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
171
The denominator of a fraction is 3 more than its numerator. If both are increased by 2, the fraction becomes 1/2. Find the original fraction.
Answer:
1/4
Let numerator be n. Denominator is n + 3. Original fraction is n / (n + 3). If both increased by 2: (n + 2) / (n + 3 + 2) = 1/2. So, (n + 2) / (n + 5) = 1/2. Cross-multiply: 2(n + 2) = n + 5. Expand: 2n + 4 = n + 5. Subtract n: n + 4 = 5. Subtract 4: n = 1. The denominator is 1 + 3 = 4. Original fraction is 1/4.
172
Solve the equation: 1.5x - 2 = 0.5x + 4
Answer:
6
Subtract 0.5x from both sides: 1.0x - 2 = 4. Add 2 to both sides: x = 6.
173
If 7 - 2x = 3, find the value of x.
Answer:
2
Subtract 7 from both sides: -2x = 3 - 7, which is -2x = -4. Divide by -2: x = 2.
174
Solve for y: 4y - 3(y - 2) = 10
Answer:
4
Distribute the -3: 4y - 3y + 6 = 10. Combine terms: y + 6 = 10. Subtract 6: y = 4.
175
Half of a number added to its third part gives 25. The number is:
Answer:
30
Let the number be n. The equation is n/2 + n/3 = 25. Common denominator is 6: (3n + 2n) / 6 = 25. This gives 5n / 6 = 25. Multiply by 6/5: n = 25 * 6 / 5 = 30.
176
If 2(3x - 4) = 5x - 3, what is x?
Answer:
5
Expand the left side: 6x - 8 = 5x - 3. Subtract 5x from both sides: x - 8 = -3. Add 8 to both sides: x = 5.
177
Solve the equation: x/5 = x/6 + 1
Answer:
30
Subtract x/6 from both sides: x/5 - x/6 = 1. Common denominator is 30: (6x - 5x) / 30 = 1. This simplifies to x / 30 = 1. Multiply by 30: x = 30.
178
If 5x + 3 = 2x + 18, find x.
Answer:
5
Subtract 2x from both sides: 3x + 3 = 18. Subtract 3: 3x = 15. Divide by 3: x = 5.
179
Solve for p: 3p - (p - 4) = p + 8
Answer:
4
Distribute negative sign: 3p - p + 4 = p + 8. Combine terms on left: 2p + 4 = p + 8. Subtract p: p + 4 = 8. Subtract 4: p = 4. Let me re-check. 3p - p + 4 = 2p + 4. 2p + 4 = p + 8 -> p = 4. My intended answer was 4. I will adjust the correct_option.
180
The sum of a number and 12 is equal to three times the number. Find the number.
Answer:
6
Let the number be n. The equation is n + 12 = 3n. Subtract n from both sides: 12 = 2n. Divide by 2: n = 6.