Quantitative Aptitude: Data Sufficiency Questions Set 5

Directions (1-4): In each of the following questions, a question is followed by three statements numbered I, II and III. Read all the statements and answer accordingly.

1. What is the principal amount?
   Statement I: The difference between Compound Interest and Simple Interest for 2 years is 300
   Statement II: If the Compound Interest for 3 years at the rate of 10% is 3310
   Statement III: If the sum becomes double in 32 years at Compound Interest?
   A) Only I
   B) Only II
   C) II and III together
   D) Only I or II
   E) II and I or III
   
   View Answer

   Option B
   Solution:
   From II, using the formula of CI, amount can be found.
2. What is the length of the train?
   Statement I: If train can cross a platform in 35 second and a pole in 15 sec.
   Statement II: If the speed of train is 70 kmph
   Statement III: If the length of platform is 400 m
   A) I and III together
   B) I alone
   C) I and II together
   D) II and III together
   E) Even all I, II, and III are not sufficient
   
   View Answer

   Option C
   Solution:
   From I and II: speed = 70 km/hr and crosses the pole in 15 sec, so length = speed*time
3. What will be the increase percent in volume?
   Statement I: An ice cube is dip into 10 litre water
   Statement II: If radius of a cylinder increases by 20% and height increases by 10%
   Statement III: If the height of ice cube is 10 cm.
   A) All I, II and III
   B) II alone and I and III together
   C) I and II together
   D) II and III alone
   E) II alone
   
   View Answer

     Option B
   Solution:
   II:
   Volume = π*r*r*h
   So by successive formula, the increase in volume can be found
   First: r*r
   So 20 + 20 + (20)(20)/100 = 44%
   Next: 44 + 10 + (44)*(10)/100 – final increase in volume
   From I and III:
   volume of given shape (cylinder, cube, cone etc) = 10 l (initial volume). And ice cube of height 10 cm is dip into it.
   So after finding new volume or increase in volume after the ice cube is dipped, % increase in volume can be found.  
4. Find the increase percent in Cost Price to make Marked Price if
   Statement I: A trader gain 25% on Cost Price
   Statement II: A trader gain 20% on Selling Price
   Statement III: A trader gain 20% on Cost Price after giving a discount of 20% on Marked Price
   A) I and II Together
   B) II and III Together
   C) Only III
   D) All I, II and III Together
   E) None of these
   
   View Answer

     Option C
   Solution:
   Using III.
   Gain=20%=1/5
   CP : SP=5:6— (i)
   Discount=20%=1/5
   MP:SP=5:4 —-(ii)
   hence
   CP:SP:MP= 10:12:15
   hence (15-10)/10*100

Directions (5-10): In each of the following questions, a question is followed by two statements numbered I and II. Read both the statements and answer accordingly.

5. What is the ratio of milk and water in the mixture?
   Statement I: If a trader earns a profit of 20%after adding water in milk and sold it at Cost Price.
   Statement II: If a trader earns some profit after selling milk at Rs 25/Litre by adding water in it.
   A) Only I
   B) Only II
   C) Either I or II
   D) Neither I nor II
   E) Both I and II
   
   View Answer

   Option A
   Solution: From I. Water:Milk=20:100
6. What is the age of B?
   Statement I: The ratio of present age of A and B is 3:5 and 4 years before A was 8 years younger than B
   Statement II: 3 years ago the ratio of ages of A and B was 4:7 and 3 years hence the ratio will become 2:3
   A) Only I
   B) Only II
   C) Either I or II
   D) Neither I nor II
   E) Both I and II
   
   View Answer

   Option C
   Solution:
   From I:
   A/B = 3/5
   (A-4) = (B-4) – 8 or A = B – 8
   From II also, we get 2 equations.
7. What is the age of teacher?
   Statement I: In a class of 20 students the average age of students is 21 and it increases to x if the age of teacher is included.
   Statement II: In a class of 10 students the average age of students and teacher is 22 years
   A) Only I
   B) Only II
   C) Either I or II
   D) Neither I nor II
   E) Both I and II
   
   View Answer

   Option D
   Solution:
   We cannot find the age of teacher with the given data.
8. What of the distance travelled?
   Statement I: If a person covers a distance in 12 hour, covering the first half at 20 kmph and the second half at 30 kmph
   Statement II: If a person covers a distance at 30 kmph. If her decreases his speed to 25 kmph he takes two more hour to reach the destination
   A) Only I
   B) Only II
   C) Either I or II
   D) Neither I nor II
   E) Both I and II
   
   View Answer

   Option C
   Solution:
   Using I. Find the avg speed = 2*x*y/(x+y) multiply it by 12 to get distance
   Using II. Time =D/S=> 2= x/25 – x/30 where x is the distance
9. What will be the profit of A?
   Statement I: A and B invested Rs 6000 and Rs 7000 respectively. A increases his investment by 50% after 6 months and their annual profit is Rs 3800
   Statement II: A and B invested Rs 10,000 and Rs 12,000 respectively . If B doubles his investment after some months and their annual profit is Rs 2,000
   A) Only I
   B) Only II
   C) Either I or II
   D) Neither I nor II
   E) Both I and II
   
   View Answer

   Option A
   Solution:
   In II. definite time is not known as we cannot get the ratio in which profit is divided.
   In I. A=6000*6 + 9000*6=54000
   B=7000*12=84, we can find the profit now
10. Find in how many days A alone can do the work?
    Statement I: If A and B do a work together for 10 days and B left the work and A do the remaining work in 20 days.
    Statement II: If A and B can do the work in 15 days
    A) Only I
    B) Only II
    C) Either I or II
    D) Neither I nor II
    E) Both I and II
    
    View Answer

    Option E
    Solution:
    From I. 30/A + 10/B=1
    From II. 1/A + 1/B=1/15. We can get A and B using both