Data Sufficiency

In each of the following problems, there is one question and three statements I, II and III given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find which of the statements is/are sufficient to answer the given question. Choose the correct alternative in each question.

Who among Siddhartha, Nikunj, Vipul and Mukul is the youngest?
I     Vipul is younger than Mukul but older than Siddhartha and Nikunj.
II   Mukul is the oldest.
III  Siddhartha is older than Nikunj.

Answer: (d)

From I, we have: M > V, V > S, V > N ...(i)

From II, we have: Mukul is the oldest ...(ii)

From III, we have: S > N ...(iii)

Combining (i) and (iii), we get :M > V, V >S > N or M>V > S > N. Clearly, Nikunj is the youngest.

In which year was Sanjay born ?
I       Sanjay is six years older than Gopal.
II     Gopal’s brother was born in 1982.
III   Sanjay’s brother is two years younger than Gopal’s brother who was eight years younger than Gopal.

Answer: (d)

From II, we know that Copal's brother was born in 1982.

From III, we find that Gopal's brother was 8 years younger to him i.e. Gopal was born in 1974.

From I, we find that Sanjay is 6 years older than Gopal. Thus, Sanjay was born in 1968.

How is ‘DATE’ written in the code language ?
I.     DEAR is written as $#@? in that code.
II.   TREAT is written as %?#@% in that code.
III.  TEAR is written as %#@? in that code,

Answer: (d)

Observing I, II and III, we find that similar letters have similar code symbols at the corresponding places in the code. So, this is direct-coding.

Thus, to find the code for DATE, we need the code for D which can be obtained from I only (i.e. $.) and the codes for A, T and E which can be obtained either from II or III (@, # and % respectively).

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Five persons – A, B, C, D and E are sitting in a row. Who is sitting in the middle?
I.     B is between E and C.
II.   B is to the right of E.
III.  D is between A and E.

Answer: (d)

From I, the order is : E, B, C or C, B, E.

From II, the order is : E, B.

From III, the order is : A, D, E.

Combining the above three, we get the order as : A, D, E, B, C. Clearly, E is sitting in the middle.

What is Suman’s rank from the top in a class of forty students ?
I .      Suman is 3 ranks below Deepak from the top.

II .    Deepak’s rank from the bottom is 23.

III.   Suman is 3 ranks above Deepak from the bottom.

Answer: (e)

From II, we conclude that in a class of 40, Deepak ranks 23rd from the bottom i.e. 18th from the top.

From I and II, we find that Suman is 3 ranks below 18th rank from the top i.e. she ranks 21st from the top.

From II and III, we find that Suman is 3 ranks above 23rd rank from the bottom

i.e. she ranks 20th from the bottom or 21st from the top.