Quantitative Aptitude: Data Sufficiency Set 1

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 probability of getting two black socks from a drawer containing only black and red socks?
   Statement I: There are total 36 socks in the drawer.
   Statement II: The probability of the first sock being black is 1/6.
   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 statement II, prob of second sock being black cannot be known.
   If we use both statements: Since total 36 socks are there and prob of first being black is 1/6, it can happen only when there are 6 black socks in the drawer to make the first prob as 6/36 = 1/36. So we can know that prob of second sock being black is 5/35. And then the prob. can be found.
   
2. In a concert in school, amount gathered by selling the tickets was Rs 60000 when all were of equal value. Each student got 1 ticket. What was the cost of 1 such ticket?
   Statement I: If the price of each ticket had been Rs 50 less, the total amount gathered would have been 15000 less.
   Statement II: If the price of each ticket had been Rs 50 more, the total amount gathered would have increased by 25%.
   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:
   Let cost of 1 ticket = Rs x. So total students who got tickets is 60000/x
   From statement I,
   (x – 50) × 60000/x = 60000 – 15000
   Solving we get cost of 1 ticket, x = Rs 200
   Similarly from statement II,
   (x + 50) × 60000/x = (125/100) × 60000
   Solving we get cost of 1 ticket, x = Rs 200
   
3. How long did it take Priyanka to drive to her home?
   Statement I: If she had driven twice as fast she would have taken 15 minutes.
   Statement II: Her average speed was 40 km per hour.
   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 statement I, distance/speed = time
   And if twice speed then
   distance/(2*speed) = 15
   Solving both equations, we can find time.
   From statement II, we also require distance to know the time.
   
4. What is the speed of man in still water?
   Statement I: The speed of man in still water is three times the speed of the stream.
   Statement II: In 20 minutes, the man can swim twice as far with the stream as he can against the stream.
   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 Statement I, speed of stream = x km/hr then man’s speed = 3x km/hr
   From Statement II, let speed of stream = a km/hr and man’s speed = b km/hr
   Since times is equal to travel upstream and downstream, 2d/(a+b) = d/(b-a)
   We get the same statement as I, man’s speed (b) = 3 times speed of stream (a).
   Thus both the statements are not sufficient to answer the question.
   
5. What was the profit earned by selling an article?
   Statement I: The article was sold for Rs 950 after getting a discount of 5% on the labelled price.
   Statement II: A profit of 2% is made on the labelled price in buying that article.
   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 statement I, we can find the MP of article as (100/95) × 950 = Rs 1000
   From statement II, we can find the CP of article by using the MP from statement I as (102/100) × 1000 = Rs 1020
   Now we have both SP and CP to find the profit%
   
6. How many people are travelling in the train?
   Statement I: There are 25% women and 35% children passengers.
   Statement II: There are 148 men passengers in the train.
   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 statement I we get 100 – (25+35) = 40% men in train
   Now from statement II, 40/100 × x = 148. So total people = x = 370.
   
7. What will be the age of Rubi after 6 years?
   Statement I: Ratio of age of Shiva and Rubi is 2 : 3.
   Statement II: Twelve times the age of Shiva equals eight times the age of Rubi.
   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:
   We require 2 equations to get the ages of both. But from both statements we get a single statement 3S – 2R = 0.
   
8. What is the length of the train travelling at uniform speed?
   Statement I: The train crossed another train of length 300 m moving in opposite direction in 24 seconds.
   Statement II: The train crossed a bridge of length 650 m in 35 seconds.
   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 length of train = x m.
   Let speed of train = y m/s
   From statement I, let speed of another train = z m/s
   So (x+300)/24 = y+z
   From statement II, (x+650)/35 = y
   So from both statements also we have 3 variables and 2 equations.
9. A man invested a sum of Rs 50,000. He invested some part at 6 % p.a. and remaining at 6.5% p.a. How much money did he invest at 6 % p.a.?
   Statement I: The total interest amount paid after 1 year was Rs 3150
   Statement II: The interest on one sum was twice that on the other.
   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:
   Let first part is Rs x, then remaining is Rs (50000-x)
   From statement I,
   [(x*6*1)/100] + [((50000-x)*6.5*1)/100] = 3150
   So x can be calculated.
   From statement II,
   [(x*6*1)/100] = 2 × [((50000-x)*6.5*1)/100]
   So x can be calculated.
   
10. What is the total cost of painting a cone at the rate of 20 Rs per square metre?
    Statement I: The radius and the slant height of the flask are 14 m and 12 m respectively
    Statement II: The area of the base of cone is 154 sq. m and its height is 7 m.
    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 statement I, r = 14 m, l = 12 m, so cost of painting = 20*(ᴨrl)
    From I: ᴨr² = 154, so r can be calculated, h = 7 m, so l = √ r² + h², so l can also be calculated.
    Cost of painting = 20*(ᴨrl)