Question

What is the total mark in the examination?
Statements:
I. A student secures 36% but fails by 6 marks.
II. The pass mark is 60.

• A. Statement I alone is sufficient to determine the answer
• B. Statement II alone is sufficient, but statement I alone is not sufficient
• C. Both the statements I and II are needed
• D. Data in both the statements together are not sufficient

Hint:

In data sufficiency, test each statement separately before combining.

Answer 1

The Correct Option is C

We need to calculate the total marks for the examination. Let's analyze the given statements one by one:

1. Statement I: "A student secures 36% but fails by 6 marks."

   This implies that the marks obtained by the student are 6 less than the pass mark. However, without knowing the actual pass mark or the total marks, we cannot determine the exact value of the total marks from this statement alone.

2. Statement II: "The pass mark is 60."

   This provides us with the pass mark but does not provide any information regarding the total marks of the examination.

To find the total marks, we need to combine both statements:

From Statement I, we know:

A student secures 36%, i.e., \( \frac{36}{100} \times \text{Total Marks} = \text{Obtained Marks} \)

And the student fails by 6 marks:

\(\text{Pass Marks} - \text{Obtained Marks} = 6\)

From Statement II, the pass mark is 60. Therefore:

Obtained Marks = 60 - 6 = 54

Using the formula from Statement I:

\( \frac{36}{100} \times \text{Total Marks} = 54 \)

Solving for Total Marks:

\(\text{Total Marks} = \frac{54 \times 100}{36} = 150\)

Thus, both Statements I and II together are needed to determine the total mark, which is 150.

The correct option is: Both the statements I and II are needed.