A, B, C, D and E took an exam. When the result was declared, the teacher wrote the following information on a piece of paper:
B has scored more than 2 marks.
C has scored more marks in the exam than A and B have scored together.
Marks scored by A are the same as the total marks scored by D and E together.
A has scored more marks than B.
No two people have scored the same marks.
If D scored more marks than B, who scored the lowest marks?
a) A
b) B
c) C
d) D
e) Data Insufficient
Answers
B scored the lowest marks
To Find:
who scored the lowest marks
Given:
B has scored more than 2 marks
C has scored more marks in the exam than A and B have scored together
Marks scored by A are the same as the total marks scored by D and E together
A has scored more marks than B
D scored more marks than B
Solution:
We can create a table of possible marks, with A being the highest possible score, and B being the lowest possible score. Then by using the information above, we can eliminate some possibilities.
A > B
D > B
A = D + E
C > A + B
Since D > B, and A > B, D's marks are not the lowest. Now we see that B is the lowest marks, as no other person has scored less marks than B.
OR
We can start by assuming that A has the highest marks among all five students, B has the lowest marks, and C, D, and E have marks in between. We can then use the information given in the problem to narrow down the possible marks for each student.
The first piece of information given is that B has scored more than 2 marks. This means that B's marks cannot be 2 or lower.
The second piece of information is that C has scored more marks in the exam than A and B have scored together. Since A has the highest marks, and B has the lowest marks, this means that C's marks must be higher than the combined marks of A and B.
The third piece of information is that the marks scored by A are the same as the total marks scored by D and E together. This means that A's marks must be equal to the sum of D's marks and E's marks.
The fourth piece of information is that A has scored more marks than B. This means that A's marks must be higher than B's marks.
The last piece of information is that D scored more marks than B. This means that D's marks must be higher than B's marks.
From all this information, we can deduce that B has the lowest marks, as no other student can have lower marks than B. All other students have marks higher than B's marks. So the answer is B.
Therefore, the answer is B.