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Data Sufficiency Problem 6

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. Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR+RQ ?
  (I)  Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.
(II) Diameter of the circumscribed circle of the triangle PQR is equal to 18 cm.
  (a) A (b) B (c) C (d) D
2. How many people are watching TV programme P ?
  (I) Number of people watching TV programme Q is 1000 and number of people watching both  the programme P and Q is 100.
(II) Number of people watching either P or Q or both is 1500.
  (a) A (b) B (c) C  (d) D
3. Let X be a real number.Is the modulus of X necessarily less than 3 ?
  (I) X(X + 3) < 0
(II) X(X – 3) > 0
  (a) A (b) B (c) C (d) D
4. Consider three real numbers, X,Y and Z. Is Z is the smallest of the these numbers ?
  (I)   X is greater than at least one of Y and Z.
(II) Y is greater than at least one of X and Z.
  (a) A (b) B (c) C  (d) D
5. There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external point D at a distance d cm from the centre. What are the angles between each tangent and X-axis ?
  (I)  The co-ordinates of D are given.
(II) The X-axis bisects one of the tangents.
  (a) A (b) B (c) C (d) D
6. A small storage tank is spherical in shape. What is the storage volume of tank ?
  (I)  The wall thickness of the tank is 1 cm.
(II) When an empty spherical tank is immersed in a large tank filled with water,20 L of water overflows from the large tank.
  (a) A (b) B (c) C (d) D
7. The average weight of students in a class is 50 Kg. What is the number of students in the class ?
  (I)  The heaviest and the lightest members of the class weigh 60 Kg and 40 Kg.
(II) Exclusion of the heaviest and the lightest members from the class does not change the average weight of the students.
  (a) A (b) B (c) C  (d) D
8. A circle circumscribes a square. What is the area of the square ?
  (I)  Radius of the circle is given.
(II) Length of the tangent from a point 5cm away from the centre of the circle is given.
  (a) A (b) B (c) C (d) D
9. What is the price of the tea ?
  (I)  Price of coffee is Rs 5  more than that of tea.
(II) Price of coffee was Rs 5 less than the price of a cold drink which cost three times the price of tea.
  (a) A (b) B (c) C (d) D
10 Radha and Megha appeared in an examination.What was the total number of questions ?
  (I)  Radha and Megha together solved 20% of the paper.
(II) Radha alone solved 3/5th part of the paper solved by Megha.
  (a) A (b) B (c) C (d) D

Answer

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

  1. navneet suman

    sir,i think answer of the below question is wrong,please provide the right answer,,,
    A small storage tank is spherical in shape. What is the storage volume of tank ?
    (I) The wall thickness of the tank is 1 cm.
    (II) When an empty spherical tank is immersed in a large tank filled with water,20 L of water overflows from the large tank.

    1. aakash kumar jha

      i also agree with you. the material volume should be substracted to find out the volume of tank , from the 20 L of water dispressed,

  2. Rajat Tripathi

    Consider the problem graphically.

    Firstly, Statement A describes a different triangle than Statement B, as diameter of incircle should be atleast lesser than half the diameter of semi circle, considering that the hypotenuse is the diameter of the circle.

    Secondly, only the value of PR^2 + RQ^2 can be established.

  3. Rajat Tripathi

    QUS 6 : From statement 2, we can find the outer volume of the spherical tank as its volume will be equal to the amount of water displaced i.e 20 litre = 20 x 1000 cm3 and hecne its outer radius can be calculated.

    From Statement 1 we can find the inner volume of spherical tank as its thickness is given and outer radius is calculated from statement 1.

    So both the statement are required. Hence [ C ]

    1. Pramod Gangboir

      (1) X(X + 3) > 0
      (X + 3) >0
      X > – 3
      and X cant be less than -3.
      Not Sufficient.

      (2) X(X – 3) < 0
      (X – 3) <0
      X < 3
      and X cant be greater than 3.
      Not Sufficient.

      1. Karan

        You have taken the opposite signs,

        first statement is:
        X(X+3)0}
        X<0, X+3<0
        X3, hence statement 1 is SUFFICIENT.

        second statement is:
        X(X-3)>0, {not X(X-3)0, X-3>0
        X>3
        which means X=4,5,6,…..infinity.
        taking modulus, |X|>3 always, hence statement 2 is SUFFICIENT.

        Answer should be (B)

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