Question:
In the three intersecting circles given below, the numbers in different sections indicate the number of persons speaking different languages. How many persons speak only two languages?
In the three intersecting circles given below, the numbers in different sections indicate the number of persons speaking different languages. How many persons speak only two languages?
Show Hint
Always double-check whether the question asks for a sum or an average of measures like mean, median, mode, and range.
Updated On: Mar 23, 2026
- 13
- 17
- 11
- 23
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Given data: 7, 6, 7, 9, 14, 9, 7, 15
Step 1: Mean:
Sum = $7 + 6 + 7 + 9 + 14 + 9 + 7 + 15 = 74$
Number of observations = 8
Mean = $\dfrac{74}{8} = 9.25$ (Approximately 9) Step 2: Median:
Arrange in order: 6, 7, 7, 7, 9, 9, 14, 15
Median = Average of 4th and 5th terms = $\dfrac{7 + 9}{2} = 8$ Step 3: Mode:
The most frequent value = 7 (appears 3 times) Step 4: Range:
Maximum - Minimum = $15 - 6 = 9$ Now combine all:
Mean $\approx 9$, Median = 8, Mode = 7, Range = 9
Sum = $9 + 8 + 7 + 9 = 33$
Average = $\dfrac{33}{4} = \boxed{8.25}$ → closest to Option (D) But as per your answer = (B) 10, let's cross-check: Clarification: Possibly the question asks for: \[ \text{Sum of Mean + Median + Mode + Range = ?} \] From above: $9.25 + 8 + 7 + 9 = 33.25$ ≈ 33 → Average = 8.3 (rounded to 8) If instead, we round mean = 10, then: $10 + 8 + 7 + 9 = 34$ → average = 8.5 → Still doesn’t lead to 10 Hence, there may be a mismatch between data and options. Conclusion: If the intended answer is (B) 10, then the data or question format might be asking for a different combination (e.g., direct sum), but with usual interpretation, \boxed{(D) 8} would be mathematically valid.
Step 1: Mean:
Sum = $7 + 6 + 7 + 9 + 14 + 9 + 7 + 15 = 74$
Number of observations = 8
Mean = $\dfrac{74}{8} = 9.25$ (Approximately 9) Step 2: Median:
Arrange in order: 6, 7, 7, 7, 9, 9, 14, 15
Median = Average of 4th and 5th terms = $\dfrac{7 + 9}{2} = 8$ Step 3: Mode:
The most frequent value = 7 (appears 3 times) Step 4: Range:
Maximum - Minimum = $15 - 6 = 9$ Now combine all:
Mean $\approx 9$, Median = 8, Mode = 7, Range = 9
Sum = $9 + 8 + 7 + 9 = 33$
Average = $\dfrac{33}{4} = \boxed{8.25}$ → closest to Option (D) But as per your answer = (B) 10, let's cross-check: Clarification: Possibly the question asks for: \[ \text{Sum of Mean + Median + Mode + Range = ?} \] From above: $9.25 + 8 + 7 + 9 = 33.25$ ≈ 33 → Average = 8.3 (rounded to 8) If instead, we round mean = 10, then: $10 + 8 + 7 + 9 = 34$ → average = 8.5 → Still doesn’t lead to 10 Hence, there may be a mismatch between data and options. Conclusion: If the intended answer is (B) 10, then the data or question format might be asking for a different combination (e.g., direct sum), but with usual interpretation, \boxed{(D) 8} would be mathematically valid.
Was this answer helpful?
0
0
Top Karnataka PGCET Quantitative Aptitude Questions
A sum of Rs. 800 amounts to Rs. 920 in 3 years at simple interest. What would be the amount, if the interest rate is increased by 3%?
- In a 100 m race, A runs at 8 km per hour. A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B?
- The perimeter of two squares are 40 cm and 32 cm. The perimeter of a third square whose area is equal to the difference of the areas of the two squares is :
In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?
- Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, what is the time required to fill the tank ?
View More Questions
Top Karnataka PGCET Mean, median, mode and standard deviation Questions
Top Karnataka PGCET Questions
A sum of Rs. 800 amounts to Rs. 920 in 3 years at simple interest. What would be the amount, if the interest rate is increased by 3%?
- In a 100 m race, A runs at 8 km per hour. A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B?
- The perimeter of two squares are 40 cm and 32 cm. The perimeter of a third square whose area is equal to the difference of the areas of the two squares is :
In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?
- Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, what is the time required to fill the tank ?
View More Questions