Question

The average of three unequal quotations for a particular share is Rs.110. If all are quoted in integral values of rupee, does the highest quotation exceed Rs.129?
I. The lowest quotation is Rs.100.
II. One of the quotations is Rs.115.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both the statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

If average and part values are given, plug values into the total and verify all conditions like inequality and integrality.

Answer 1

The Correct Option is C

We are told the average of 3 unequal quotations is Rs.110. So: \[ \frac{x + y + z}{3} = 110 \Rightarrow x + y + z = 330 \] We are to find whether the highest of the three exceeds 129. From Statement I: The lowest quotation is Rs.100
Let’s assume $x = 100$ (lowest).
Then $y + z = 230$
But without knowing either $y$ or $z$, we can’t determine if the maximum exceeds 129. Try values like $y = 100$, $z = 130$ (✓) or $y = 115$, $z = 115$ — but these could be equal. So I alone is insufficient. From Statement II: One quotation is Rs.115
That helps us plug in one variable, but without knowing the lowest, the other two could still be anywhere. Combining I and II:
Let $x = 100$, $y = 115$
So $z = 330 - 215 = 115$
But now $y = z = 115$, which violates the condition that all quotations are unequal. So $z \neq 115$
Try $z = 115 + 1 = 116$
Then $x + y + z = 100 + 115 + 116 = 331$ too high
So we reduce $z$: try $z = 114$ → total = 329 ⇒ average = 109.67
Eventually, we can find that the only valid setup with $x = 100$, $y = 115$ will force $z$ to be $115$, making two equal. To maintain inequality, the third must be higher than 115 and raise the total above 330. Hence, for the total to remain 330, and values to be unequal integers, one of the values must go above 129 to balance lower entries like 100 and 115. Therefore, both statements together are needed.