# Quantitative Aptitude: Data Sufficiency Set 2

Directions (1-10): In each of the following questions, a question is followed by two statements numbered I and II. Read both the statements and answer accordingly.

1. What is the average speed of truck?
Statement I: Average speed of car is twice that of average speed of truck. Average speed of bus is 60 km/hr.
Statement II: Average speed of bus is two-third of average speed of train. The car can travel same distance in 3 hrs as bus can travel in 2 hrs.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option E
Explanation:

From both:
Distance that bus travelled = 60Ã—2 = 120 km
So from II, car can travel 120 km in 3 hrs. So speed of car = 120/3 = 40 km/hr
Now from I, speed of truck = 40/2 = 20 km/hr
2. In how much time can pipe C empty the tank?
Statement I: Pipes A and B can fill half the tank in 4 hrs 30 minutes.
Statement II: Together with emptying pipe C, pipes A and B can fill the tank in 22 1/2 hrs.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option E
Explanation:

A and B can fill half the tank in 4 hrs 30 minutes. So full tank in double time ie 9 hrs.
So from II 1/C = 2/45 – 1/9 = – 1/15
So C can empty full tank in 15 hrs.
3. A, B and C invested Rs 52000 in a business in ratio 6 : 3 : 4 respectively. What is the profit % earned by them after a year?
Statement I: C got Rs 8000 as his share of profit.
Statement II: The difference in profits earned by A and B is Rs 6000.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option C
Explanation:

From I, C got 8000 so 4x = 8000
So x = 2000
So total profit = 6x + 3x + 4x = 13x = 13Ã—2000 = 26,000
So profit% = 26000/52000 * 100 = 50%From II, 6x – 3x = 6000
So x = 2000
Further same as in I.
4. How much money did Yami borrow?
Statement I: If borrowed for 6 years at 6% rate of interest per annum, she has to give double interest as earlier.
Statement II: If the rate of interest per annum increases from 6% to 8% then she could borrow 25% less to give same amount of interest.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option D
Explanation:

From I: 2I = P*6*6/100
From II: I = P*6*1/100
And also I = 3P/4 * 8*1/100
So cannot be determined from any statement or both.
5. What is the time taken by train to go from point A to point B?
Statement I: If the train increases its speed by 10%, then it reaches 20 mins earlier.
Statement II: If the train decreases its speed by 20%, then it reaches 45 mins late.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option E
Explanation:

From I: d/(110s/100) = t – 20
From II: d/(80s/100) = t + 45
Divide both equations, and t can be found
6. If the selling price of an article is Rs 12000, then what is the profit/loss% on it?
Statement I: The ratio of the selling and price and cost price of the article is 4 : 3.
Statement II: The difference between the cost price and selling price of the article is Rs 2000
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option A
Explanation:

From I, 4x = 12000. So CP 9000
And profit% can be found.
From II we do not know that SP is greater than CP or less
7. What is the ratio of ages of A to B?
Statement I: A’s age will be twice B’ age after 5 years.
Statement II: A’ s present age is 5 more than twice B’ present age.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option D
Explanation:

From both statements we get same equation. So 1 equation in 2 variables cannot be solved.
8. There are 5 people in a group. Average age of the group decreases by 4 when two more people join the group. Find the average age of the new group.
Statement I: Average age of the two people who joined later is 36 yrs.
Statement II: Total of the ages of people originally was 160 yrs.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option C
Explanation:

From I: People becomes 7 from 5, and average decreases by 4. Len â€˜nâ€™ is previous average and then â€˜n-4â€™ is new average.
So average age of 2 new people becomes 2*(n-4) â€“ 5*4 which is given 36
So n = 32
So av age of new group = 32 â€“ 4 = 28
From II: Total age of 5 people is 160 yrs, so their average = 160/5 = 32
So av age of new group = 32 â€“ 4 = 28
9. What is the rate of interest per annum on a sum of money invested?
Statement I: The difference between the compound interest and simple interest at the end of 2 years at same rate of interest is Rs 80.
Statement II: A compound interest of Rs 4912 is obtained after 3 years of investment.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option E
Explanation:

From I: Pr2/1002 = 80
From II: 4912 = P [(1 + r/100)3 – 1]
From I and II we have 2 equations in 2 variables which can be solved to find the rate of interest.
10. What is the two digit number?
Statement I: The difference between the digits of the two digit number is 6.
Statement II: The number obtained by interchanging the digits of original number is 26 more than twice the original number.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option D
Explanation:

Let number is 10x+y
From I: x â€“ y = 4 or y â€“ x = 4
From II: 10y+x = 2(10x+y) + 26
So 8y â€“ 19x = 26
Solving from both I and II, we get 28 and 82, so cannot be determined

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