Quantitative Aptitude: Data Sufficiency Questions Set 9

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. How much time will Train P take to cross Train Q (from the moment they meet) running in opposite directions (towards each other) ?
   statement I: The respective ratio of speeds of Train P and Train Q is 3 : 4. The sum of the lengths of Train P and Train Q is 700 metre.
   statement II: Train P can cross a signal pole in 12 seconds. It can cross 600  metre long station in 25 seconds.
   A) Only I
   B) Both I and II
   C) Only II
   D) Either I or II
   E) Neither I nor II
   
   View Answer

     Option E
   Solution:
   From statement I:
   Relative speed = 3x + 4x = 7x units
   Sum of Length of trains = 700 m
   Required time = 700/7x = no result
   From statement II:
   speed of train P = x/12 = (x + 600)/25
   => 25x = 12x + 7200
   => 13x = 7200
   => x = 7200/13
2. What is the area the isosceles triangle A ?
   statement I: The length of the side opposite the single largest angle in the triangle is 8cm.
   statement II: The perimeter of triangle X is 20cm.
   A) Only II
   B) Only I
   C) Neither I nor II
   D) Both I and II
   E) Either I or II
   
   View Answer

     Option  D
   Solution:
   In a triangle, the side opposite the largest angle will be the longest. Correspondingly, the side opposite the smallest angle will be the shortest.
   
3. What is the ratio between the two numbers a and b ?
   statement I: 50% of a is 25% of 80.
   statement II: 20% of b is 10% of 100.
   A) Both I and II
   B) Only I
   C)Only II
   D) Either I or II
   E) Neither I nor II
   
   View Answer

     Option A
   Solution:
   Both I and II required together.
   
4. What is the age of R, in a group of P,Q, R,S and T whose average age is 45 years?
   statement I: Average of the age of S and T is 47 years?
   statement II: Average of the age of P and Q is 53 years?
   A)  Only II
   B) Only I
   C) Both I and II
   D) Neither I nor II
   E) Either I or II
   
   View Answer

     Option C
   Solution:
   From statement I and II:
   P + Q + R + S + T = 5 * 45 = 225 years ———-(1)
   P + Q = 106 years ————–(2)
   S + T = 94 years —————(3)
   From (1), (2) and (3), we get
   We get the age of  R .
5. How many people are there in the aeroplane ?
   statement I: There are 45 females in the aeroplane.
   statement II: 30% of passengers are males and 10% are children.
   A) Either I or II
   B) Only II
   C) Only I
   D) Neither I nor II
   E) Both I and II
   
   View Answer

     Option E
   Solution:
   From statements I and II:
   Number of female passengers = 45
   There are  60% of the female in the aeroplane.
   Total no. of passengers = 45 *(100/60) = 75
   
6.  The ratio between the present ages of the Rohit and Rina is 1 : 3. Find the present age of the Rina.
   statement I: Difference between the present ages of the Pooja and Rohit is 22 years.
   statement II:The present age of Pooja is 4 years less than thrice the present age of Rohit.
   statement III:Difference between the present ages of the Rina and Rohit is 26 years.
   A) Only III
   B) Either I and II together or III alone.
   C) All are together
   D) Only I and II
   E) None of the statements
   
   View Answer

     Option B
   Solution:
   From statement III: Age of Rina = 26/2 *13 = 39 years
   From statement I and II:
   Rina = 3Rohit , Pooja – Rohit = 22 and 3Rohit – Pooja = 4
   On solving, we get  Rina = 39 years
   
7. What are the marks obtained by Sushil in Physics?
   statement I: Marks obtained in Biology is as much more than that in Chemistry as the marks obtained in Chemistry is more than that in Physics.
   statement II:The average marks obtained by Sushil in Physics, Biology and Chemistry are 65.
   statement III: Marks obtained by Sushil in Biology is 6 more than that obtained in Physics.
   A) None of  these
   B) Only I and II
   C) All statements together
   D) Only II and III
   E)  Only I
   
   View Answer

     Option C
   Solution:
   From statement I: Biology – Chemistry = Chemistry – Physics
   From statement II: Physics + Chemistry + Biology = 3*65 = 195
   From statement III: Biology = Physics + 6
   From all the above equations , Physics  = 62
   
8. What is the area of the hall?
   statement I: Total cost of flooring the hall is Rs. 14,500.
   statement II: Labour cost of flooring the hall is Rs. 3000.
   statement III: Material cost of flooring per sq. metre is Rs. 150.
   A) All statements together
   B) Only II and III
   C)Only I and II
   D) None of these
   E) Only III
   
   View Answer

     Option A
   Solution:
   Let the area of the hall be x m^2.
   Then , total material cost  = Rs. 150x
   Labour cost = Rs. 3000
   Therefore,Total cost = 150x + 3000 = 14500
   From this we get the value of x.
   Hence , all the three statements are required.
9. A,B,C,D and E are five friends. Their mean age is 18. What is the age of C ?
   Statement I : A’s age is 18
   Statement II : B’s age is 2 years less than E and E’s age is 6 years less than D.
   Statement III : C’s age is 6 years more than B’s age and 4 years more than E’s age.
   A) Only III
   B) Neither I and II nor III
   C) Only I and III
   D) All statements together
   E) Either I and III or II alone
   
   View Answer

     Option D
   Solution:
   A+B+C+D+E = 90
   From statement I : B+C+D+E = 72
   From statement II: B = E – 2 and E = D – 6
   so, D = E + 6
   From statement III: D = B + 6 and D = E + 4
   Combining all three statements, we get the age of C.
   
10. What is the area of the right angled triangle ?
    statement I: The perimeter of the triangle is 5 times of the base.
    statement II: The one of the angles of the triangle is 60deg.
    statement III: The length of hypotenuse is 4 cm.
    A) Neither I and III nor II
    B) Either I and II or III
    C) All statements together
    D) Only II and III
    E) Only I and III
    
    View Answer

      Option D
    Solution:
    From statement II and III are sufficient to answer the question.