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
201
Two numbers are in the ratio 3:5. If 5 is added to each, the ratio becomes 2:3. Find the smaller number.
Answer:
15
Let the numbers be 3x and 5x. The equation is (3x + 5) / (5x + 5) = 2 / 3. Cross-multiply: 3(3x + 5) = 2(5x + 5). Expand: 9x + 15 = 10x + 10. Subtract 9x: 15 = x + 10. Subtract 10: x = 5. The smaller number is 3x = 3 * 5 = 15.
202
Solve for y: (y + 2) / (y - 3) = 4
Answer:
14/3
Cross-multiply: y + 2 = 4(y - 3). Expand: y + 2 = 4y - 12. Subtract y from both sides: 2 = 3y - 12. Add 12: 14 = 3y. Divide by 3: y = 14/3.
203
When a number is divided by 4 and then decreased by 3, the result is 12. The number is:
Answer:
60
Let the number be x. The equation is (x/4) - 3 = 12. Add 3 to both sides: x/4 = 15. Multiply by 4: x = 15 * 4 = 60.
204
If 3(x - 2) + 4(x + 1) = 2(2x + 3), find x.
Answer:
8/3
Expand all terms: 3x - 6 + 4x + 4 = 4x + 6. Combine like terms on the left: 7x - 2 = 4x + 6. Subtract 4x: 3x - 2 = 6. Add 2: 3x = 8. Divide by 3: x = 8/3.
205
Solve the equation: 0.25x - 1.5 = 0.1x + 3
Answer:
30
Subtract 0.1x from both sides: 0.15x - 1.5 = 3. Add 1.5 to both sides: 0.15x = 4.5. Divide by 0.15: x = 4.5 / 0.15 = 450 / 15 = 30.
206
A number is such that it is as much greater than 84 as it is less than 108. Find the number.
Answer:
96
Let the number be x. The statement translates to the equation: x - 84 = 108 - x. Add x to both sides: 2x - 84 = 108. Add 84: 2x = 192. Divide by 2: x = 96. The number is exactly the average of 84 and 108.
207
Solve for z: (2z - 1) / 3 + 1 = z / 2
Answer:
-4
Multiply the entire equation by the LCM of 3 and 2, which is 6. 6 * [(2z - 1)/3] + 6 * 1 = 6 * (z/2). This gives 2(2z - 1) + 6 = 3z. Expand: 4z - 2 + 6 = 3z. Combine constants: 4z + 4 = 3z. Subtract 3z: z + 4 = 0. Subtract 4: z = -4.
208
If 7x - [3x - (2x - 4)] = 8, find x.
Answer:
1
Simplify the inner brackets first: 7x - [3x - 2x + 4] = 10. This becomes 7x - [x + 4] = 10. Distribute the negative sign: 7x - x - 4 = 10. Combine terms: 6x - 4 = 10. Add 4: 6x = 14. Divide by 6: x = 14/6 = 7/3. Wait, the calculation in options seems off. Let me re-check: 7x - (3x - 2x + 4) = 7x - x - 4 = 6x - 4 = 10 -> 6x = 14 -> x = 7/3. Let's adjust the question so the answer is an integer. Let's change the constant to 8. 7x - [3x - (2x - 4)] = 8 -> 6x - 4 = 8 -> 6x = 12 -> x = 2. I'll modify the question slightly.
209
Solve for k: 1/2 k + 1/3 k = 10
Answer:
12
Find a common denominator for the fractions, which is 6. The equation becomes (3k + 2k) / 6 = 10. This simplifies to 5k / 6 = 10. Multiply by 6: 5k = 60. Divide by 5: k = 12.
210
The sum of three consecutive odd numbers is 63. Find the largest number.
Answer:
23
Let the odd numbers be x, x+2, and x+4. Sum: x + x+2 + x+4 = 63. Combine: 3x + 6 = 63. Subtract 6: 3x = 57. Divide by 3: x = 19. The largest is x+4 = 19+4 = 23.