0 correct out of 0 attempted (0%)
Correct answer: D
I is incorrect: the number of positive divisors of 36 → 9. 36 = 2² × 3², giving (2+1)(2+1)=9 divisors. II is correct: the remainder when 2^10 is divided by 7 → 2. 2³ leaves remainder 1, so 2^10 leaves remainder 2.
Correct answer: A
The next multiple is 143, so the difference is 5.
Correct answer: A
I is correct: the greatest integer less than -2.3 → -3. On the number line -3 is the greatest integer strictly below -2.3. II is correct: the integer n if n is positive and n²=169 → 13. The positive square root of 169 is 13.
Correct answer: D
The LCM uses 2³ and 3², giving 72.
Correct answer: C
I is correct: the last digit of 7^23 → 3. The last-digit cycle is 7,9,3,1 and 23 leaves remainder 3 on division by 4. II is correct: the least positive number added to 138 to make a multiple of 11 → 5. The next multiple is 143, so the difference is 5.
Correct answer: D
36 = 2² × 3², giving (2+1)(2+1)=9 divisors.
Correct answer: D
I is correct: the number of zeros at the end of 25! → 6. Count factors of 5: floor(25/5)+floor(25/25)=5+1. II is correct: the least positive number added to 138 to make a multiple of 11 → 5. The next multiple is 143, so the difference is 5.
Correct answer: B
I is incorrect: the smallest positive integer divisible by 8, 12 and 18 → 72. The LCM uses 2³ and 3², giving 72. II is correct: the number of positive divisors of 36 → 9. 36 = 2² × 3², giving (2+1)(2+1)=9 divisors.
Correct answer: D
For equal periods, profit follows investment ratio. A receives 2/5 of 1500.
Correct answer: B
Increase = 100; percentage increase = 100/500 × 100 = 20%.
Correct answer: A
240 × 15/100 = 36.
Correct answer: C
Net rate = 1/3 − 1/6 = 1/6 tank per hour.
Correct answer: B
Probability = red/total = 3/10, or 30%.
Correct answer: A
Selling price = cost × (1 + profit rate) = 400 × 115/100.
Correct answer: D
Cross multiplication gives 2b = 5 × 4.
Correct answer: D
Hypotenuse = √((3)² + (4)²) = 5.
Correct answer: C
There are 8 equal parts. B receives 5/8 of 120.
Correct answer: A
I is correct: the average of five numbers totalling 185 → 37. Average equals 185/5. II is correct: the value of x in the proportion 5:8=x:40 → 25. x=40×5/8.
Correct answer: D
Milk forms 3/5 of 30 litres.
Correct answer: A
I is correct: the mode of 2, 4, 4, 5, 7, 7, 7, 9 → 7. Seven occurs three times, more than any other value. II is correct: the combined mean of 10 students averaging 40 and 15 averaging 50 → 46. The combined total is 400+750=1150 across 25 students.
Correct answer: D
There are seven parts; the larger share is 840×4/7.
Correct answer: A
I is incorrect: the geometric mean of positive numbers 9 and 16 → 12. The positive square root of 9×16 is 12. II is correct: the fourth proportional to 4, 6 and 10 → 15. 4:6=10:x gives x=6×10/4.
Correct answer: B
x=40×5/8.
Correct answer: C
I is correct: the milk volume in litres in 30 litres of milk-water mixture at ratio 3:2 → 18. Milk forms 3/5 of 30 litres. II is correct: the litres of water added to 20 litres of pure milk to make milk 80% of the mixture → 5. The final volume is 20/0.8=25 litres, requiring 5 litres of water.
Correct answer: A
The weighted mean is (60×3+80×2)/5.