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# In five football games thus far this season, Barry has run for 98, 107

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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06 Feb 2015, 06:44
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:17) correct 42% (01:39) wrong based on 136 sessions

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In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards will he need to gain this Sunday if he wants to keep his season average above 100 yards?

A. 101
B. 116
C. 130
D. 131
E. 141

Kudos for a correct solution.

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Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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06 Feb 2015, 12:06

Bunuel wrote:
In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards will he need to gain this Sunday if he wants to keep his season average above 100 yards?

A. 101
B. 116
C. 130
D. 131
E. 141

Kudos for a correct solution.

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Kudos to you, for helping me with some KUDOS.

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Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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06 Feb 2015, 12:16
98+107+85+89+91+x=6*100
470+x=600
x=130

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Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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06 Feb 2015, 15:21
1
I think it's 131, but I'm not sure. He's asking: At a minimum, how many yards will he need to gain this Sunday if he wants to keep his season average above 100 yards

With 130 -> Average is 100 yards
With 131 -> Average is above 100 yards
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Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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07 Feb 2015, 02:03
1

If barry rushes for 130 yards, his average will be exactly 100/game. 131 yards will get above the 100 average.
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Posts: 7334
Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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07 Feb 2015, 04:15
shriramvelamuri wrote:

Bunuel wrote:
In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards will he need to gain this Sunday if he wants to keep his season average above 100 yards?

A. 101
B. 116
C. 130
D. 131
E. 141

Kudos for a correct solution.

hi sriram,
a 130 score will get his avg to exact 100...
so 1 more run reqd to increase above 100..
ans D..131
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Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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07 Feb 2015, 11:16
Bunuel wrote:
In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards will he need to gain this Sunday if he wants to keep his season average above 100 yards?

A. 101
B. 116
C. 130
D. 131
E. 141

Kudos for a correct solution.

I hope that I have tried to find a less time consuming approach to this problem. By letting the value of the yards needed (on sunday) equate to $$x$$. We can use the basic formula - average yards = total yards run/total games played - to find out the value the $$x$$ that is needed to keep Barry's average above 100 yards. Therefore; $$\frac{(98 + 107 + 85 + 89 + 91 + x)}{6}$$$$> 100$$. This is equal to $$\frac{(100-2) + (100+7) + (90-5) + (90-1) + (90+1) + x}{6}$$$$> 100$$......$$\frac{(90*3 + 100*2) + x}{6}$$$$> 100$$......$$\frac{470 + x}{6}$$$$> 100$$......$$470 + x > 600$$......$$x > 130$$. Therefore the minimum amount of yards needed to run to keep the average above 100 we need at least 131 yards.

I think the answer is D!

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Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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07 Feb 2015, 11:28
2
Hi All,

When an "average formula" question gives you all of the numbers that you need to solve for 1 variable, there are usually several ways that you can organize your information. When you were younger, you were probably taught to do straight-forward arithmetic. That's not the only way to get to the answer here....

Given the values 98, 107, 85, 89, 91 and X along with "goal" to get the average ABOVE 100 with the minimum possible value of X, we can figure out "how far away" each value is from 100...

The numbers BELOW 100:
98 is 2 below
85 is 15 below
89 is 11 below
91 is 9 below
Total for these 4 numbers = 37 below

Since we have just 1 number ABOVE 100 (the 107), we have a "net effect" of...

37 below + 7 above = 30 below.

This means that IF the value of X was 100+30 = 130, then the OVERALL average would be 100. We're asked to make the average ABOVE 100, so X MUST be greater than 130, but still be as small as possible. Even though the question did not state it, we're meant to assume that all values are integers, so X would be 131 (at the minimum).

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Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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09 Feb 2015, 05:08
Bunuel wrote:
In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards will he need to gain this Sunday if he wants to keep his season average above 100 yards?

A. 101
B. 116
C. 130
D. 131
E. 141

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Solution: D.

In this average problem, the “bait” is that the GMAT wants you to spend time calculating several two- and three-digit numbers. But because the desired average is 100, you can simply look for how close he is to that average on each attempt. 98 yards is -2 from the average; 107 is +7 (bringing a net of +5), 85 is -15 (the running net is now -10), and 89 (-11) and 91 (-9) bring -20 more to the net, making Barry 30 yards short of his desired average. In order to get above that average, he will need to first earn the minimum 100 yards, then make up his shortfall (another 30) and then earn one more to tip the average above 100. Therefore, the correct answer is 131.
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Re: In five football games thus far this season, Barry has run for 98, 107  [#permalink]

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20 Oct 2018, 17:38
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Re: In five football games thus far this season, Barry has run for 98, 107   [#permalink] 20 Oct 2018, 17:38
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