This EduRev document offers 20 Multiple Choice Questions (MCQs) from the topic Number System (Level - 1). These questions are of Level - 1 difficulty and will assist you in the preparation of CAT & other MBA exams. You can practice/attempt these CAT Multiple Choice Questions (MCQs) and check the explanations for a better understanding of the topic.
Question for Practice Questions Level 1: Number System - 2
Try yourself:Find the number of divisors of 1420.
Explanation
1420 = 142 × 10 = 2^{2} × 71^{1} × 5^{1}.
Thus, the number of factors of the number would be (2 + 1) (1 + 1) (1 + 1) = 3 × 2 × 2 = 12.
Option (d) is correct.
Question for Practice Questions Level 1: Number System - 2
Try yourself: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.
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself: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.
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself: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.
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself:The units digit of the expression 125^{813} × 553^{3703} × 4532^{828} is
Explanation
5 × 7 × 6 = 0. Option (c) is correct.
Question for Practice Questions Level 1: Number System - 2
Try yourself:Which of the following is not a perfect square?
Explanation
All these numbers can be verified to not be perfect squares. Option (d) is correct.
Question for Practice Questions Level 1: Number System - 2
Try yourself:The LCM of 5, 8,12, 20 will not be a multiple of
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself:GCD of x^{2} – 4 and x^{2} + x – 6 is
Explanation
x^{2} – 4 = (x – 2) (x + 2) and x^{2} + x – 6 = (x + 3)(x – 2) GCD or HCF of these expressions = (x – 2).
Option (b) is correct.
Question for Practice Questions Level 1: Number System - 2
Try yourself:Find the remainder when the number 9^{100} is divided by 8.
Explanation
9^{100}/8 = (8 + 1)^{100}/8 → Since this is of the form (a + 1)^{n}/a, the Remainder = 1. Option (a) is correct.
Question for Practice Questions Level 1: Number System - 2
Try yourself:Decompose the number 20 into two terms such that their product is the greatest.
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself:Which of the following can be a number divisible by 24?
Explanation
Checking each of the options it can be seen that the value in option (c)[viz: 1362480]is divisible by 24.
Question for Practice Questions Level 1: Number System - 2
Try yourself: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?
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself:The square of a number greater than 1000 that is not divisible by three, when divided by three, leaves a remainder of
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself: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.
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself:The product of a natural number by the number written by the same digits in the reverse order is 2430. Find the numbers.
Explanation
trying the value in the options you get that the product of 54 × 45 = 2430. Option (a) is correct.
Question for Practice Questions Level 1: Number System - 2
Try yourself:Find the pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13.
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself: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.
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself:For Question 72, if it is known that he has left 10 questions unanswered, the number of correct answers are:
Explanation
Continuing the thought process for the previous question our thinking would go as follows: 10 questions unanswered → loses 12.5 marks To lose another 33 marks he needs to get 22 incorrects.
Thus, the number of corrects would be 80 – 10 – 22 = 48.
Option (b) is correct.
Question for Practice Questions Level 1: Number System - 2
Try yourself: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?
Explanation
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.
Question for Practice Questions Level 1: Number System - 2
Try yourself: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.
Explanation
The number would be given by the 2 × (LCM of 2, 3 and 4) + 1 → which is 24 + 1 = 25.
Option (a) is correct.