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15 Oct 2021, 01:30
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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:
48% (02:53) correct
52%
(02:34)
wrong
based on 115
sessions
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In a certain game, a player will randomly select one marble each time. There are three kinds of marbles, red, blue, or green. For each of the green marbles he selected, he will earn 5 points. For each of the blue and red marbles he selected, he will lose 4 and 3 points, respectively. Did he make less than 10 selections during the game?
(1) He earned a total of 16 points during the game.
(2) He selected all the three kinds of marbles during the game.
(1) He earned a total of 16 points during the game.
(2) He selected all the three kinds of marbles during the game.
18 Oct 2021, 21:40
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Bunuel
In a certain game, a player will randomly select one marble each time. There are three kinds of marbles, red, blue, or green. For each of the green marbles he selected, he will earn 5 points. For each of the blue and red marbles he selected, he will lose 4 and 3 points, respectively. Did he make less than 10 selections during the game?
(1) He earned a total of 16 points during the game.
(2) He selected all the three kinds of marbles during the game.
(1) He earned a total of 16 points during the game.
(2) He selected all the three kinds of marbles during the game.
Let the number of green, red and blue marbles picked up be g, r and b respectively.
Total selections =S=g+b+r
Total points = 5g-4b-3r
We have to find whether S<10.
The maximum points when S<10 will be 5*9 and minimum (-4)*9
(1) He earned a total of 16 points during the game.
So, 5g-4b-3r=16
Clearly, each of g and b combined will give 1 point, so we can have 16 each of g and b => 5*16-4*16-3*0=16…..S=16+16
For minimum we pick only g first, so 4 of g will give 20 and one of b will remove 4 out of it => 5*4-4*1-3*0=16…..S=4+1
Insufficient
(2) He selected all the three kinds of marbles during the game.
S could be infinite or minimum 3.
Insufficient
Combined
5g-4b-3r=16
As we have one of each, let us remove one of each
5a-4d-3c+5-4-3=16
5a-4d-3c=18
Let us find minimum value of a+d+c.
Maximise a, so a >3.
a) a=4….5*4-4d-3c=18…..4d+3c=2….Not possible.
b ) a=5….5*5-4d-3c=18…..4d+3c=7….possible when d and c are 1.
Thus minimum selections are
g=a+1=5+1=6
b=d+1=1+1=2
r=c+1=1+1=2
\(S \geq 10\)
Answer is NO
Sufficient
C
03 Nov 2021, 06:49
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This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
