Consider the given question and decide which of the following statements is sufficient to answer the question. If X scored an average of 50 marks in History, Language and Science, how much did he score in Science? Statements: 1. his average score in History and Language is 25.
1 alone is sufficient while 2 alone is not sufficient to answer the given question.
Understanding the Problem: Finding the Science Score
The question asks us to determine X's score in Science. We are given that X's average score in three subjects: History, Language, and Science, is 50. We need to evaluate two statements to see if either or both are sufficient to find the specific score in Science.
Let's represent the scores as follows:
- History score = \(H\)
- Language score = \(L\)
- Science score = \(S\)
The given information is the average score across these three subjects, which is 50. The formula for average is:
\[ \text{Average} = \frac{\text{Sum of scores}}{\text{Number of subjects}} \]So, for X's scores, we have:
\[ \frac{H + L + S}{3} = 50 \]Multiplying both sides by 3, we get the total score:
\[ H + L + S = 50 \times 3 = 150 \]This is our main equation: \(H + L + S = 150\). We need to find the value of \(S\).
Analyzing Statement 1: Average in History and Language
Statement 1 says: His average score in History and Language is 25.
This can be written as:
\[ \frac{H + L}{2} = 25 \]Multiplying both sides by 2, we get the sum of scores in History and Language:
\[ H + L = 25 \times 2 = 50 \]Now, let's use our main equation from the problem: \(H + L + S = 150\). We can substitute the value of \((H + L)\) from Statement 1 into this equation:
\[ (H + L) + S = 150 \] \[ 50 + S = 150 \]To find \(S\), we subtract 50 from both sides:
\[ S = 150 - 50 \] \[ S = 100 \]Using Statement 1 alone, we were able to find a unique value for X's score in Science (which is 100). Therefore, Statement 1 alone is sufficient to answer the question.
Analyzing Statement 2: Score in Language
Statement 2 says: He got 30 marks in Language.
This means:
\[ L = 30 \]Now, let's use our main equation from the problem: \(H + L + S = 150\). We can substitute the value of \(L\) from Statement 2 into this equation:
\[ H + 30 + S = 150 \]Rearranging the terms to isolate \(H\) and \(S\):
\[ H + S = 150 - 30 \] \[ H + S = 120 \]This equation, \(H + S = 120\), involves two unknown variables, \(H\) and \(S\). We have one equation but two unknowns, which means there are multiple possible values for \(H\) and \(S\) that satisfy this equation. For example:
- If \(H = 20\), then \(S = 120 - 20 = 100\). (Total score \(20+30+100 = 150\), Average \(150/3 = 50\))
- If \(H = 50\), then \(S = 120 - 50 = 70\). (Total score \(50+30+70 = 150\), Average \(150/3 = 50\))
Since Statement 2 alone does not allow us to find a unique value for \(S\), Statement 2 alone is not sufficient to answer the question.
Conclusion on Data Sufficiency
Based on our analysis:
- Statement 1 alone is sufficient to find the Science score.
- Statement 2 alone is not sufficient to find the Science score.
Therefore, the correct answer is that Statement 1 alone is sufficient, while Statement 2 alone is not sufficient.
| Statement | Information Provided | Can find Science Score (S)? | Sufficiency |
|---|---|---|---|
| Given | \(H + L + S = 150\) | No (3 unknowns) | Insufficient |
| 1 | \(H + L = 50\) | Yes (\(50 + S = 150 \implies S = 100\)) | Sufficient Alone |
| 2 | \(L = 30\) | No (\(H + 30 + S = 150 \implies H + S = 120\)) | Insufficient Alone |
Revision Table: Key Concepts
| Concept | Description | Application in this Problem |
|---|---|---|
| Average | Sum of values divided by the number of values. | Used to set up the initial equation \(H+L+S = 150\). |
| Data Sufficiency | Evaluating if given statements provide enough information to answer a question. | Checking if Statement 1 or Statement 2 uniquely determines the value of \(S\). |
| Linear Equations | Equations involving variables to the first power. | Solving for \(S\) requires manipulating linear equations derived from the statements and the initial average. |
Additional Information: Data Sufficiency Strategies
Data sufficiency questions test your ability to determine if you have enough information to solve a problem, not necessarily to actually solve it completely (though solving is often the easiest way to check sufficiency). Here are some tips:
- Read the question carefully to understand exactly what you need to find.
- Analyze the given information to set up initial equations or relationships.
- Evaluate Statement 1 alone. Assume Statement 2 is not known. See if Statement 1 gives a unique answer to the question.
- Evaluate Statement 2 alone. Assume Statement 1 is not known. See if Statement 2 gives a unique answer to the question.
- If neither alone is sufficient, evaluate if both statements together are sufficient. (Not needed in this specific problem as Statement 1 was sufficient alone).
- Remember, for a statement to be sufficient, it must provide a single, unique answer. If you can get multiple possible answers, it is not sufficient.
In this question, the core task was to use the average information to get a sum of scores, and then see which statement, when combined with the initial sum, allowed us to isolate the Science score.
Similar Questions
A question is followed by two statements. Decide which of the given statements is sufficient to answer the question.
What is the percentage increase in the profit of Company X in 2016 with respect to that in 2014?
Statements:
1. Company profit in 2014 was Rs. 1 lakh, which is 10% more than that m 2015.
2. Company profit in 2016 was Rs. 2 lakh, which was Rs. 1 lakh more than that in 2014.
Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question.
What is the average daily wage of X, Y and Z?
Statements:
- Y’s salary is half of (X + Z)
- X and Y together earn Rs. 40 more than Z and Z earns Rs. 500
Consider the given question and decide which of the following statements is sufficient to answer the question.
Which of the natural numbers A, B, C, D and E are odd numbers?
Statements :
1. A, B, C, D and E are natural numbers.
2. B is a prime number.
You are given a question and two statements. Identify which of the statements is/are necessary/sufficient to answer the question.
Question: What was the discount percent offered on the soap by the store?
Statements:
I) The store is giving 1 soap free on purchase of three.
II) Rs. 10 discount is offered on purchase of soap worth 36.
Which of the following statement is sufficient to answer the question?
Find the value of x, if x is a smaller number out of two numbers.
Statements:
I: Sum of squares of positive consecutive even numbers is 52.
II: Difference of the number is 2Which of the following statement is sufficient to answer the question?
Find the values of x, y, z from the given statements.
Statements:
I: x + y = 12 : x + z = 4
II: x - y = 6Read the following question and decide which of the given statements is/are sufficient.
What is the total number of illegal immigrants?Statements:
1. 30% of the total illegal immigrants are from Bangladesh.
2. Remaining are from India.Consider the given question and decide which of the following statements is sufficient to answer the question.
Which of these natural numbers X, Y, Z, U, and V are even numbers?
Statements:
- X, Y, Z, U, and V are consecutive numbers.
- Z is an odd number.
Consider the given question and decide which of the following statements is sufficient to answer the question.
The trains are very punctual in Malaysia. For a maximum of how long should Mr. Z wait for the train?
Statements:
1. Mr. Z had reached the railways station at 10 am
2. There is a train at 11 am and the next train is at 12 pm
Consider the given question and decide which of the following statements is sufficient to answer the question.
What is the weight of ten iron balls if each ball is of the same weight?
Statements:
1. One-fourth of each ball’s weight is 5 kg.
2. The total weight of three iron balls is 20 kg more than the total weight of two iron balls.
Important Questions from Data Sufficiency
Consider two Statements and a Question:
Statement 1: Priya is 4 ranks below Seema and is 31 st from the bottom.
Statement 2: Ena is 2 ranks above Seema and is 37" from the bottom.
Question: What is Seema’s rank from the top in the class of 40 students ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question:
Statement 1: Each of A and D is heavier than each of B, E and F, but none of them is the-heaviest.
Statement 2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A,B,C, D and E?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question :
Statement-1 : The last day of the month is a Wednesday.
Statement-2 : The third Saturday of the month was the seventeenth day.
Question : What day is the fourteenth of the given month ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider the Question and two Statements given below :
Question : Is xan integer?
Statement-1 : x / 3 is not an integer.
Statement-2 : 3 xis an integer.
Which one of the following is correct in respect of the Question and the Statements?
Consider the Question and two Statements given below:
Question : What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother.
Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3 : 5.
Which one of the following is correct in respect of the Question and the Statements?
