English and Logical Reasoning Prep Guide
- Exam
- English and Logical Reasoning Prep Guide
- Subject
- Logical Reasoning
- Chapter
- Data Sufficiency
English and Logical Reasoning Prep Guide · Logical Reasoning · Data Sufficiency
Directions: Each of the questions below consists of a question and...
Directions: Each of the questions below consists of a question and two or more statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:
5 students P, Q, R, S and T were standing according to their heights with the shortest one being at the left most corner and highest one being at the right end.
I. Q was standing between R and P. S was standing at the right end of the line.
II. T did not have the greatest height of all. P had more height than only R and Q.
III. R, Q, P all were shorter than T.
II. T did not have the greatest height of all. P had more height than only R and Q.
III. R, Q, P all were shorter than T.
Who was the 4th highest among all five students?
Options
- AStatement (I) and Statement (II) together are sufficient.
- BStatement (II) and Statement (III) together are sufficient.
- CEither statement (I) and statement (III) together or statement (II) is sufficient
- DAll the statement (I), statement (II) and statement (III) together are sufficient.
Correct answer
C.
Either statement (I) and statement (III) together or statement (II) is sufficient
Step-by-step solution
Statement I: I Q was standing between R and P. S was standing at the right end of the line.
Reference:
S was standing at the right end of the line.
As it is given shortest one is sitting at extreme left and highest one is sitting at extreme right end and given reference is that S was standing at the right end of the line. So, S will be standing at extreme right end.
_ < _ < _ < _ < S
Reference:
Q was standing between R and P.
With this piece of information, we can clearly see that there are two cases possible.
Case 1:
_ < R/P < Q < P/R < S
Case 2:
R/P < Q < P/R < _ < S
Hence, Statement I is not sufficient
Statement II: T did not have the greatest height of all. P had more height than only R and Q.
References:
P had more height than only R and Q.
T did not have the greatest height of all.
R/Q < Q/R < P < T < _
Hence, only II statement is sufficient.
Statement III: R, Q, P all were shorter than T.
Reference:
R, Q, P all were shorter than T.
R/Q/P < Q/P/R < P/R/Q < T
Combining statements I and III, we get:
R/P < Q < P/R < T < S
Hence, statements I and III are sufficient.
Hence, the correct answer is option C.
Reference:
S was standing at the right end of the line.
As it is given shortest one is sitting at extreme left and highest one is sitting at extreme right end and given reference is that S was standing at the right end of the line. So, S will be standing at extreme right end.
_ < _ < _ < _ < S
Reference:
Q was standing between R and P.
With this piece of information, we can clearly see that there are two cases possible.
Case 1:
_ < R/P < Q < P/R < S
Case 2:
R/P < Q < P/R < _ < S
Hence, Statement I is not sufficient
Statement II: T did not have the greatest height of all. P had more height than only R and Q.
References:
P had more height than only R and Q.
T did not have the greatest height of all.
R/Q < Q/R < P < T < _
Hence, only II statement is sufficient.
Statement III: R, Q, P all were shorter than T.
Reference:
R, Q, P all were shorter than T.
R/Q/P < Q/P/R < P/R/Q < T
Combining statements I and III, we get:
R/P < Q < P/R < T < S
Hence, statements I and III are sufficient.
Hence, the correct answer is option C.