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Five friends Adi, Brian, Close, Derek and Eli appeared in two aptitude tests. In the first aptitude test, Derek’s score was 50 percent less than the average (arithmetic mean) score of the five people. In the second aptitude test, Derek scored 50 percent more than what he scored on the first aptitude test. If the scores of his friends in the second aptitude test were same as their scores in the first aptitude test, by approximately what percentage was Derek’s score less than the average (arithmetic mean) score of the 5 people in the second aptitude test?
- a)25%
- b)28%
- c)33%
- d)40%
- e)50%
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Five friends Adi, Brian, Close, Derek and Eli appeared in two aptitude...
Given:
- 1st Aptitude Test
- Let the scores of Adi, Brian, Close, Derek and Eli be a, b, c, d and e respectively
- Let the average score be x
- d = x – 50% of x = 0.5x
- 2nd Aptitude Test
- Adi, Brian, Close and Eli scored a, b, c and e respectively
- Derek’s score = d + 50% of d = 1.5d
- Let the average score be y
To Find: By approximately what percentage was Derek’s score less than the average (arithmetic mean) score of the 5 people in the second aptitude test?
Approach:
We can see from the expression above that if we could express y or d in terms of a common variable, we will be able to calculate our answer
- Expression of y: As y is the average score of the 2 aptitude test, we can express y in terms of a, b, c, d and e.
- Expression of x: Also, in the 1 aptitude test, as x is the average score, we can express x in terms of a, b, c, d, and e.
- Using (2) and (3), we can express y in terms of x and d( We cannot express y solely in terms of x, because in, the coefficient of d is different to the coefficient of d in x.)
- Expression of d : Using the relation “Derek’s score was 50 percent less than the average (arithmetic mean) score of the five people “ in the 1 aptitude test, we can also express d in terms of x.
- Using (2.a) and (3), we can express y in terms of x only.
- As in (3), we have already expressed d in terms of x only, we have achieved our objective of expressing y and d in terms of a common variable i.e. x, which will give us the answer
Working out:
- Expression of y: Average score in the 2nd aptitude test
- Expression of x: Average score in the 1st aptitude test
- Using (1) and (2), we can
- Expression of d: As “Derek’s score was 50 percent less than the average (arithmetic mean) score of the five people” in the 1 aptitude test, we can write d = 0.5x
Answer B
Most Upvoted Answer
Five friends Adi, Brian, Close, Derek and Eli appeared in two aptitude...
Question Analysis:
- Five friends Adi, Brian, Close, Derek, and Eli appeared in two aptitude tests.
- In the first aptitude test, Dereks score was 50 percent less than the average score of the five people.
- In the second aptitude test, Derek scored 50 percent more than what he scored on the first aptitude test.
- The scores of his friends in the second aptitude test were the same as their scores in the first aptitude test.
- We need to find the percentage by which Dereks score was less than the average score of the 5 people in the second aptitude test.
Given:
- Number of friends = 5
- Derek's score in the first test = 0.5 * average of the five scores
- Derek's score in the second test = 1.5 * Derek's score in the first test
- Scores of friends in the second test = scores of friends in the first test
Solution:
Step 1: Find the average score of the five people in the first test.
Let the scores of Adi, Brian, Close, Derek, and Eli in the first test be A, B, C, D, and E respectively.
Average score of the five people in the first test = (A + B + C + D + E) / 5
Derek's score in the first test = 0.5 * Average score of the five people in the first test
= 0.5 * (A + B + C + D + E) / 5
= (A + B + C + D + E) / 10
Step 2: Find Derek's score in the second test.
Derek's score in the second test = 1.5 * Derek's score in the first test
= 1.5 * (A + B + C + D + E) / 10
= (3/20) * (A + B + C + D + E)
Step 3: Find the average score of the five people in the second test.
Since the scores of friends in the second test are the same as their scores in the first test, the average score of the five people in the second test will be the same as the average score of the five people in the first test.
Average score of the five people in the second test = (A + B + C + D + E) / 5
Step 4: Find the percentage by which Derek's score was less than the average score of the 5 people in the second test.
Percentage by which Derek's score was less than the average score of the 5 people in the second test
= [(Average score of the five people in the second test) - (Derek's score in the second test)] / (Average score of the five people in the second test) * 100%
= [(A + B + C + D + E) / 5 - (3/20) * (A + B + C + D + E)] / [(A + B + C + D + E) / 5] * 100%
= (17/60) * 100%
= 28.33%
Therefore, the percentage by which Dereks score was less than the average (arithmetic mean) score of the 5 people in the second aptitude test is approximately 28%.
- Five friends Adi, Brian, Close, Derek, and Eli appeared in two aptitude tests.
- In the first aptitude test, Dereks score was 50 percent less than the average score of the five people.
- In the second aptitude test, Derek scored 50 percent more than what he scored on the first aptitude test.
- The scores of his friends in the second aptitude test were the same as their scores in the first aptitude test.
- We need to find the percentage by which Dereks score was less than the average score of the 5 people in the second aptitude test.
Given:
- Number of friends = 5
- Derek's score in the first test = 0.5 * average of the five scores
- Derek's score in the second test = 1.5 * Derek's score in the first test
- Scores of friends in the second test = scores of friends in the first test
Solution:
Step 1: Find the average score of the five people in the first test.
Let the scores of Adi, Brian, Close, Derek, and Eli in the first test be A, B, C, D, and E respectively.
Average score of the five people in the first test = (A + B + C + D + E) / 5
Derek's score in the first test = 0.5 * Average score of the five people in the first test
= 0.5 * (A + B + C + D + E) / 5
= (A + B + C + D + E) / 10
Step 2: Find Derek's score in the second test.
Derek's score in the second test = 1.5 * Derek's score in the first test
= 1.5 * (A + B + C + D + E) / 10
= (3/20) * (A + B + C + D + E)
Step 3: Find the average score of the five people in the second test.
Since the scores of friends in the second test are the same as their scores in the first test, the average score of the five people in the second test will be the same as the average score of the five people in the first test.
Average score of the five people in the second test = (A + B + C + D + E) / 5
Step 4: Find the percentage by which Derek's score was less than the average score of the 5 people in the second test.
Percentage by which Derek's score was less than the average score of the 5 people in the second test
= [(Average score of the five people in the second test) - (Derek's score in the second test)] / (Average score of the five people in the second test) * 100%
= [(A + B + C + D + E) / 5 - (3/20) * (A + B + C + D + E)] / [(A + B + C + D + E) / 5] * 100%
= (17/60) * 100%
= 28.33%
Therefore, the percentage by which Dereks score was less than the average (arithmetic mean) score of the 5 people in the second aptitude test is approximately 28%.
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Five friends Adi, Brian, Close, Derek and Eli appeared in two aptitude tests. In the first aptitude test, Derek’s score was 50 percent less than the average (arithmetic mean) score of the five people. In the second aptitude test, Derek scored 50 percent more than what he scored on the first aptitude test. If the scores of his friends in the second aptitude test were same as their scores in the first aptitude test, by approximately what percentage was Derek’s score less than the average (arithmetic mean) score of the 5 people in the second aptitude test?a)25%b)28%c)33%d)40%e)50%Correct answer is option 'B'. Can you explain this answer?
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