 and x - y = 2
x + 2(x - 2) = 8
x + 2x - 4 = 8
3x = 12
x = 4
Since x - y = 2, this implies that y = 2.

Test Level 2: Number System - 1 - Question 7

A lady says that her age will be 18 years if only weekend days are counted. What is her actual age?

Detailed Solution for Test Level 2: Number System - 1 - Question 7

If only weekend days are counted, only 2/7 portion of the whole week is calculated to arrive at her age.
So, 18 years of age = 2/7 (Actual age) ⇒ Actual age = 63 years

Test Level 2: Number System - 1 - Question 8

Find the last digit of (173)99.

Detailed Solution for Test Level 2: Number System - 1 - Question 8

31 = 3, 32 = 9, 33 = 27, 34 = 81 and 35 = 81 × 3 = 243.
Use the concept of power cycle (units digit repeats after the power of 4 and then after all powers that are multiples of 4).
Now, 99 = 24 × 4 + 3
Thus, 99 has 24 complete cycles of 4 and 3 is left as the remainder.
So, units digit of (173)99 will be units digit of 33, which is 7.

Test Level 2: Number System - 1 - Question 9

What is the right most non-zero digit of 1378000013780000?

Detailed Solution for Test Level 2: Number System - 1 - Question 9

The required answer is nothing but the last digit of 813780000.
We know that, the cyclicity of 8 is 4. 
As 13780000 is divisible by 4 (cyclicity of 8).
That is, the last digit of 84 = 6

Test Level 2: Number System - 1 - Question 10

The highest factor of 1573, except itself, is

Detailed Solution for Test Level 2: Number System - 1 - Question 10

1573 = 11 × 143
= 11 × 11 × 13
So, highest factor = 11 × 13 = 143

Information about Test Level 2: Number System - 1 Page
In this test you can find the Exam questions for Test Level 2: Number System - 1 solved & explained in the simplest way possible. Besides giving Questions and answers for Test Level 2: Number System - 1, EduRev gives you an ample number of Online tests for practice

Top Courses for CAT

Download as PDF

Top Courses for CAT