Matt gets a $1,000 commission on a big sale. This commission alone

Question

Matt gets a $1,000 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Kudos for a correct  solution .

chetan2u · Accepted Answer

Hi,
i think you are wrong..
initial average =400-150=250...
let the sales be n, so total commission=250n...
now we are increasing the sale by one and commission becomes 400....
so total commission=(n+1)*400....
this should be equal to 250n+1000 (1000 is the amount of new commission on n+1 th sale..)
(n+1)*400=250n+1000..
150n=600..
n=4..
total sales =4+1=5..
ans C

balamoon · Answer

Matt gets a $1,000 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $400, how many sales has Matt made?

A. 3
B. 4
C. 5
D. 6
E. 7

Solution -

For $1000 commission, average commission increased $150.
Old Commission = 400 - 150 = 250
For $X commission, average commission was $250.

(1000/X) = 150/250 = 3/5 -----------> For $1000 commission, Matt made a sales of 3. ANS A.

camlan1990 · Answer

New Average Commission = $400, which increased by $150 => Old Aver commission = 400 - 150 = 250

1000 + 250X = 400   => X = 4 => x+1=5

GMATinsight · Answer

Let, Average Commission = x
No. of items sold = y
Total Commission = xy

New Commission = xy+1000
New Average = (xy+1000) / (y+1) = 150+x
i.e. (xy+1000) = (y+1)* (150+x)
i.e. (xy+1000) = (xy+x+150y+150)
i.e. (850) = (x+150y)

New Commission = 400 = 150+x
i.e. x=250
i.e. y = 4

New Sales = y+1 = 5

Answer: option C

ashokk138 · Answer

This is like a weighted average problem.
Assume, the no of sales made by Matt as x
Adding Rs. 1000 for a new sale, increases his average commission to Rs. 400

hence,
Avg. Commission = (250x + 1000) / (x + 1) = 400
Solving for x, x = 600 / 150, x = 4.

But, No of sale made by Matt including the big sale = x + 1 => 4+1 => 5

Options C

lipsi18 · Answer

# of sale =n; new avg = 400 -150 =250
hence final equation will be 1000+250n= 400(n+1); solving for n, we get n=4
total sale=5

Hence answer is C
Thanks,

adityadon · Answer

suppose no. of commisions made before latest commision = n

old average commision = 400 - 150 =250

Now ,

(n*250 + 1000 )/ n+1 = 400
so , 250n+1000 = 400n +400

150n = 600
n = 4

we need to add latest commision , so answer = 4+1 = 5

Answer C

noTh1ng · Answer

Old average commission:

S/n = 250
S = 250*n

New average commission:
(S + 1000) / (n + 1) = 400 Insert S

(250n + 1000) = (400n + 400)
600 = 150n
n = 4

n+1 = 5

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Before the $1,000 commission, Matts average commission was $250; you can express this algebraically with the equation S = 250n.

After the sale, the sum of Matts sales increased by $1,000, the number of sales made increased by 1, and his average commission was $400. You can express this algebraically with the equation:

S + 1,000 = 400(n + 1)

250n + 1,000 = 400(n + 1)
250n + 1,000 = 400n + 400
150n = 600
n = 4

Before the big sale, Matt had made 4 sales. Including the big sale, Matt has made 5 sales.

Answer: C.

jabhatta2 · Answer

Bunuel

Hi Bunuel -- Is there any other way to perform this math ? I am trying to solve GMAT problems NOT with algebra but it seems like this problem can only be done with Algebra

ScottTargetTestPrep · Answer

We know that Matt’s original average commission was $250. If we let x denote the number of sales Matt made prior to the big sale, we can create the equation:

(1,000 + 250x)/(x + 1) = 400

1,000 + 250x = 400x + 400

600 = 150x

4 = x

Including the big sale (on which he earned a $1,000 commission), Matt made 5 sales.

Answer: C

JarvisStark · Answer

Let X be the sales
New average is 400 then it'll be 400x
The old average is 400-150 = 250
Then it'll be 250(x-1)

400x = 250(x-1) + 1000

X = 5

the total sales is 5

We assume x-1 because it is before the big sale.

Posted from my mobile device

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=88040 --- Harsha GMAT-Club-Forum-so0p8w3j.png

egmat · Answer

Hi jabhatta2,

Great question — you absolutely do NOT need algebra here. Two non-algebra methods:

Method 1: Backsolving (Test the Answers)

Start with choice C:  5  total sales.
- Total commissions =  5  ×  $400  =  $2,000 
- Remove the big sale:  $2,000  -  $1,000  =  $1,000  from the previous  4  sales
- Old average =  $1,000  ÷  4  =  $250 
- Did the average rise by  $150 ?  $400  -  $250  =  $150  ✓ Yes!

Done.   Answer: C

Method 2: The "Balancing" Method (my favorite)

The new average is  $400 . Matt's big sale of  $1,000  is  $600  above this new average. Think of that  $600  as "extra" that gets spread equally across all previous sales to pull each one up by  $150 .

So the number of previous sales =  $600  ÷  $150  =  4 .

Total sales (including the big one) =  4  +  1  =  5 .

General Principle:   On the GMAT, whenever a question asks "how many" and gives you  5  answer choices,  backsolving is almost always faster than algebra . Start with C — if it works, you're done. If not, you'll know which direction to go. Save algebra as a backup.

Matt gets a $1,000 commission on a big sale. This commission alone

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