Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
141
A student divided a number by 12 instead of 21 and received 35. Find the correct answer. (a) 20 (b) 15 (c) 26 (d) 25
Answer:
20
**Step 1:** Let the original number be $N$. The student performed the incorrect calculation: $N \div 12 = 35$.
142
A number when divided by 7 leaves a remainder 4. What will be the remainder when the square of the same number is divided by 7? (a) 2 (b) 4 (c) 1 (d) 3
Answer:
2
**Method 1: Using Algebra**
143
In a five-digit number, the digit in the hundred's place is 2 and the digit in the unit's place is twice the digit in the hundred's place. The digit at thousands place is zero. The digit in the ten thousand's place is the sum of the digit in the hundred's place and the digit in the unit's place. The digit in the ten's place is the digit in the ten thousand's place minus 1. The number is: (a) 60234 (b) 60224 (c) 60254 (d) 60264
Answer:
60254
Let's build the five-digit number place by place.
144
Find the sum of the smallest and the largest positive numbers of 6 digits which contain only digits 0, 4, 6 and each of these digits appears at least once. (a) 666444 (b) 604604 (c) 666666 (d) 1066646
Answer:
1066646
**Step 1: Find the smallest 6-digit number.**
145
How many numbers of the first 100 positive integers are divisible by 3 or 4 without a remainder? (a) 50 (b) 5 (c) 58 (d) 85
Answer:
50
We use the Principle of Inclusion-Exclusion: $N(A \cup B) = N(A) + N(B) - N(A \cap B)$.
146
Find the remainder, when $3^{10}$ is divided by 7. (a) 4 (b) 3 (c) 5 (d) 6
Answer:
4
We can use modular arithmetic to find the pattern of remainders of powers of 3 when divided by 7.
147
If 3 is added to each odd digit and 1 is subtracted from each even digit in the number 42514563, what will be the difference between the highest and lowest digits thus formed? (a) 2 (b) 7 (c) 5 (d) 8
Answer:
7
**Step 1:** Apply the rules to each digit of the number 42514563.
148
Which of the following numbers is NOT divisible by 9? (a) 49104 (b) 77832 (c) 35253 (d) 45390
Answer:
45390
The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. We will check the sum of the digits for each option.
149
Which numbers have a remainder of 0 when divided by 5?
Answer:
Multiples of 5
Numbers that are divisible by 5 are multiples of 5, meaning they can be divided by 5 without leaving a remainder.
150
Find the least 6-digit number that is a multiple of 18. (a) 100000 (b) 999900 (c) 100008 (d) 100006
Answer:
100008
**Step 1:** The smallest 6-digit number is 100000.