Quantitative Aptitude: Data Sufficiency Set 3

Directions (1-5): 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. A and B are two numbers. What is the ratio of A/B
   Statement I: Their average is 5/2 times B
   Statement II: Their sum is 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 A
   Explanation:
   From I : (A+B)/2 = 5B/2 => (A+B)/B = 5 =>A/B=4
2. Average age of employees working in Bank is 30 years. Next year, 10 workers will retire. What will be the average age next year?
   Statement I: There are 90 employees in bank
   Statement II: Retirement age is 60 year
   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:
   Total age now = 90*30 =2700 (Using I)
   Total age of outgoing people next year =60*10=600 (Using II)
   New total age of remaining 80 people next year = 2700 -600 +80 =2180
   Average = 2180/80
3. Fine the average of 7 consecutive odd numbers.
   Statement I: The 5^th number exceeds the 1^st number by 8.
   Statement II: The 4^th number is three times the first 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 B
   Explanation:
   Using II : (x+6)=3x
   find x, find all the 7 terms and hence average.
4.  What is the difference between present ages of Amit and Sumit ?
   Statement I: The ratio of the present age of Amit to that of Sumit six years ago is 2 : 1.
   Statement II: The ratio of the present age of Amit and Sumit is 4 : 3.
   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:
   Using both we will get two equations of two variables. Solve and get.
5. What is the profit earned by selling an article for Rs. 900?
   Statement I: 25% of profit would have been earned if it had been sold for Rs. 750.
   Statement II: Selling price is 300% of the profit earned.
   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 : Find CP using SP and Profit %. Get profit
   From II : Given SP =300/100 * profit => 900=300/100* profit =>Profit = Rs 300

Directions (6-10): 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.

6. What is the measure of the diagonal of a rectangle?
   Statement I: Length of the rectangle is 9 metre
   Statement II: Area of the rectangle is 72 square metre
   Statement III: Breadth of the rectangle is 8 metre
   A) All I, II and III 
   B) Only I and II
   C) Any two of the three
   D) Only II
   E) Only II and III
   
   View Answer

     Option C
   Explanation:
   Diagonal = Root(Length² + Breadth²)
7. A shopkeeper sells a homogeneous mixture of X and Y at a rate of Rs 400 per kg. Find the profit percentage of the shopkeeper
   Statement I: He brought X at the rate of Rs 350 per kg
   Statement II:  He bought Y at Rs 10 higher than the rate of X per kg.
   Statement III: He brought Y at the rate of Rs 420 per kg
   A) Only I and II
   B) Only I and III
   C) Any two of the three
   D) All three together are sufficient
   E) I , II and III together are not sufficient
   
   View Answer

     Option E
   Explanation:
   We don’t know the ratio in which the mixture is mixed. So we cannot find the CP and hence profit.
8. How many students are there in all in the institute of Computer, Electrical and Mechanical ?
   Statement I: 20% of the students study Mechanical.
   Statement II: The number of students studying Computer and Electrical are in the ratio of 5:3.
   Statement III: The number of students studying Electrical is more than that of studying Mechanical by 100.
   A) Only II and III
   B) III and either I or II only
   C) Any two of the three
   D) All I, II and III
   E) Question cannot be answered even with the information in all the three statements
   
   View Answer

     Option D
   Explanation:
   Using I and II, percentage of students in three institute can be found out. Using this data and III, we will get final answer.  
9. What is the speed of the train ?
   Statement I: The train crosses 300 metres long platform in 45 seconds.
   Statement II: The train crosses another stationary train of same length in 60 seconds.
   Statement III: The train crosses a signal pole in 30 seconds.
   A) Only III and either I or II
   B) Any two of the three
   C) Only II and either I or III
   D) Only I and II
   E) Only I and either II or III
   
   View Answer

     Option E
   Explanation:
   Use Speed=D/T ; As speed in all case is same.
10. What is the cost of flooring a rectangular hall?
    Statement I: The ratio of length and breadth of the hall is 5:4.
    Statement II: The length of the hall is 50 metres and the cost of flooring is Rs. 1000 per square metre.
    Statement III: The perimeter of the hall is 180 metres and the cost of flooring is Rs. 1000 per square metre.
    A) Only I and II
    B) Only II and III
    C) Any two of the three
    D) Only I and III
    E) I and either II or III
    
    View Answer

      Option C
    Explanation:
    Using any two statement, the length and breadth can be found. And Rate of flooring is also available.