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# At a bowling alley, Neil can win a free pair of bowling shoes if he av

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Math Expert
Joined: 02 Sep 2009
Posts: 52360
At a bowling alley, Neil can win a free pair of bowling shoes if he av  [#permalink]

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10 Apr 2018, 03:12
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:30) correct 17% (01:45) wrong based on 61 sessions

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At a bowling alley, Neil can win a free pair of bowling shoes if he averages a score of at least 200 over 8 games. If his scores in his first seven games were 192, 188, 195, 197, 205, 208, and 203, what is the minimum score he needs in his last game to win the shoes?

A. 199
B. 201
C. 205
D. 212
E. 220

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Re: At a bowling alley, Neil can win a free pair of bowling shoes if he av  [#permalink]

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10 Apr 2018, 03:33
Bunuel wrote:
At a bowling alley, Neil can win a free pair of bowling shoes if he averages a score of at least 200 over 8 games. If his scores in his first seven games were 192, 188, 195, 197, 205, 208, and 203, what is the minimum score he needs in his last game to win the shoes?

A. 199
B. 201
C. 205
D. 212
E. 220

In 8 games , Neil has to score 1600.

Sum of score of the 7 games:

192+208=400
197+203=400
195+205=400

1200+ 188=1388
now we have to deduct 1388 from 1600: 1600-1388=212

So the correct answer will be D.
Intern
Joined: 24 Apr 2016
Posts: 31
Re: At a bowling alley, Neil can win a free pair of bowling shoes if he av  [#permalink]

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10 Apr 2018, 04:09
I tried to see if I could pair up all 7 of these scores.
I noticed that 195 + 205 = 400. Similarly, all the other scores paired off except for 188. As a result, 200 - 188 = 12. So the pair for 188 would be 212.
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Joined: 08 Sep 2016
Posts: 115
Re: At a bowling alley, Neil can win a free pair of bowling shoes if he av  [#permalink]

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10 Apr 2018, 15:46
Total possible score = 1600.

Looking at the answer choices, all of the answers have a different units digit. So adding up the units digit of the 7 scores and subtracting it from 1600 will lead to an answer with a units digit of 2.

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Joined: 26 Mar 2013
Posts: 2001
At a bowling alley, Neil can win a free pair of bowling shoes if he av  [#permalink]

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11 Apr 2018, 07:30
Bunuel wrote:
At a bowling alley, Neil can win a free pair of bowling shoes if he averages a score of at least 200 over 8 games. If his scores in his first seven games were 192, 188, 195, 197, 205, 208, and 203, what is the minimum score he needs in his last game to win the shoes?

A. 199
B. 201
C. 205
D. 212
E. 220

We can use logic

Rearrange numbers as follows

188 192 195 197 203 205 208 x

First glance: numbers that above 200 is less that numbers that below 200, therefore we need a number more than 200 to balance and also 201 does not help to balance.

Eliminate choices A & B

Second glance: insert 200 as imaginary number

188 192 195 197 (200) 203 205 208 x

Measure the distance between each number to see the balance

We will find that the distance between 197 & 200 is same 203 & 200 = 3 units

We will find that the distance between 195 & 200 is same 203 & 205 = 5 units

We will find that the distance between 192 & 200 is same 203 & 208 = 8 units

Therefore to balance the last distance the number should be 12 units from 200, the same distance between 200 & 188.......So minimum score is 212

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Re: At a bowling alley, Neil can win a free pair of bowling shoes if he av  [#permalink]

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11 Apr 2018, 15:17
Bunuel wrote:
At a bowling alley, Neil can win a free pair of bowling shoes if he averages a score of at least 200 over 8 games. If his scores in his first seven games were 192, 188, 195, 197, 205, 208, and 203, what is the minimum score he needs in his last game to win the shoes?

A. 199
B. 201
C. 205
D. 212
E. 220

We see that 192, 188, 195, and 197 together are 8 + 12 + 5 + 3 = 28 less than 200.

We see that 205, 208, and 203 together are 5 + 8 + 3 = 16 greater than 200.

Thus the net result is 28 - 16 = 12 less than 200. To make up the “12 less than 200”, we need to add 12 to 200. Thus, the score he needs on his final game must be at least 200 + 12 = 212.

Alternate Solution:

We recall that average = sum/#. Neil wants an average of 200 for 8 games, so we substitute the known information as follows, letting x = the minimum score on the eighth game:

average = sum/#

200 = (192 + 188 + 195 + 197 + 205 + 208 + 203 + x)/8

1600 = 1388 + x

212 = x

He needs a minimum of 212 on the eighth game to have an average of 200.

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Re: At a bowling alley, Neil can win a free pair of bowling shoes if he av &nbs [#permalink] 11 Apr 2018, 15:17
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