Number system questions are the fastest marks in placement tests, bank exams and CAT-style papers once you know the shortcuts. This set covers unit digits, HCF and LCM word problems, divisibility rules, remainders, counting factors, trailing zeros and recurring decimals, with a short worked solution for every question.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 15 questions.
Topics covered in this set
- Unit digit and cyclicity
- HCF and LCM word problems
- Divisibility rules (especially 11)
- Remainder theorem shortcuts
- Number of factors and trailing zeros
- Recurring decimals as fractions
Aptitude MCQs with answers and explanations
Q1. What is the unit digit of 7^95?
a) 7
b) 9
c) 1
d) 3
Q2. The HCF of two numbers is 12 and their LCM is 360. If one number is 60, what is the other?
a) 72
b) 48
c) 84
d) 90
Q3. What is the largest number that divides 70 and 125 leaving remainders 5 and 8 respectively?
a) 65
b) 13
c) 9
d) 15
Q4. What is the smallest number that leaves a remainder of 4 when divided by 12, 15 and 20?
a) 60
b) 124
c) 64
d) 184
Q5. How many trailing zeros does 100! have?
a) 20
b) 25
c) 22
d) 24
Q6. Which of these numbers is divisible by 11?
a) 4832718
b) 4832717
c) 4832719
d) 4832716
Q7. What is the remainder when 2^31 is divided by 5?
a) 1
b) 2
c) 3
d) 4
Q8. How many factors (divisors) does 360 have?
a) 24
b) 18
c) 20
d) 36
Q9. Three bells ring at intervals of 6, 8 and 12 seconds. They ring together at the start. How many times will they ring together in 30 minutes, including the first time?
a) 75
b) 76
c) 74
d) 150
Q10. What is the HCF of 2/3, 8/9 and 16/81?
a) 2/3
b) 16/3
c) 2/81
d) 1/81
Q11. The product of two co-prime numbers is 117. What is their LCM?
a) 1
b) 9
c) 13
d) 117
Q12. A number leaves remainder 3 when divided by 6. What remainder does its square leave when divided by 6?
a) 3
b) 0
c) 1
d) 9
Q13. What is the largest four-digit number divisible by 88?
a) 9988
b) 9944
c) 9900
d) 9856
Q14. What is 0.363636... (0.36 recurring) as a fraction in its simplest form?
a) 9/25
b) 36/100
c) 4/11
d) 3/8
Q15. What is the sum of all natural numbers from 1 to 50?
a) 1225
b) 1250
c) 2550
d) 1275
Quick revision notes
- Unit digits repeat in cycles of 4 (2, 3, 7, 8), 2 (4, 9) or 1 (0, 1, 5, 6). Use the power modulo 4.
- HCF x LCM = product of the two numbers (only for two numbers).
- Greatest number dividing with remainders: HCF of the differences. Smallest number leaving a common remainder: LCM + remainder.
- Divisibility by 11: the difference between alternate digit sums must be 0 or a multiple of 11.
- For N = a^p x b^q x c^r, the number of factors is (p + 1)(q + 1)(r + 1).
- Trailing zeros in n! = floor(n/5) + floor(n/25) + floor(n/125) + ...
Frequently asked questions
How do I find the unit digit of a large power quickly?
Find the cycle of unit digits for the base (for 7 it is 7, 9, 3, 1), divide the exponent by the cycle length and use the remainder to pick the digit. A remainder of 0 means the last digit in the cycle.
When should I use HCF and when should I use LCM in word problems?
Use HCF when something is being divided into the largest equal parts or groups. Use LCM when events repeat and you need the first time they coincide, such as bells ringing or runners meeting at the start.
Why do we only count 5s for trailing zeros?
Each trailing zero needs a factor of 10 = 2 x 5. A factorial always has far more factors of 2 than 5, so the number of 5s decides how many 10s can be formed.
Comments
Post a Comment