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09 Apr 2020, 11:41
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
33% (02:25) correct
67%
(02:23)
wrong
based on 144
sessions
History
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Not Attempted Yet
In a certain law firm there are five senior partners and five junior partners, and all senior partners receive bonuses greater than those of the junior partners. Does senior partner Johnson receive the largest bonus of the lawyers at the firm?
(1) Johnson receives a bonus greater than twice the average bonus for all the senior partners
(2) All partners receive some bonuses, and Mr. Johnson receives five times the average given to all the partners
(1) Johnson receives a bonus greater than twice the average bonus for all the senior partners
(2) All partners receive some bonuses, and Mr. Johnson receives five times the average given to all the partners
09 Apr 2020, 19:54
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Statement 1-
\(2*(\frac{S_1 +S_2+S_3+S_4+ JO }{5}) < JO\)
\(S_1 +S_2+S_3+S_4 < 1.5JO\)
Case 1 -\( S_1 = 1.1JO; S_2=S_3=S_4 = 0.1JO\) (No)
Case 2 - \(S_1 = S_2 = S_3 = S_4 = 0.1JO \) (Yes)
Insufficient
Statement 2-
\(5*(\frac{S_1 +S_2+S_3+S_4+ JO +J_1 +J_2+J_3+J_4+J_5 }{10}) = JO\)
\(S_1 +S_2+S_3+S_4 +J_1 +J_2+J_3+J_4+J_5 = JO\)
Since each term is positive, JO must be greatest among all.
Sufficient
\(2*(\frac{S_1 +S_2+S_3+S_4+ JO }{5}) < JO\)
\(S_1 +S_2+S_3+S_4 < 1.5JO\)
Case 1 -\( S_1 = 1.1JO; S_2=S_3=S_4 = 0.1JO\) (No)
Case 2 - \(S_1 = S_2 = S_3 = S_4 = 0.1JO \) (Yes)
Insufficient
Statement 2-
\(5*(\frac{S_1 +S_2+S_3+S_4+ JO +J_1 +J_2+J_3+J_4+J_5 }{10}) = JO\)
\(S_1 +S_2+S_3+S_4 +J_1 +J_2+J_3+J_4+J_5 = JO\)
Since each term is positive, JO must be greatest among all.
Sufficient
GKomoku
14 Jun 2021, 09:36
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For Statement 1, Johnson might get the largest bonus (he might get $5000 while the others get $1 each, say). But he might not, since Statement 1 only means he got more than 40% of the bonus money paid to senior partners. So he might have gotten 41%, another partner might have gotten 56%, and the remaining three 1% each, and he may not have received the largest bonus (or, numerically, he might get $41, and the other bonuses could be $56, $1, $1 and $1, among many other possibilities).
For Statement 2, if the average bonus is a, then the sum of all of the bonuses is 10a. If Johnson's bonus is 5a, then all of the other bonuses add up to 10a - 5a = 5a, and since the bonuses are all positive, they all must be less than 5a. So Johnson must receive the largest bonus, and the answer is B.
For Statement 2, if the average bonus is a, then the sum of all of the bonuses is 10a. If Johnson's bonus is 5a, then all of the other bonuses add up to 10a - 5a = 5a, and since the bonuses are all positive, they all must be less than 5a. So Johnson must receive the largest bonus, and the answer is B.
