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# In a certain game, players have three chances during each turn to earn

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
In a certain game, players have three chances during each turn to earn  [#permalink]

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01 Nov 2018, 00:49
00:00

Difficulty:

15% (low)

Question Stats:

91% (01:19) correct 9% (01:45) wrong based on 26 sessions

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In a certain game, players have three chances during each turn to earn points. Each consecutive win awards more points than the previous win. The second win awards 100 points more than the first, and the third win awards twice as many points as the second win. Tammy won the maximum number of points during her turn and received a total of 700 points. How many points are awarded for the first win?

A. 50
B. 75
C. 100
D. 200
E. 400

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Re: In a certain game, players have three chances during each turn to earn  [#permalink]

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01 Nov 2018, 04:31
First win points = x
Second win points = x + 100
Third win points = 2(x+100)

x+x+100+2x+200 = 700 or 4x + 300 = 700
Hence x = 100

Option C
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Re: In a certain game, players have three chances during each turn to earn  [#permalink]

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01 Nov 2018, 04:57

Solution

Given:
• Player has three chances during each chance to earn points
• Each consecutive win awards more points than the previous win
• The second win awards 100 points more than the first, and
• The third win awards twice as many points as the second win
• Tammy received a total of 700 points, which is the maximum number of points

To find:
• The number of points awarded for the first win

Approach and Working:
Tammy will receive maximum number of points, when he wins all the rounds

• Let us assume that the number of points awarded for the first win = x
• Number of points awarded for the second win = x + 100
• Number of points awarded for the third win = 2(x + 100) = 2x + 200
• Total number of points = x + (x + 100) + (2x + 200) = 4x + 300 = 700
o Implies, x = 100

Hence, the correct answer is Option C.

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Re: In a certain game, players have three chances during each turn to earn   [#permalink] 01 Nov 2018, 04:57
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