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Data Sufficiency Problem 2

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 cost price of the chair ?
  (I) The chair and the table are sold,respectively, at profits of 15% and 20%.
(II) If the cost price of the chair is increased by 10% and that of the table is increased by 20%,the profit reduces by Rs 20.
  (a) A (b) B (c) C (d) D
2. What is the area bounded by the two lines and the co-ordinates axes in the first quadrant ?
  (I)  The lines intersect at a point which also lies on the lines 3x – 4y = 1 and 7x – 8y = 5.
(II) The lines are perpendicular and one of them intersects the Y-axis at an intercept of 4.
  (a) A (b) B (c) C (d) D
3. What is the ratio of the volume of the given right circular cone to the one obtained from it ?
  (I) The smaller cone is obtained by passing a plane parallel to the base and dividing a the original height in the ratio of 1 : 2.
(II) The height and the base of the new cone are one-third those of the original cone.
  (a) A (b) B (c) C (d) D
4. What is the speed of the car ?
  (I)   The speed of a car is 10 more than that of the a motorcycle.
(II) The motorcycle takes 2 Hours more than the car to cover 100 Km.
  (a) A (b) B (c) C (d) D
5. Three friends P, Q and R are wearing hats,either black or white. Each person can see the hats of the other two persons. What is the color of P’s hat ?
  (I)  P says that he can see one black hat and one white hat.
(II) Q says that he can see one white hat and one black hat.
  (a) A (b) B (c) C (d) D
6. What are the values of x and y ?
  (I)   3x + 2y = 45
(II) 10.5x + 7y = 157.5
  (a) A (b) B (c) C (d) D
7. What are the values of 3 integers a, b and c ?
  (I) ab=8
(II) bc =9
  (a) A (b) B (c) C (d) D
8. Is the number completely divisible by 99 ?
  (I) The number is divisible by 9 and 11 simultaneously.
(II) If the digits of the numbers are reversed, the number is divisible by 9 and 11.
  (a) A (b) B (c) C (d) D
9. What is the value of a+ b3 ?
  (I)  a+ b= 22
(II) ab=3
  (a) A (b) B (c) C (d) D
10 After what time will the two persons Tez and Gati meet while moving around the circular track? Both of them start at the same point and at the same time ?
  (I) Tex moves at a constant speed of 5 m/s , while Gati starts at a speed of 2m/s and increases his speed by 0.5m/s at the end of every second thereafter.
(II) Gati can complete one entire lap in exactly 10s.
  (a) A (b) B (c) C (d) D


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

Detailed Solution

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  1. avinashjha

    Question7: ab=8.so. We can have values as(1,8)(8,1)(2,4)(4,2).so not sufficient.again bc=9 so we can have values has(9,1)(1,9)(3,3). So not sufficient.now taking 1 &2 togethr. By compairing the values of b in both statements we can conclude dat b=1 so a=8 n c=9.so option c. Plz say where I am wrong

    1. ElitmusZone Post author

      You analysis and answer about the given below questions incorrect.
      You are making assumptions while taking the value of B=1, -1.

      Using statement I alone we find possible values of a, b as ( -1, -8) (-2, -4) (-8, -1) (-4, -2) (1, 8) (8, 1) (2, 4) (4, 2) from these option we cannot find a and b.
      Using statement II alone we get, possible values of (b, c) as (1,9) (9,1) (-1, -9) (-9, -1) (3, 3) (-3,-3) again as before we cannot find b, c.
      Next if we combine I and II then also we cannot find unique values a, b, c. Hence answer is (D).
      You are not considering the cases when the values of a, b, and c can be negative also.

    1. Ankur

      Actually,we can find answer but by statement(1)+statement(2),but we don’t know the direction of motion i.e. both move in same direction or in opposite direction.we have two answer one for same direction and one for opposite direction so we don’t have unique solution foe this.

      1. Sarath

        Actually, the circumference is not given in the question. It alone is sufficient to decide the answer

  2. Kaushal

    In question 3, the answer should be A in my opinion as statement 1 is not sufficient to answer the question.
    It gives no indication about the radius of the new cone.
    Statement 2 is sufficient though

    1. Ankur

      In question 2, the lines given in question and the lines mentioned in statement 1 are same?Its not mentioned that the eqn given in statement 1 are those of original lines? Please help.

  3. govind

    solution of Q9—-
    we know that (a+b)2=a2+b2+2ab=22+3=25
    a+b=5 (put value of a+b in eq 1)
    so a3+b3=95

    1. Sarthak

      (a+b)^2 = 25

      (a+b) = |5|

      a+b = 5 or -5

      Therefore,solution of Q9 should be D because a^3 + b^3 = 95 or -95. Answer should be unique and we have two values of the expression.

    1. jagabandhu

      Both the equations are parallel to each other. [ you can find it by using x=1 in both you will get y same for both]

      so 2 parallel line no intersection point. so no exact value for x and y.

  4. Rajni

    In ques 9 , the ans will be C , bocz by using above 2 statment we determine the value of (a+b) and then ( a3+b3)

  5. charan kumar

    Please explain q 2? as the data from statement 1 and statement 2 are used together to find the answer and so option c but how it is A?

  6. charan kumar

    Explain q 7? as three alphabets a,b,c are intergers according to statement 1 ab = 8, possible values of 8 = 1*8 =2*4 therefore a= 1 if b =8 or a =8, b = 1, a = 2 , b = 4 or a =4, b = 2 but according to statement 2 bc = 9, means 9 = 1*9 = 3*3 so in statement 1 and statement 2 b is in common there fore common factor is 1 it implies b = 1 and so a = 8, c = 9 there fore answer is c. but how it is D?

  7. abhijit

    in qs no 1 we can get the cp of chair by using two statement..
    s1. if we take cp of chair is ‘x’, we can get profit and sp in terms of x…
    s2.now due to increse of cp ,we will get new cp ,as we already know the sp of chair from s1,we can get profit for 2nd case..
    now we have two one eqn regarding profit(before cp increse,after cp increse in terms of ‘x’) which is nothing but
    20.so solve fr x to get cp of chair….

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