A particular school management wants to contact all parents, all businessmen and all engineers. The following statistics are available with the school.
Businessmen = 50
Engineers = 25
Parents = 2500
Businessmen who are engineers = 0
Businessmen who are parents = 25
Engineers who are parents = 15
The number of people who need to be contacted are _________.
Businessmen = 50
Engineers = 25
Parents = 2500
Businessmen who are engineers = 0
Businessmen who are parents = 25
Engineers who are parents = 15
The number of people who need to be contacted are _________.
Show Hint
Correct Answer: 2535
Solution and Explanation
- \( B \) = Businessmen = 50,
- \( E \) = Engineers = 25,
- \( P \) = Parents = 2500.
We are also given the intersections:
- \( B \cap E = 0 \) (No businessmen are engineers),
- \( B \cap P = 25 \) (Businessmen who are parents),
- \( E \cap P = 15 \) (Engineers who are parents).
We are tasked with finding the total number of distinct individuals to contact, which corresponds to the union of the three sets: \[ |B \cup E \cup P| = |B| + |E| + |P| - |B \cap E| - |B \cap P| - |E \cap P| + |B \cap E \cap P|. \] Since no businessmen are engineers, \( B \cap E = 0 \), and thus: \[ |B \cup E \cup P| = 50 + 25 + 2500 - 0 - 25 - 15 + 0 = 2535. \] Thus, the total number of people to contact is \( 2535 \).
Top Questions on Data Interpretation
A pie chart shows the distribution of students across 5 faculties in a university. If 20% are in Arts, 25% in Science, 15% in Law, 30% in Engineering, and the rest in Commerce, what is the angle (in degrees) for Commerce?
- CUET (UG) - 2025
- General Aptitude
- Data Interpretation
The table given below provides the details of monthly sales (in lakhs of rupees) and the value of products returned by the customers (as a percentage of sales) of an e-commerce company for three product categories for the year 2024. Net sales (in lakhs of rupees) is defined as the difference between sales (in lakhs of rupees) and the value of products returned (in lakhs of rupees).
- IPMAT - 2025
- Logical Reasoning
- Data Interpretation
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- General Aptitude
- Data Interpretation
- Eight employees of an organization have been rated on a scale of 1 to 50 for their performance. All ratings are integers. The overall average rating of the eight employees is 30. While the five employees with the highest ratings average 38, the five employees with the lowest ratings average 25. Which of the following, about the ratings obtained by the eight employees, is DEFINITELY FALSE?
- XAT - 2025
- Quantitative Ability and Data Interpretation
- Data Interpretation
The plots below depict and compare the average monthly incomes (in Rs. ’000) of males and females in ten cities of India in the years 2005 and 2015. The ten cities, marked A-J in the records, are of different population sizes. For a fair comparison, to adjust for inflation, incomes for both the periods are scaled to 2025 prices. Each red dot represents the average monthly income of females in a particular city in a particular year, while each blue dot represents the average monthly income of males in a particular city in a particular year. The gender gap for a city, for a particular year, is defined as the absolute value of the average monthly income of males, minus the average monthly income of females, in that year.
- XAT - 2025
- Quantitative Ability and Data Interpretation
- Data Interpretation
Questions Asked in GATE XH- C6 exam
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?
Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.
Abuse \( \rightarrow \) Insult \( \rightarrow \) Ridicule
__________ \( \rightarrow \) Praise \( \rightarrow \) Appreciate
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is:
- Had I learnt acting as a child, I ________ a famous film star.
Select the most appropriate option to complete the above sentence. - A car started from city P at 9:40 AM. The time taken for the car to reach city Q is 4 hours and 50 minutes. The time of arrival of the car at city Q is: