Data Sufficiency

Questions asked in data sufficiency are varied and can come from any topic. And that is why we have decided to discuss each topic one-by-one. This will help you cover all the topics and help you in the exam. Because questions from this topic are very common in the exam. Today we are going to discuss the average related questions. In the average data sufficiency, the questions asked are very simple. They are usually of easy to moderate level.

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Data Sufficiency

Directions for the questions:

Each question given will be followed by two statements.

• If statement I alone is sufficient, but statement II alone is not sufficient mark (A)
• Statement II alone is sufficient, but the statement I alone is not sufficient mark (B).
• If both the statements I and II together are sufficient, but neither statements alone is sufficient mark (C).
• Each statement alone is sufficient mark (D).
• If statement I and II together are not sufficient mark (E).

Example of Average Data Sufficiency

Q. What is the maximum possible age of any woman, if the average of the three women’s age is 26 years?

Statement I: Not one of them is greater than 34.

Statement II: No one of them is less than 22.

Here we are required to find the maximum possible age of a woman and the average age of three women are given to us. Suppose the age of three women individually is a, b, and c. Now we are given that (a + b + c)/3 = 26. So, a + b + c = 78. Let the age of the youngest woman be ‘a’ and the age of the oldest woman be ‘c’ years. We will start solving the question from the statements individually and then combine both the statements to find the answer.

From the statement I, it is given that neither of them can be greater than 34. So the age of third women which is ‘c’ is 34 years. So, a + b + 34 = 78 => a + b = 44. But here maximum age can be greater than 34 or 34, but there is no definite answer. In statement II it is mentioned that no one is lesser than 22. So we will replace ‘a’ by 22. Similarly, we will find that b + c = 78 – 22 =  56. Again there is no definite answer from statement II.

But when we combine both the statements, we can find that b = 22 years, a = 22 years, and c = 34 years. So we can only find the answer using both the statements. Thus, the correct answer is the option C.

Practice Questions

1. Assuming that the passing grade is 50%, how many students out of 31 students have passed in the exam?

Statement I: The median grade was 51%.

Statement II: The average grade is 50%.

Ans: The correct answer is E.

2. A scooter company has 1000 employees. What will be the average yearly average wage of its executives?

Statement I: The total wages of the employees is Rs. 4,00,000 per year.

Statement II: The company has 150 executives.

Ans: The correct answer is E.

3. Find the average weight of the four new team members recently included in the team.

Statement I: The average weight of the team increases by 20 kg.

Statement II: The four new men substitute the 4 earlier team members whose weight was 64, 75, 76, and 66 kg.

Ans: The correct answer is E.