General Mathematics & Basic Arithmetic — Part 6 MCQs with Explanations

Percentage is a way of expressing a number as a fraction of 100. Example : 25% means 25 out of 100. Percentage Formula Percentage= (Part ÷ Total) × 100 ​

78 must be divided into two even numbers. The two even numbers should add up to 78: 38 + 40 = 78. Therefore, the smallest possible even number is 38 .

Numbers up to 200 divisible by both 2 and 3 are multiples of 6. 6, 12, 18, 24, …, 198 Formula: 200 ÷ 6 = 33 remainder 2 Total numbers = 33

Average of 10 values = 200 Total sum = Average × Number of values = 200 × 10 = 2000 Sum of 9 values = 1850 10th value = 2000 − 1850 = 150 1069.31x900.979 (Original: 1080x91

24679 has five digits. Its first digit 2 is even , and its last digit 9 is odd .

Started with 10 red balls. 1 red ball is removed. 10 - 1 = 9

Look at how much it increases each time: Term 1: x Term 2: x + 6 → increased by 6 Term 3: x + 18 → increased by 12 Pattern of increases: 6, 12, ... It goes up by 6 each time. So next increase = 18 Term 4 = Term 3 + 18 = (x + 18) + 18 = x + 36 If we take x = 18, then the terms are 18, 24, 36, 54

Put x = -2 and y = 3 in x³y² + x²y x³ = (-2)³ = -8 x² = (-2)² = 4 y² = 3² = 9 So x³y² = -8 x 9 = -72 And x²y = 4 x 3 = 12 Now add both: -72 + 12 = -60

The equation |-x| = 0 simplifies to x = 0 since the absolute value of any number is zero only when the number itself is zero. Therefore, the solution set contains only {0} .

1, 8, 27, 64, 125, 216, 343, and 512 1^3 = 1 2^3 = 8 3^3 = 27 4^3 = 64 5^3 = 125 6^3 = 216 7^3 = 343 8^3 = 512

First find 3/4 of 92 3/4 of 92 = 92 divided by 4 = 23 23 times 3 = 69 Then add 13 69 + 13 = 82

Just add them all together: 3 + 5 + 8 + 10 + 12 + 15 = 53

Formula: SI = (P × R × T) / 100 SI = (10,000 × 8 × 2) / 100 = Rs. 1,600

Let the ages today be 4x and 7x So younger age = 4x and older age = 7x After 12 years Younger age = 4x + 12 Older age = 7x + 12 New ratio is 2:3 So (4x + 12) / (7x + 12) = 2 / 3 Cross multiply 3(4x + 12) = 2(7x + 12) 12x + 36 = 14x + 24 36 - 24 = 14x - 12x 12 = 2x x = 6 Younger age today = 4x = 4 x 6 = 24

Total work = people × days = 500 × 25 = 12500 person-days Work done in first 12 days by 500 people = 500 × 12 = 6000 person-days Remaining work = 12500 - 6000 = 6500 person-days Now 300 people will do the remaining work. Days needed = Remaining work / people = 6500 / 300 = 21⅔ days

Let son's age = x. Then mother's age = 3x because it is 3 times the son's age. Sum of ages = 70, so x + 3x = 70 → 4x = 70. Solve: x = 70 ÷ 4 = 17.5. So son's present age = 17.5 years

The pattern in the series appears to be alternating between adding and subtracting. 27 + 5 = 32 32 - 2 = 30 30 + 5 = 35 35 - 2 = 33 33 + 5 = 38

Year 1: 250 × 1.10 = Rs. 275 Year 2: 275 × 1.10 = Rs. 302.50 Or directly: 250 × (1.10)² = 250 × 1.21 = Rs. 302.50

Pattern: 90 ÷ 2 = 45 45 + 3 = 48 48 ÷ 2 = 24 24 + 5 = 29 29 ÷ 2 = 14.5 The pattern alternates ÷2, +3, ÷2, +5, ÷2 .

Arrange the study hours in ascending order: 0, 0, 3, 4, 4, 4, 5 There are 7 values, so the median is the 4th value. The 4th value is 4 hours.

Let the son's present age = x years. Mother's age = 5x years. After 10 years: 5x + 10 = 3(x + 10) 5x + 10 = 3x + 30 2x = 20 → x = 10

The sequence is repeating every 4 terms: 2, 3, 5, 8 | 2, 3, 5, 8 | ... Since: 307 ÷ 4 = 76 remainder 3 So the 307th term corresponds to the 3rd term of the repeating pattern. Answer: 5

A number is decreased by 20%, so 80% of the original number remains. 80% = 240 100% = 240 × 100 ÷ 80 = 300

Discount = 2500 − 1600 = Rs. 900 Discount % = (900 ÷ 2500) × 100 = 36%

25% = 75 100% = 75 × 4 = 300 Last verified 07-09-2026

Worker-days = Workers × Days = 5 × 12 = 60 worker-days .

Each number is multiplied by 2: 3 × 2 = 6 → 6 × 2 = 12 → 24 → 48 → 96 .

Using A = 1, B = 2, C = 3, ... Z = 26 C = 3 A = 1 T = 20 CAT = 3 + 1 + 20 = 24

There are 4 Aces in a deck of 52 cards. Probability = 4/52 = 1/13 .

Even numbers are 2, 4, 6 → 3 favorable outcomes out of 6. Probability = 3/6 = 1/2 .

Step 1: Total seats 48 + 50 + 52 + 44 + 46 = 240 seats Step 2: Apply 10% reserve Reserve = 10% of 240 = 24 seats Usable capacity = 240 - 24 = 216 seats Or: 90% of 240 = 0.9 x 240 = 216 seats Step 3: Compare to pilgrims Pilgrims to carry = 214 Usable capacity = 216 216 ≥ 214, so they can be carried. Answer: Yes; total capacity is 240 and 90% of it is 216.

Pattern: 2 duty days, 1 rest day, repeat until 7 duty days are done. First duty day = Monday Let’s list them: Day 1: Monday → Duty 1 Day 2: Tuesday → Duty 2 Day 3: Wednesday → Rest Day 4: Thursday → Duty 3 Day 5: Friday → Duty 4 Day 6: Saturday → Rest Day 7: Sunday → Duty 5 Day 8: Monday → Duty 6 Day 9: Tuesday → Rest Day 10: Wednesday → Duty 7 The 7th duty day is Wednesday .

Total = 60 pilgrims Accommodation = 35 Transport = 42 Both = 25 Step 1: Only accommodation = Accommodation - Both = 35 - 25 = 10 Step 2: Only transport = Transport - Both = 42 - 25 = 17 Step 3: Exactly one confirmation = Only accommodation + Only transport = 10 + 17 = 27

The sequence: 18, 24, 30, 36 Check for constant percentage growth = each step should multiply by the same number. Step 1: 24 / 18 = 1.333... = 33.33% increase Step 2: 30 / 24 = 1.25 = 25% increase Step 3: 36 / 30 = 1.20 = 20% increase The ratios are different: 1.333, 1.25, 1.20 So the percentage increases are not the same. Answer: The ratios 24/18, 30/24 and 36/30 differ, so the percentage increases are not constant.

Step 1: Morning distribution 40% of 1200 = 0.40 x 1200 = 480 units issued Remaining = 1200 - 480 = 720 units Step 2: Afternoon distribution 40% of the remainder = 0.40 x 720 = 288 units issued Remaining = 720 - 288 = 432 units Step 3: Damaged units 432 - 54 = 378 units remaining usable Step 4: Find percentage remaining (378 / 1200) x 100 = 31.5% Answer: 31.5%, being 720, then 432, then 378 units.

Given: P = Q + 8 = x + 8 R = 2 x Q = 2x S = P - 4 = (x + 8) - 4 = x + 4 Total = 92 So: Q + P + R + S = 92 x + (x + 8) + 2x + (x + 4) = 92 5x + 12 = 92 5x = 92 - 12 5x = 80 x = 16 Check: Q = 16 P = 16 + 8 = 24 R = 2 x 16 = 32 S = 24 - 4 = 20 Total = 16 + 24 + 32 + 20 = 92 Answer: 16 pilgrims, giving P 24, R 32 and S 20

Step 1: Find time for each part Time = Distance / Speed Part 1: 36 km at 45 km/h = 36 / 45 = 0.8 hours = 48 minutes Part 2: 24 km at 30 km/h = 24 / 30 = 0.8 hours = 48 minutes Part 3: Wait = 12 minutes Part 4: Return 60 km at 40 km/h = 60 / 40 = 1.5 hours = 90 minutes = 1 hour 30 minutes Step 2: Add all times 48 minutes + 48 minutes + 12 minutes + 90 minutes = 198 minutes 198 minutes = 3 hours 18 minutes Answer: 3 hours 18 minutes, being 48 + 48 + 12 minutes plus 1 hour 30 minutes.

Pattern = Previous × 2 + 1 4 × 2 + 1 = 9 9 × 2 + 1 = 19 19 × 2 + 1 = 39 39 × 2 + 1 = 79 79 × 2 + 1 = 159 Verified & Updated

Given : Average weight of 5 persons = 60 kg New average of 6 persons = 62 kg Step 1: Total weight of 5 persons 5 × 60 = 300kg Step 2: Total weight of 6 persons 6 x 62 = 372kg 6 times 62 = 372text{ kg} Step 3: Weight of the new person = 372 − 300 = 72 kg ​

Given ratio: Copper : Silver = 3 : 5 Step 1: Find the total parts: 3+5=8 Step 2 : Silver represents 5 parts out of total 8 parts . Fraction of Silver = Silver parts/Total parts =5/8 =frac{5}{8}