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.
   
   View Answer

   Option E
   Explanation:
   From both:
   Distance that bus travelled = 60×2 = 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.
   
   View Answer

   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.
   
   View Answer

   Option C
   Explanation:
   From I, C got 8000 so 4x = 8000
   So x = 2000
   So total profit = 6x + 3x + 4x = 13x = 13×2000 = 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.
   
   View Answer

   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.
   
   View Answer

   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.
   
   View Answer

   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.
   
   View Answer

   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.
   
   View Answer

   Option C
   Explanation:
   From I: People becomes 7 from 5, and average decreases by 4. Len ‘n’ is previous average and then ‘n-4’ is new average.
   So average age of 2 new people becomes 2*(n-4) – 5*4 which is given 36
   So n = 32
   So av age of new group = 32 – 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 – 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.
   
   View Answer

   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.
    
    View Answer

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