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Sam earned a $2,000 commission on a big sale, raising his average comm
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09 Apr 2022, 07:24
09 Apr 2022, 07:24
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Sam earned a $2,000 commission on a big sale, raising his average commission by $100. If Sam's new average commission is $900, how many sales has he made?
a) 12
b) 13
c) 15
d) 21
e) 8
a) 12
b) 13
c) 15
d) 21
e) 8
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Re: Sam earned a $2,000 commission on a big sale, raising his average comm
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09 Apr 2022, 07:37
09 Apr 2022, 07:37
1
Carcass wrote:
Sam earned a $2,000 commission on a big sale, raising his average commission by $100. If Sam's new average commission is $900, how many sales has he made?
a) 12
b) 13
c) 15
d) 21
e) 8
a) 12
b) 13
c) 15
d) 21
e) 8
Note: If Sam's average commission increased by $100 to $900, then his FORMER average commission was $800 and his NEW average commission is $900
When it comes to averages, we know that average value = (sum of n values)/n
We can rewrite this into a useful formula: sum of n values = (average value)(n)
Let n = the number of sales Sam made to calculate his FORMER average commission.
When we apply the above formula, we get: sum of FORMER commissions = 800n
Once Sam collects his $2,000 commission, the NEW sum of commissions = 800n + 2000
At this point, n + 1 = the total number of commissions (since we just added the $2000 commission)
Since Sam's NEW average commission is $900, we can write: 800n + 2000/(n + 1) = $900
Multiply both sides of the equation by (n + 1) to get: 800n + 2000 = 900(n + 1)
Expand the right side: 800n + 2000 = 900n + 900
Subtract 800n from both sides: 2000 = 100n + 900
Subtract 900 from both sides: 1100 = 100n
Solve: n = 11
The question asks us to determine how many sales Sam HAS made, which means we must include the latest sale.
Since n represents the number of sales Sam made to calculate his FORMER average commission, we must add the latest sale (the one that landed Sam a $2,000 commission).
So the total number of sales made = 11 + 1 = 12
Answer: A
gmatclubot
Re: Sam earned a $2,000 commission on a big sale, raising his average comm [#permalink]
09 Apr 2022, 07:37
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