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
151
A number is 10 more than another. Their sum is 50. Find the smaller number.
Answer:
20
Let the smaller number be x. The larger is x + 10. Sum: x + (x + 10) = 50. Combine terms: 2x + 10 = 50. Subtract 10: 2x = 40. Divide by 2: x = 20.
152
Solve the equation: 7 - 3(2x - 1) = 4
Answer:
1
Distribute the -3: 7 - 6x + 3 = 4. Combine constants: 10 - 6x = 4. Subtract 10: -6x = -6. Divide by -6: x = 1.
153
If x/3 - x/4 = 2, find x.
Answer:
24
Find a common denominator (12): (4x - 3x) / 12 = 2. This simplifies to x / 12 = 2. Multiply by 12: x = 24.
154
Solve for k: 3k - 2(k - 5) = 14
Answer:
4
Distribute the -2: 3k - 2k + 10 = 14. Combine terms: k + 10 = 14. Subtract 10: k = 4.
155
The difference of two numbers is 15. If the larger is twice the smaller, find the smaller number.
Answer:
15
Let the smaller number be s. The larger is 2s. Their difference is 2s - s = 15, which means s = 15. The smaller number is 15.
156
Solve the equation: 0.5(x - 4) = 0.2(x + 5)
Answer:
10
Multiply the entire equation by 10 to remove decimals: 5(x - 4) = 2(x + 5). Expand: 5x - 20 = 2x + 10. Subtract 2x: 3x - 20 = 10. Add 20: 3x = 30. Divide by 3: x = 10.
157
If 5x - 7 = 3x + 9, what is the value of x^2?
Answer:
64
First, solve for x. Subtract 3x: 2x - 7 = 9. Add 7: 2x = 16. Divide by 2: x = 8. The question asks for x^2, so 8^2 = 64.
158
Solve for a: 2a/3 + a/2 = 14
Answer:
12
Find a common denominator (6): (4a + 3a) / 6 = 14. This gives 7a / 6 = 14. Divide both sides by 7: a/6 = 2. Multiply by 6: a = 12.
159
Four times a number minus 10 equals the number plus 11. Find the number.
Answer:
7
Let the number be n. The equation is 4n - 10 = n + 11. Subtract n: 3n - 10 = 11. Add 10: 3n = 21. Divide by 3: n = 7.
160
Solve the equation: 3(2x - 5) - 4(x - 3) = 5
Answer:
4
Expand all terms: 6x - 15 - 4x + 12 = 5. Combine like terms: 2x - 3 = 5. Add 3: 2x = 8. Divide by 2: x = 4.