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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
82% (01:54) correct
18%
(01:46)
wrong
based on 82
sessions
History
Date
Time
Result
Not Attempted Yet
While analyzing my scores across 8 mock CATs that I had taken, I realized that the average marks when the worst seven scores are considered is 5 less than the average marks when the best seven scores are considered. What is the difference between the highest and the lowest scores?
1. 20
2. 25
3. 30
4. 35
5. 40
1. 20
2. 25
3. 30
4. 35
5. 40
28 Apr 2019, 19:45
Kudos
Bookmarks
Relatively confident that the answer is wrong and should be D:
Construct 8 blank spaces:
_ _ _ _ _ _ _ _
Let the middle 6 be equal to x:
_ x _
let the lowscore be equal to A, and the highscore be equal to B:
A x B
Introduce low score variable: L, then:
A + x = 7*L
x + B = 7*(L+5) ----> x + B - 35 = 7L
substitute:
A + x = x + B - 35
eliminate x:
A = B - 35 ...... or ...... A + 35 = B
therefore, the highscore is 35 greater than the lowscore
Construct 8 blank spaces:
_ _ _ _ _ _ _ _
Let the middle 6 be equal to x:
_ x _
let the lowscore be equal to A, and the highscore be equal to B:
A x B
Introduce low score variable: L, then:
A + x = 7*L
x + B = 7*(L+5) ----> x + B - 35 = 7L
substitute:
A + x = x + B - 35
eliminate x:
A = B - 35 ...... or ...... A + 35 = B
therefore, the highscore is 35 greater than the lowscore
29 Apr 2019, 05:14
Kudos
Bookmarks
Yes, the answer is definitely 35, and the OA reported in the OP is not correct. Suppose the sum of the six middle scores is S, the highest score is H, and the lowest score is L. Then the average of the seven highest scores is (S + H)/7 and the average of the seven lowest scores is (S + L)/7. These differ by 5:
(S + H)/7 - (S + L)/7 = 5
S + H - S - L = 35
H - L = 35
(S + H)/7 - (S + L)/7 = 5
S + H - S - L = 35
H - L = 35
