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Test Level 1: Number System - 2 - CAT MCQ


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

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

Find the number of divisors of 1420.

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

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.

Test Level 1: Number System - 2 - Question 2

The sides of a pentagonal field (not regular) are 1737 metres, 2160 metres, 2358 metres, 1422 metres and 2214 metres respectively. Find the greatest length of the tape by which the five sides may be measured completely.

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

The sides of the pentagon being 1422, 1737, 2160, 2214 and 2358, the least difference between any two numbers is 54.
Hence, the correct answer will be a factor of 54.
Further, since there are some odd numbers in the list, the answer should be an odd factor of 54.
Hence, check with 27, 9 and 3 in that order. You will get 9 as the HCF.

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Test Level 1: Number System - 2 - Question 3

A milkman has three different qualities of milk. 403 gallons of 1st quality, 465 gallons of 2nd quality and 496 gallons of 3rd quality. Find the least possible number of bottles of equal size in which different milk of different qualities can be filled without mixing.

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

The HCF of the given numbers is 31 and hence the number of bottles required would be
403/31 + 465/31 + 496/31 = 13 + 15 + 16 = 44.
Option (d) is correct.

Test Level 1: Number System - 2 - Question 4

Find the least number that when divided by 16, 18 and 20 leaves a remainder 4 in each case, but is completely divisible by 7.

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

The LCM of 16, 18 and 20 is 720. The numbers which would give a remainder of 4, when divided by 16, 18 and 20 would be given by the series: 724, 1444, 2164, 2884 and so on.
Checking each of these numbers for divisibility by 7, it can be seen that 2884 is the least number in the series that is divisible by 7 and hence is the correct answer.
Option (d) is correct.

Test Level 1: Number System - 2 - Question 5

The units digit of the expression 125813 × 5533703 × 4532828 is

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

5 × 7 × 6 = 0. Option (c) is correct.
please learn cyclicity of power
125813 unit digit will be 5
5533703   unit digit will be 3703/4  calculated as remainder will be 3 so 33 will be 27 so unit digit will be 7
4532828  unit digit will be calculate as 828/4 remainder will be 0 so unit digit 2

Test Level 1: Number System - 2 - Question 6

Which of the following is not a perfect square?

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

All these numbers can be verified to not be perfect squares. Option (d) is correct.

Test Level 1: Number System - 2 - Question 7

The LCM of 5, 8,12, 20 will not be a multiple of

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

It is obvious that the LCM of 5,8,12 and 20 would never be a multiple of 9.
At the same time it has to be a multiple of each of 3, 8 and 5. Option (b) is correct.

Test Level 1: Number System - 2 - Question 8

GCD of x2 – 4 and x2 + x – 6 is

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

x2 – 4 = (x – 2) (x + 2) and x2 + x – 6 = (x + 3)(x – 2) GCD or HCF of these expressions = (x – 2).
Option (b) is correct.

Test Level 1: Number System - 2 - Question 9

Find the remainder when the number 9100 is divided by 8.

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

9100/8 = (8 + 1)100/8 → Since this is of the form (a + 1)n/a, the Remainder = 1. Option (a) is correct.

Test Level 1: Number System - 2 - Question 10

Decompose the number 20 into two terms such that their product is the greatest.

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

The condition for the product to be the greatest is if the two terms are equal. Thus, the break up in option (a) would give us the highest product of the two parts.
Option (a) is correct.

Test Level 1: Number System - 2 - Question 11

Which of the following can be a number divisible by 24?

Detailed Solution for Test Level 1: Number System - 2 - Question 11

Checking each of the options it can be seen that the value in option (c)[viz: 1362480]is divisible by 24.

Test Level 1: Number System - 2 - Question 12

Some birds settled on the branches of a tree. First, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?

Detailed Solution for Test Level 1: Number System - 2 - Question 12

When the birds sat one on a branch, there was one extra bird. When they sat 2 to a branch one branch was extra.
To find the number of branches, go through options. Checking option (a), if there were 3 branches, there would be 4 birds. (this would leave one bird without branch as per the question.)
When 4 birds would sit 2 to a branch there would be 1 branch free (as per the question).
Hence, the answer (a) is correct.

Test Level 1: Number System - 2 - Question 13

The square of a number greater than 1000 that is not divisible by three, when divided by three, leaves a remainder of

Detailed Solution for Test Level 1: Number System - 2 - Question 13

The number would either be (3n + 1)2 or (3n + 2)2. In the expansion of each of these the only term which would not be divisible by 3 would be the square of 1 and 2 respectively.
When divided by 3, both of these give 1 as remainder. 

Test Level 1: Number System - 2 - Question 14

The sum of the squares of the digits constituting a positive two-digit number is 13. If we subtract 9 from that number, we shall get a number written by the same digits in the reverse order. Find the number.

Detailed Solution for Test Level 1: Number System - 2 - Question 14

For the sum of squares of digits to be 13, it is obvious that the digits should be 2 and 3.
So the number can only be 23 or 32.
Further, the number being referred to has to be 32 since the reduction of 9, reverses the digits.

Test Level 1: Number System - 2 - Question 15

The product of a natural number by the number written by the same digits in the reverse order is 2430. Find the numbers.

Detailed Solution for Test Level 1: Number System - 2 - Question 15

trying the value in the options you get that the product of 54 × 45 = 2430. Option (a) is correct.

Test Level 1: Number System - 2 - Question 16

Find the pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13.

Detailed Solution for Test Level 1: Number System - 2 - Question 16

The pairs given in option (d) 78 and 13 and 26 and 39 meet both the conditions of LCM of 78 and HCF of 13.
Option (d) is correct.

Test Level 1: Number System - 2 - Question 17

A hundred and twenty digit number is formed by writing the first x natural numbers in front of each other as 12345678910111213… Find the remainder when this number is divided by 8.

Detailed Solution for Test Level 1: Number System - 2 - Question 17

The last 3 digits of the number would determine the remainder when it is divided by 8.
The number upto the 120th digit would be 1234567891011… 646.
646 divided by 8 gives us a remainder of 6.

Test Level 1: Number System - 2 - Question 18

In an exam, a candidate attempts 20 questions and scores 72 marks. If 5 marks are awarded for each correct answer and 2 marks are deducted for each wrong answer, then how many questions were answered correctly by him?

Detailed Solution for Test Level 1: Number System - 2 - Question 18

Given:

A candidate attempts 20 questions and scores 72 marks.

The marks awarded for the correct answer is 5.

Marks deducted for the wrong answer is 2.

Concept Used:

Total Marks = Number of question correct × marks given for correct answer - Number of question wrong × marks deduct for wrong answer

Calculation:

Let the number of question answer correct be x.

The number of question answer wrong = 20 - x

Total marks = 72

⇒ 5 × x - (20 - x) × 2 = 72

⇒ 5x - 40 + 2x = 72

⇒ 7x = 112

⇒ x = 16

∴ The questions were answered correctly by him is 16.

Test Level 1: Number System - 2 - Question 19

Three mangoes, four guavas and five watermelons cost ₹750. Ten watermelons, six mangoes and 9 guavas cost ₹1580. What is the cost of six mangoes, ten watermelons and 4 guavas?

Detailed Solution for Test Level 1: Number System - 2 - Question 19

3M + 4G + 5W = 750 (i)
6M + 9G + 10W = 1580 (ii)
Adding the two equations we get:
9M + 13G + 15W = 2330 (iii)
Dividing this expression by 3 we get:
3M + 4.33G + 5W =776.666
(iv) - (i) → 0.33 G = 26.666 Æ G = 80
Now, if we look at the equation (i) and multiply it by 2, we get: 6M + 8G + 10W = 1500.
If we subtract the cost of 4 guavas from this we would get: 6M + 4G + 10W = 1500 – 320 = 1180
Option (b) is correct.

Test Level 1: Number System - 2 - Question 20

A number when divided by 2, 3 and 4 leaves a remainder of 1. Find the second lowest number (not counting 1) that satisfies this requirement.

Detailed Solution for Test Level 1: Number System - 2 - Question 20

The number would be given by the 2 × (LCM of 2, 3 and 4) + 1 → which is 24 + 1 = 25.
Option (a) is correct.

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