Data Sufficiency Reasoning: Solved Examples

Directions for data sufficiency questions (1-10):
  1. If data in the  statement I alone is sufficient to answer the question.
  2. If data in the statement II alone is sufficient to answer the question.
  3. If data either in the statement I alone or statement II alone are sufficient to answer the question.
  4. If data given in both I & II together are not sufficient to answer the question.
  5. If data in both statements I & II together are necessary to answer  the question.
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Question 1. Who is taller among P, Q, R, S & T?
  1. S is shorter than Q. P is shorter than only T.
  2. Q is taller than only S. T is taller than P and R.
Answer : (C)
From I : P is shorter than only T, this means that P is taller than all Q, R & S, so T is tallest.
From II : Q only taller than S, so S is shortest, and Q is second shortest, Now T taller than P and R both, So tallest of all.
Question 2. What is the distance between point P and point Q?
  1. Point R is 10 m west of point P and point S is 10 m north of point P.
  2. Point Q is 10 m south-east of point R. Point S is 20 m north-west of point Q.
Answer : (D)
From I : No relation between points P and Q
From II : In this since we don’t know the angles between sides of triangle forming with points PQS and PQR, PQ cannot be determined.
Question 3. How is Shubham related to Shivani?
  1. Shubham is brother of Meenal. Shivani is niece of Pooja.
  2. Neeraj is Meenal’s uncle and Preeti’s brother
Answer : (D)
Either statement cant give the answer.
From both statements we can get the relationship as Pooja is Neeraj’s sister but it cannot be clearly said that Shubham & Meenal are Pooja’s children or not & Shivani is Neeraj’s daughter, because there can be other siblings of Neeraj and Pooja also.
Question 4. How is PRODUCT written in that code language?
  1. In a certain code language, AIEEE is written as BJFFF.
  2. In a certain code language, GYPSY is written as FXORX
Answer : (E)
From I: All vowels are coded as next alphabets
From II: All consonants are coded as previous alphabets
So from both the statements.
Question 5. How is ‘face’ written in that code language?
  1. In a certain code language, ‘no one with face’ is coded as ‘fo to om sop’ and ‘no one has face’ is coded as ‘om sit fo sop’
  2. In a certain code language, ‘face of no light’ is coded as ‘om mot fo kiz’ and ‘no one is smart’ is coded as ‘sop fo sip lik’.
Answer : (E)
From I : ‘no one face’ is coded as ‘om fo sop’
From II : ‘no’ is ‘fo’
Now from both – ‘one face’ is ‘om sop’ and now from II: ‘face of no light’ is written as ‘om mot fo kiz’, ‘face’ is ‘om’
Question 6. What is Monica’s position with respect to Rahul?
  1. In a row of 25 students, Monica is sitting 12th from right end of row and Rahul is sitting 20th from left end of the row.
  2. Monica is 4th from right end and Rahul is 8th from left end.
Answer : (A)
From I: The position of both of them  in a row can be known, so Monica’s position can be known.
From II: Since the total number of students is not known in this case, Monica’s position with respect to Rahul cannot be known.
Question 7. Who has secured less marks among P, Q, R , S & T ?
  1. S has secured less marks than only R and T.
  2. Q secured more marks than P.
Answer :  (A)
From I: S is at 3rd position from top, & R and T at 1st or 2nd.
From II : Q’s marks more than P
From both, order in descending is R/T, T/R, S, Q, P
So P has secured less marks among all.
Question 8. On which floor is Shikha residing?
  1. In a six storey building (Ground floor is parking space), Rekha is on fourth floor. Shikha likes to reside only on even numbered floors. Reema is not on the topmost floor.
  2. Reema is two floors below Peter who is 3 floors above Shikha.
Answer :  (E)
From I: 6 storey building has 2, 4 and 6 even numbered floors, out of which Rekha is on 4th, so Shruti is on either 2 or 6. Reema is not on 6 (top-most), but since it is not given Reema also stays on an even numbered floor, nothing can be known about Shikha
From II : Peter is 3 floors above Shikha, this means that Shikha will have to be at 1, 2 or 3 floor, so that Peter is at 3 above Shikha’s floor.
From both, Shikha is at 2nd floor.
Question 9 : Amit is facing which direction?
  1. Shikha is facing east direction and if she turns to her right she will face Raj.
  2. Amit is facing opposite direction as that of Kiran who is facing Shikha.
Answer :  (D)
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From I: Can't be found from I because no mention of Amit.
From II : Cannot be found because don’t know the direction of either Kiran or Shikha.
From both also we cannot found because we don’t know when Kiran is facing Shikha – when Shikha facing east or when Shikha after turning right faces south.
Question 10: In which month is Meena’s birthday?
  1. Shikha remembers that Meena’s birthday was 4 months ago.
  2. Raj remembers that after 2 months from now, Meena’s birthday will be 6 months back.
Answer :  (D)
Since in each statement we do not know that which month is going on right now, question cannot be answered.