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
191
The sum of three consecutive even integers is 48. What is the middle integer?
Answer:
16
Let the integers be x, x+2, and x+4. Sum: x + (x+2) + (x+4) = 48. Combine terms: 3x + 6 = 48. Subtract 6: 3x = 42. Divide by 3: x = 14. The middle integer is x+2 = 14+2 = 16.
192
Solve the equation: x/2 + x/3 = 10
Answer:
12
Find a common denominator (6). The equation becomes 3x/6 + 2x/6 = 10, which is 5x/6 = 10. Multiply by 6: 5x = 60. Divide by 5: x = 12.
193
If 4x - 3 = 21, what is the value of 2x?
Answer:
12
First find x. Add 3: 4x = 24. Divide by 4: x = 6. The question asks for the value of 2x, so 2 * 6 = 12.
194
Find x if 0.3x + 0.4 = 0.5x - 0.2
Answer:
3
Subtract 0.3x from both sides: 0.4 = 0.2x - 0.2. Add 0.2: 0.6 = 0.2x. Divide by 0.2: x = 0.6 / 0.2 = 3.
195
The difference between two numbers is 14 and their ratio is 5:3. Find the larger number.
Answer:
35
Let the numbers be 5x and 3x. Their difference is 5x - 3x = 14, so 2x = 14, which means x = 7. The larger number is 5x = 5 * 7 = 35.
196
Solve: 5 - 2(x - 1) = 3x + 2
Answer:
1
Expand: 5 - 2x + 2 = 3x + 2. Combine constants: 7 - 2x = 3x + 2. Add 2x to both sides: 7 = 5x + 2. Subtract 2: 5 = 5x. Divide by 5: x = 1.
197
A father is 30 years older than his son. In 12 years, the man will be three times as old as his son. Find the present age of the son.
Answer:
3
Let son's age be s. Father's age is s + 30. In 12 years, son is s + 12 and father is s + 42. Equation: s + 42 = 3(s + 12). Expand: s + 42 = 3s + 36. Subtract s: 42 = 2s + 36. Subtract 36: 6 = 2s. Divide by 2: s = 3.
198
Solve for x: (2x - 1) / 5 = (x + 2) / 3
Answer:
13
Cross-multiply: 3(2x - 1) = 5(x + 2). Expand: 6x - 3 = 5x + 10. Subtract 5x: x - 3 = 10. Add 3: x = 13.
199
If 1/3 of a number is 4 more than 1/4 of the same number, the number is:
Answer:
48
Let the number be n. The equation is n/3 = n/4 + 4. Subtract n/4: n/3 - n/4 = 4. Common denominator is 12: (4n - 3n) / 12 = 4. This gives n / 12 = 4. Multiply by 12: n = 48.
200
Solve the equation: 2(a - 3) = a + 5
Answer:
11
Expand the left side: 2a - 6 = a + 5. Subtract 'a' from both sides: a - 6 = 5. Add 6 to both sides: a = 11.