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Follow the given instructions. Each item...

Follow the given instructions. Each item has a question followed by two statements.The average of three quotation for a particular item is 120. Is the highest quotation less than or equal to 139?
I The lowest quotation is 90.
II. One of the quotations is 125.

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 the question can be answered with the help of both the statements but not with the help of either statement itself

D

if the question cannot be answered even with the help of both the statements.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine if the highest quotation is less than or equal to 139, given the average of three quotations is 120. ### Step-by-Step Solution: 1. **Calculate the Total Sum of Quotations:** - The average of the three quotations is given as 120. - To find the total sum of the quotations, we multiply the average by the number of quotations: \[ \text{Total Sum} = \text{Average} \times \text{Number of Quotations} = 120 \times 3 = 360 \] 2. **Analyze Statement I:** - Statement I states that the lowest quotation is 90. - If the lowest quotation is 90, we can denote the three quotations as \( Q_1, Q_2, Q_3 \) where \( Q_1 = 90 \) (the lowest). - Let \( Q_2 \) and \( Q_3 \) be the other two quotations. Thus, we have: \[ Q_1 + Q_2 + Q_3 = 360 \implies 90 + Q_2 + Q_3 = 360 \implies Q_2 + Q_3 = 270 \] 3. **Analyze Statement II:** - Statement II states that one of the quotations is 125. - This means either \( Q_2 = 125 \) or \( Q_3 = 125 \). Let's assume \( Q_2 = 125 \). - Then, substituting \( Q_2 \) into the equation from Statement I: \[ 90 + 125 + Q_3 = 360 \implies Q_3 = 360 - 215 = 145 \] 4. **Determine the Highest Quotation:** - Now we have the three quotations: \( Q_1 = 90 \), \( Q_2 = 125 \), and \( Q_3 = 145 \). - The highest quotation among these is \( 145 \). 5. **Compare with 139:** - We need to check if the highest quotation (145) is less than or equal to 139. - Since \( 145 > 139 \), we conclude that the highest quotation is not less than or equal to 139. ### Conclusion: - Both statements together allow us to conclude that the highest quotation is 145, which is greater than 139. Therefore, the answer to the question is **No**. ### Final Answer: - The answer is that the highest quotation is **not less than or equal to 139**.
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