Quantitative Aptitude: Data Sufficiency Questions Set 6

Directions: In each of the following questions, a question is followed by two or three statement. Read all the statements and find that which statements are required to answer the question and answer accordingly. 

1. What is the volume of the cylindrical tank ?
   Statement I: Diameter of the base is equal to the height of the tank.
   Statement II: Height of the tank is 20 m.
   Statement III: Area of the base is 320 sq. m.
   A) Only I and III.
   B) Only I
   C) Only III
   D) Any of the two
   E) None of these
   
   View Answer

   
   Option  D
   Solution:
   From I and II :
   Height = 20 m     radius = 10 m
   Then ,Volume of the cylindrical tank = (22/7) *10 *10 *20 sq. m
   From II and III :
   Volume = Area of the base * Height = 320 *20 sq. m
   From I and III:
   Area of the base = (22/7) * radius ^2  = 320
   we can calculate radius then , from I diameter is equal to the height so 2*radius = height
   Now we can calculate volume of the cyndrical tank .
   Hence , Any of the two is enough to get the volume .
   
2. What is the selling price of the camera if no discount is offered ?
   Statement I: Cost price of the camera is Rs.10,000.
   Statement II: Profit earned was  20%.
   Statement III: Had 20% discount been offered on selling price  the profit would have been Rs. 700.
   A) Only III
   B) Only II and III
   C) Only I and II
   D) All of these
   E) Any two of these
   
   View Answer

     Option E
   Solution:
   From I and II :
   SP can be calculated .
   From II and III:
   Let cp = x
   sp = (120x)/100 = 6x/5
   After ,20% discount on sp =New sp = (80/100)*6x/5
   From I and III:
   Let sp = x
   After 20% discount ,
   sp = 8x/10
   => 8x/10 -10,000 = 700
   sp can be calculated .
   Hence ,from any of two options ,we can get the value of sp.
   
3. How many students failed in class 6 ?
   Statement I: 400 students passed in class .
   Statement II: Number of students failed in class 6 is 10% of those of failed in class 7?
   Statement III: 75% of the students who appeared in examination have passed either in class 8.
   A) Only II and III
   B) Only I and II
   C) Only III
   D) None of these
   E) All of these
   
   View Answer

     Option D
   Solution:
   Data is not sufficient to find the number of failed students in class 6.
    
4. What is the rate of interest p.c.p.a?
   Statement I: Simple Interest accrued in two years on the same amount at the same rate of interest is Rs. 44,000.
   Statement II: The amount becomes Rs. 15,400 in two years on simple interest .
   Statement III: Difference between the compound  interest and simple interest earned in two years on the amount invested is Rs. 120.
   A)  Only I and II
   B) Only II and III
   C) Only II
   D) Only I and III
   E) All of the above
   
   View Answer

     Option D
   Solution:
   From Statement I:
   (PR * 2 ) / 100 = 44,000
   PR = 22,00,000
   From Statement II:
   (PR1 * 3 ) / 100 = 15,400 -P
   From Statement III:
   Let Amount be Rs.P  and rate be R p.c.p.a.
   then ,
   Difference  = (P R^2)/10000 = 120
   By dividing  equations of Statement I and Statement III ,
   we get rate of interest .
   
5. Two persons P and Q . P bought some copies and some books from a shopkeeper .The shopkeeper charged extra Rs.15 ,though he was getting a  profit of Rs. 60/copy and Rs 350/book . For what price did P and Q sell the book if they both earned a profit of 50%?
   Statement I: The selling price of 4 copies and 2 books was Rs. 600.
   Statement II: P and Q sold equal number of copies and books .
   Statement III: They invested a total amount of Rs.10,000  on copies and Rs .15,000 on books.
   A) Only II
   B) None of the above
   C) Only II and III
   D) Only I and II
   E) All of these
   
   View Answer

   
   Option B
   Solution:
   From the statements we are not able to get the information of either cp or sp .
   
6. In how many days will Mohit alone complete the work?
   Statement I: Soham alone can do the work in 20 days .Mohit is 10% more efficient than Soham  and Rita . 30% of work is done by Mohit ?
   Statement II: Soham and Mohit together can finish the work in 8(2/11) days , Mohit and Rita in 7(1/5) days and, Rita and  Soham  can do the same work in 6(2/3) days .
   A) Only II
   B) Both I and II
   C) Either  I or II
   D) Neither I nor II
   E) Only I
   
   View Answer

   
   Option A
   Solution:
   From Statement II :
   (Soham + Mohit + Rita  )’s 1 day’s work =  37 /180
   Mohit’s  1 day’s of work = 37/180 – 3/20 = 18 days
   
7. What is the population of city X ?
   Statement I: The population of city X is 80% of that of city Y .The difference of population of city X and city Y is 312500.
   Statement II: The ratio of the population of males and females in city X is 27 : 23 and the difference between their population is 1,00,000.
   A) Only II
   B) Either I or II
   C) Only II
   D) Both I and II
   E) None of the above
   
   View Answer

   
   Option B
   Solution:
   From Statement I:
   city Y = 100x/80 = 5x/4
   Therefore ,
   5x/4 – x = 3,12,500
   => x= 12,50,000
   From Statement II:
   27x – 23x = 1,00,000
   => x = 25,000
   Therefore ,
   27x+23x =50x = 12,50,000
   
8. Raman mixed two types of wheat  for selling the mixture in his shop .What is the quantity (in kg) of the first type wheat in the mixture ?
   Statement I: The price of the second type of wheat is Rs. 50/kg . The difference between the quantity of first type of wheat and second type of wheat in the mixture is 3 kg.
   Statement II: The price of the first type of wheat is Rs. 47 /kg. Raman earned a profit of 20% by selling the mixture at the rate of Rs. 57.60 /kg.
   A) Neither I nor II
   B) Either I or II
   C) Both I and II
   D) Only I
   E) Only II
   
   View Answer

     Option C
   Solution:
   From both the statements :
   Let the quantity of first wheat and second wheat be x kg and (x-3) kg resp.
   Quantity of the mixture = (2x – 3 ) kg
   Therefore ,
   (x * 47 + (x – 3 )*50) * (120/100) = (2x – 3) * 57.60
   => 282x + 300x – 900 = 576x – 864
   => x = 6 kg
   
9. What is the monthly salary of Himesh ?
   Statement I: The salary of Himesh increased by 33(1/3) % two years ago and 25 % a year ago. The difference in increase was Rs. 32000/3.
   Statement II: Himesh spends 18% of his salary on grocery and 14 % of it on sports. 14% of total salary is spent on transportation and entertainment . (3/10)th part of the total salary is spent on house rent and thereafter he saves Rs. 32000.
   A) Only I
   B) Either I and II
   C) Neither I nor II
   D) Both I and II
   E) Only II
   
   View Answer

   
   Option B
   Solution:
   From Statement I:
   If the monthly salary be Rs. x ,then
   x(100/3 – 25)% = 32000/3
   => x(25/300) = 32000/3
   => x = Rs. 1,28,000
   From Statement II:
   Total expenditure of Himesh  = (18 + 14 + 13) /100 + (3/10)  = ¾
   Remaining = 1 – (3/4) = 1/4
   Therefore ,
   Total salary = 4 * 32000 = Rs. 1,28,000 
10. How many students are there in the class?
    Statement I: If two students weighing 44 kg and 52 kg leave the class and are replaced by two students weighing 64 kg and 56 kg .The average weight of the class increases by 1.2 kg .
    Statement II: The average weight of the class is Rs. 52 kg.
    A) Only II
    B) Either I or II
    C) Neither I nor II
    D) Both I and II
    E) Only I
    
    View Answer

    
    Option  D
    Solution:
    From Statement I:
    52x – 44 – 52 + 64 + 56 = 53.6x
    => 52x + 24 = 53.2x
    => x= 20
    From Statement II:
    Total weight = 52x kg