This EduRev document offers 10 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 - 1
Try yourself:The last digit of the number obtained by multiplying the numbers 81 × 82 × 83 × 84 × 85 × 86 × 87 × 88 × 89 will be
Explanation
The units digit in this case would obviously be ‘0’ because the given expression has a pair of 2 and 5 in it’s prime factors.
Question for Practice Questions Level 1: Number System - 1
Try yourself:When we multiply a certain two-digit number by the sum of its digits, 405 is achieved. If you multiply the number written in reverse order of the same digits by the sum of the digits, we get 486. Find the number.
Explanation
The two numbers should be factors of 405. A factor search will yield the factors. (look only for 2 digit factors of 405 with sum of digits between 1 to 19).
Also 405 = 5 × 3^{4}. Hence: 15 × 27
45 × 9 are the only two options.
From these factors pairs only the second pair gives us the desired result.
i.e. Number × sum of digits = 405.
Hence, the answer is 45.
Question for Practice Questions Level 1: Number System - 1
Try yourself:The difference between two numbers is 48 and the difference between the arithmetic mean and the geometric mean is two more than half of 1/3 of 96. Find the numbers.
Explanation
Two more than half of 1/3rd of 96 = 18. Also since we are given that the difference between the AM and GM is 18, it means that the GM must be an integer.
From amongst the options, only option (a) gives us a GM which is an integer.
Thus, checking for option 1, we get the GM = 7 and AM = 25.
Question for Practice Questions Level 1: Number System - 1
Try yourself:If 381A is divisible by 9, find the value of smallest natural number A.
Explanation
For 381A to be divisible by 9, the sum of the digits 3 + 8 + 1 + A should be divisible by 9.
For that to happen A should be 6.
Option (d) is correct.
Question for Practice Questions Level 1: Number System - 1
Try yourself:Find the ratio between the LCM and HCF of 5, 15 and 20.
Explanation
LCM of 5, 15 and 20 = 60.
HCF of 5, 15 and 20 = 5.
The required ratio is 60:5 = 12:1
Question for Practice Questions Level 1: Number System - 1
Try yourself:If the number A is even, which of the following will be true?
Explanation
Only the first option can be verified to be true in this case.
If A is even, 3A would always be divisible by 6 as it would be divisible by both 2 and 3.
Options b and c can be seen to be incorrect by assuming the value of A as 4.
Question for Practice Questions Level 1: Number System - 1
Try yourself:A number 15B is divisible by 6. Which of these will be true about the positive integer B?
Explanation
B would necessarily be even- as the possible values of B for the three digit number 15B to be divisible by 6 are 0 and 6.
Also, the condition stated in option (c) is also seen to be true in this case — as both 0 and 6 are divisible by 6.
Thus, option (d) is correct.
Question for Practice Questions Level 1: Number System - 1
Try yourself:Find the units digit of the expression 25^{6251} + 36^{528} + 73^{54}.
Explanation
The units digit would be given by 5 + 6 + 9 (numbers ending in 5 and 6 would always end in 5 and 6 irrespective of the power and 3^{54} will give a units digit equivalent to 3^{4n+2} which would give us a unit digit of 3^{2} i.e.9).
Question for Practice Questions Level 1: Number System - 1
Try yourself:Find the units digit of the expression 11^{1} + 12^{2} + 13^{3} + 14^{4} + 15^{5} + 16^{6}.
Explanation
The respective units digits for the six parts of the expression would be: 1 + 4 + 7 + 6 + 5 + 6 = 29 → required answer is 9.
Option (b) is correct.
Question for Practice Questions Level 1: Number System - 1
Try yourself:Find the number of zeroes at the end of 1090!
Explanation
The number of zeroes would be given by adding the quotients when we successively divide 1090 by 5 : 1090/5 + 218/5 + 43/5 + 8/5 = 218 + 43 + 8 + 1 = 270. Option (a) is correct.