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Data Sufficiency Problem 5

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. If m is an integer, is m odd ?
  (I) m/2 is not an even number .
(II) m – 3 is an even integer.
  (a) A (b) B (c) C (d) D
2. Total amount of Rs 38500 was distributed among Praveen, Ranjan and Nitesh. How much does each get ?
  (I)   Praveen gets 2/9 of what other two get.
(II)  Ranjan gets 3/11 of what other two get.
  (a) A (b) B (c) C (d) D
3. Of the 300 students who speak French,Russian or both, how many speak only French ?
  (I)  196 students speak both French and Russian.
(II) 58 students speak Russian only.
  (a) A (b) B (c) C (d) D
4. If the teacher adds four students to the class,can he evenly distribute the class in groups of 4 students ?
  (I) If 12 students are added to the class,then the teacher can divide students evenly in groups of 8.
(II) Initially, the number of students is not divisible by 8.
  (a) A (b) B (c) C (d) D
5. Is average (arithmetic mean) score of GMAT 500 ?
  (I)  Half of the students scored more than 500 and half less than 500.
(II) Highest is 800 and lowest is 200.
  (a) A (b) B (c) C (d) D
6. Is x = y ?
  (I)  (x + y) (1/x + 1/y) = 4
(II) (x – 50)(x – 50)=(y – 50)(y – 50)
  (a) A (b) B (c) C (d) D
7. Is |x – 2| < 1 ?
  (I) |x| < 1
(II)|x-1| < 2
  (a) A (b) B (c) C (d) D
8. Two Friends,Ram and Gopal, bought apples from a wholesale dealer. How many apples did they buy ?
  (I)   Ram bought one-half the number of apples that Gopal bought.
(II) The wholesale dealer had a stock of 500 apples.
  (a) A (b) B (c) C (d) D
9. What is the value of X ?
  (I)  X and Y are unequal even integers,less than 10 and X/Y is an odd integer.
(II) X and Y are even integers,each less than 10 and product of X and Y is 12.
  (a) A (b) B (c) C (d) D
10 What are the values of m and n ?
  (I)  n is an even integer m is an odd integer and m is greater than n.
(II) Product of m and n is 30.
  (a) A (b) B (c) C (d) D


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

Detailed Solution

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    1. Rasmita

      i think in question no 9 negative integer is consider but not in question no 10 and in question 6
      (x+y)(1/x+1/y) when u solve this u will get x=-y while when u solve (x-50)(x-50)=(y-50)(y-50) u will get x=y that’s y the answer is A.

        1. Amit

          Yes for 6th question, both are sufficient alone. as both gives x=y. So answer should be B i..e both alone.

          For question 9 & 10, negative values should be considered, hence D for 9 and D also for 10. ( because negative integers are also considered as ODD and EVEN )

          1. Amit

            ^^ Sorry my bad.
            Statement 2 is not sufficient In question 6. So answer is A., and not D.

            Couldn’t edit above post.

        2. Abhishek Thakur

          Ans should be A.
          x^2-50^2 = y^2-50^2
          so x^2=y^2

          so x=+- y
          x=y or x=-y

          so only 1 statement is right so answer will be A

          1. Sai Chandra N

            Answer is A.. but I believe the solution you proposed is wrong..

            so no definite solution from statement 2.. i.e x=y or x+y=100

    1. Amit

      NO because, you can have multiple values for X. Consider negative values too, you will get the answer as D only.
      To answer why do we consider negative values is because statement says x,y<10, but it doesn't mean that they cannot be less than 0, as (-2<10) which is valid.
      Same is with statement two, multiple values are possible.

      Hope it helps.

      1. Manish

        What about X= -6 and Y= -2? These values of X and Y are satisfied by both statements together.So according to me, C should be the answer to the 9th question. If I am wrong, justify your answer with these two values.

  1. Samiksha Panwar

    can any one tell me when to consider negative integers and when not to? It’s really confusing.

  2. Ashu Agarwal ( NIT BHOPAL)

    if given like ×< 0 , then we can consider the negative value othervwise only positive values will be considered by default.
    in question no 9.. there is no way to consider the negaitive value because there is nothing mentioned like x<0

  3. Rohit Yadav

    For questions related to data sufficiency we have to consider both +ve nd -ve values unless the term positive integers is stated in the question.
    The answer for question 10 is wrong. It should be D.

  4. maniish

    answer to 6 shud be B since both the statements are correct (x-50)(x-50) = (y-50)(y-50) (x-50)^2 = (y-50)^2 x-50 = y-50
    x = y…… plzz help..e

  5. Prabhat Gupta

    Answer to question 10 should be D
    because (2,15) ,(-10,-3) and (-30,-1) also satisfies both the statements .

  6. Sai Chandra N

    The answer to question 7, I believe it must be B
    |X-2|<1 i.e -1<x<3
    |X|<1 i.e -1<x<1
    |X-1|<2 i.e -1<x<3

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