Sectional Test on Quantitative Techniques for CLAT UG [Part 8]
Q1. A group of eight numbers has an average of 46. If one number is excluded, the average of the remaining seven numbers drops to 42. Determine the value of the number that was taken out.
a. 74
b. 78
c. 82
d. 86
b. 78
c. 82
d. 86
Q2. An article is marked by a shopkeeper at ₹2,400. A 20% discount is applied to this price. Despite offering the discount, the shopkeeper still achieves a 20% profit. Calculate the original cost price of the article.
a. ₹1,400
b. ₹1,500
c. ₹1,600
d. ₹1,800
b. ₹1,500
c. ₹1,600
d. ₹1,800
Q3. A college has students where the proportion of boys to girls is 5 to 7. Given that the total enrollment is 720 students, determine the total number of boys in the college.
a. 250
b. 280
c. 300
d. 320
b. 280
c. 300
d. 320
Q4. A train travels a specific distance in 5 hours when moving at a speed of 60 km/h. If the speed is increased to 75 km/h, what would be the time required to travel the identical distance?
a. 3 hours
b. 4 hours
c. 5 hours
d. 6 hours
b. 4 hours
c. 5 hours
d. 6 hours
Q5. What is the average age of the four people remaining, given that the average age of ten people is 40 years and the average age of the first six of them is 35 years?
a. 45 years
b. 47.5 years
c. 50 years
d. 52.5 years
b. 47.5 years
c. 50 years
d. 52.5 years
Q6. A rectangle has a perimeter of 140 m. If the ratio of its length to breadth is 4 : 1, what is the area of the rectangle?
a. 1200 sq m
b. 1225 sq m
c. 1400 sq m
d. 1575 sq m
b. 1225 sq m
c. 1400 sq m
d. 1575 sq m
Q7. If a town’s population first grows by 20% and then shrinks by 25% the following year, what is the overall percentage change in its population over the two-year period?
a. No change
b. 5% increase
c. 5% decrease
d. 10% decrease
b. 5% increase
c. 5% decrease
d. 10% decrease
Q8. Two balls are drawn sequentially, without replacement, from a box that holds 5 white, 7 black, and 8 red balls. What is the likelihood that the two balls selected are both red?
a. 14/95
b. 8/95
c. 7/95
d. 13/95
b. 8/95
c. 7/95
d. 13/95
Q9. The average of 20 numbers is 30. If the average of the first 12 numbers is 28, what is the average of the remaining 8 numbers?
a. 32
b. 33
c. 34
d. 35
b. 33
c. 34
d. 35
Q10. A person allocates 45% of their monthly earnings to food expenses and an additional 30% to rent. Given that they save ₹6,250, determine their total monthly income.
a. ₹15,000
b. ₹20,000
c. ₹22,500
d. ₹25,000
b. ₹20,000
c. ₹22,500
d. ₹25,000
Q11. If 12 workers can complete a job in 18 days, how many workers are required to complete the same job in 12 days?
a. 15
b. 16
c. 18
d. 20
b. 16
c. 18
d. 20
Q12. The ratio of two numbers is 5:9. Given that their difference is 80, find the greater of the two numbers.
a. 160
b. 180
c. 200
d. 220
b. 180
c. 200
d. 220
Q13. An 8% discount on an article’s marked price of ₹1,500 results in a selling price of ₹1,380. How much was the discount?
a. ₹150
b. ₹140
c. ₹130
d. ₹120
b. ₹140
c. ₹130
d. ₹120
Q14. What is the average speed for a car’s journey if it covers the first half of the distance at 40 km/h and the remaining half at 60 km/h?
a. 48 km/h
b. 50 km/h
c. 52 km/h
d. 54 km/h
b. 50 km/h
c. 52 km/h
d. 54 km/h
Q15. A student’s average score across 6 subjects is 72. To achieve an average of 75 over 7 subjects, what score is needed in the seventh subject?
a. 67
b. 93
c. 73
d. 80
b. 93
c. 73
d. 80
Answers
1. Correct Answer: A
Original total = 8 × 46 = 368
New total = 7 × 42 = 294
Removed number = 368 − 294 = 74
Original total = 8 × 46 = 368
New total = 7 × 42 = 294
Removed number = 368 − 294 = 74
2. Correct Answer: C
SP after discount = 80% of 2400 = 1920
1920 = 120% of CP
CP = 1920/120 × 100 = ₹1600
SP after discount = 80% of 2400 = 1920
1920 = 120% of CP
CP = 1920/120 × 100 = ₹1600
3. Correct Answer: C
Total parts = 12
1 part = 720/12 = 60
Boys = 5 × 60 = 300
Total parts = 12
1 part = 720/12 = 60
Boys = 5 × 60 = 300
4. Correct Answer: B
Distance = 60 × 5 = 300 km
Time = 300/75 = 4 hours
Distance = 60 × 5 = 300 km
Time = 300/75 = 4 hours
5. Correct Answer: B
Total age = 10 × 40 = 400
Age of first 6 = 6 × 35 = 210
Remaining age = 400 − 210 = 190
Average = 190/4 = 47.5 years
Total age = 10 × 40 = 400
Age of first 6 = 6 × 35 = 210
Remaining age = 400 − 210 = 190
Average = 190/4 = 47.5 years
6. Correct Answer: B
Perimeter = 140 ⇒ L + B = 70
Ratio L : B = 4 : 1 ⇒ total parts = 5
1 part = 70/5 = 14
Breadth = 14 m
Length = 56 m
Area = 56 × 14 = 1225 sq m
Perimeter = 140 ⇒ L + B = 70
Ratio L : B = 4 : 1 ⇒ total parts = 5
1 part = 70/5 = 14
Breadth = 14 m
Length = 56 m
Area = 56 × 14 = 1225 sq m
7. Correct Answer: C
Net % = +20 − 25 − (20×25)/100 = −5%
Net % = +20 − 25 − (20×25)/100 = −5%
8. Correct Answer: A
Probability = (8/20) × (7/19) = 56/380 = 14/95
Probability = (8/20) × (7/19) = 56/380 = 14/95
9. Correct Answer: B
Total = 20 × 30 = 600
First 12 total = 12 × 28 = 336
Remaining = 600 − 336 = 264
Average = 264/8 = 33
Total = 20 × 30 = 600
First 12 total = 12 × 28 = 336
Remaining = 600 − 336 = 264
Average = 264/8 = 33
10. Correct Answer: D
Spent = 75%, Savings = 25%
Income = 6250 × 4 = ₹25,000
Spent = 75%, Savings = 25%
Income = 6250 × 4 = ₹25,000
11. Correct Answer: C
Work = 12 × 18 = 216
Workers needed = 216/12 = 18
Work = 12 × 18 = 216
Workers needed = 216/12 = 18
12. Correct Answer: C
Let the numbers be 5x and 9x.
Difference = 9x − 5x = 4x.
Given difference = 80, so 4x = 80
x = 20
Larger number = 9x = 9 × 20 = 180
Let the numbers be 5x and 9x.
Difference = 9x − 5x = 4x.
Given difference = 80, so 4x = 80
x = 20
Larger number = 9x = 9 × 20 = 180
13. Correct Answer: D
Discount = 1500 − 1380 = ₹120
Discount = 1500 − 1380 = ₹120
14. Correct Answer: A
Average speed = (2ab)/(a+b) = (2×40×60)/(100) = 48 km/h
Average speed = (2ab)/(a+b) = (2×40×60)/(100) = 48 km/h
15. Correct Answer: B
Total needed = 7 × 75 = 525
Current total = 6 × 72 = 432
Marks needed = 525 − 432 = 93
Total needed = 7 × 75 = 525
Current total = 6 × 72 = 432
Marks needed = 525 − 432 = 93
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Adtiya Aryan
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