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Data Sufficiency Problem 3

Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question.
Mark A If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone.
Mark B If the question can be answered by using either statement alone.
Mark C If the question can be answered by using both statements together, but cannot be answered by using the either statement alone.
Mark D If the question cannot be answered even by using both the statements together.
1. What is the number of type-2 widgets produced, if total number of widgets produced is 20,000 ?
  (I) If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same.
(II) The ratio in which type-1 and type-2 widgets are produced is 2 : 1.
  (a)  A (b) B (c) C (d) D
2. How old is Sachin in 1997 ?
  (I)  Sachin is 11 yr  younger than Anil whose age will be a prime number in 1998.
(II) Anil’s age was a prime number is 1996.
  (a) A (b) B (c) C  (d) D
3. What is the total worth of Lakhriram’s assets ?
  (I) A compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs. 1500 this year.
(II) The interest is compounded once every four months.
  (a) A (b) B (c) C (d) D
4. How many different triangles can be formed ?
  (I)  There are 16 co-planer straight lines.
(II)  No two lines are parallel.
  (a) A (b) B (c) C (d) D
5. What is the selling price of the article ?
  (I)  The profit on sales is 20%.
(II) The profit on each unit is 25% and the cost price is Rs 250.
  (a) A (b) B (c) C (d) D
6. What is the cost price of the article ?
  (I)  After selling the article, a loss of 25% on cost price is incurred.
(II) The selling price is three-fourths of the cost price.
  (a) A (b) B (c) C (d) D
7. If p and q are the roots of the equation (ax+ bx + c=0) then what is the value of ( p+ q) ?
  (I)  p + q = -b/a
(II) 2pq = c/a
  (a) A (b) B (c) C (d) D
8. If a, b and c are integers, is (a – b + c) > (a + b – c) ?
  (I)  b is negative.
(II) c is positive.
  (a) A (b) B (c) C (d) D
9. What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together ? (The containers are of equal volume) Assume container volume=volume of liquids
  (I)  The ratio of liquid A to liquid B in the first and second vessels are 3 : 5, 2 : 3 respectively.
(II) The ratio of liquid A to liquid B in vessel 3 is 4 : 3.
  (a) A (b) B (c) C (d) D
10 A tractor traveled a distance of 5 M. What is the radius of the rear wheel ?
  (I)  The front wheels rotates ‘N’ times more than the rear wheel over this distance.
(II)The circumference of the rear wheel is ‘t’ times that of the front wheel.
  (a) A (b) B (c) C (d) D


1. B 2. D
3. C 4. D
5. A 6. D
7. C 8. C
9. D 10. D

Detailed Solution 

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  1. Sanket

    In sum 9, answer should be c
    let k be volume of each vessel.
    For vessel 1,
    Quantity of A and B are 3x,5x.
    so, Quantity of A and B are 3k/8, 5k/8
    Similary for vessel 2,
    Quantities for A and B would be 2k/5, 3k/5
    And for vessel 3,
    A and B are 4k/7,3k/7.
    So now adding A quantites and B Quantities ratio can be found.
    Correct me if I am wrong.

  2. Amit

    The answer to problem 1 should be D,

    because it is not mentioned as if ONLY Type 1 and Type 2 products are produced. What if Type 3 is also there ?

    & as per your given solution, u have assumed that these are the only two types produced which is not correct.

  3. Prabhat Gupta

    The answer to problem 10 should be C.

    Statement 1 : (N+n)*2*pi*r = n*2*pi*R=5 ;
    Statement 2 : r*t = R ;

    Solving 1 and 2 ;

    R = 5(t-1)/(2*pi*N);

    r : front radius
    R : rear radius
    pi : 22/7
    n : revolutions by rear wheel

  4. Naveen ram

    In question 1 for option 1 how can you take 1.1A + 0.94B since total production percentage is not given?

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