At a bowling alley, Neil can win a free pair of bowling

Hi All,

We're told that 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 and his scores in his first seven games were 192, 188, 195, 197, 205, 208, and 203. We're asked for the minimum score he needs in his last game to win the shoes. This question comes down to Arithmetic, but there's a way to do the math that require fewer steps than others.

With these 7 scores, we can determine how far above/below 200 the total currently is.
192 is '8 less' than 200
188 is '12 less' than 200
195 is '5 less' than 200
197 is '3 less' than 200
205 is '5 more' than 200
208 is '8 more' than 200
203 is '3 more' than 200

Those differences sum to... - 8 - 12 - 5 - 3 + 5 + 8 + 3 = -12... meaning that Neil's total is currently 12 less than it needs to be for him to have an average of 200. Thus, on the 8th game, Neil would have to bowl 200 + 12 = 212 to 'make up' the missing points and hit the average score he needs.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:Source: Veritas Prep

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

The OA is D.

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 the average of the 8 games = 200, then we can write: (sum of all 8 scores)/8 = 200
Multiply both sides by 8 to get: sum of all 8 scores = 1600

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?
We need a sum of AT LEAST 1600
Let x = the score in the last game
So, we need: 192 + 188 + 195 + 197 + 205 + 208 + 203 + x = 1600

Aside: Notice that there are several pairs of values that add to 400
192 + 208 = 400
195 + 205 = 400
197 + 203 = 400

So, if we add those pairs first, we get: 400 + 188 + 400 + 400 + x = 1600
Simplify: 1200 + 188 + x = 1600
Subtract 1200 from both sides: 188 + x = 400
Solve: x = 212

Answer: D

Cheers,
Brent

BTGmoderatorLU wrote:Source: Veritas Prep

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.

Answer: D