A company purchased at least 10 units of a certain product from each

Question

A company purchased at least 10 units of a certain product from each of Suppliers X and Y. Supplier X charged a $100 fixed cost, $20 per unit for each of the first 10 units, and $5 per unit for each unit purchased in excess of 10 units. Supplier Y charged a $150 fixed cost, $15 per unit for each of the first 10 units, and $10 per unit for each unit purchased in excess of 10 units. Including the fixed costs, the combined average cost for the units was $20 per unit.

Select a number of units purchased from Supplier X and a number of units purchased from Supplier Y that are jointly consistent with the given information. Make only two selections, one in each column.

Select a number of units purchased from Supplier X and a number of units purchased from Supplier Y that are jointly consistent with the given information. Make only two selections, one in each column.

Garvesh · Accepted Answer

Atleast 10 units from each product  means min. 10 products of X and 10 products of Y.
Cost = Fixed cost + Cost of first 10 products + Cost of remaining products.
For X,
Cost = 100 + 20x10 + 5 (X-10)  ---- 
For Y,
Cost = 150 + 10x10 + 10 (Y-10) ----

Avg price per unit is 20.

Therefore,

(  +  )/ (X+Y) = 20

On solving above equation we get ,
3X + 2Y = 90

Hence from answer options we have  X = 20 , Y = 15.

KarishmaB · Answer

Video solution given here:

https://www.youtube.com/watch?v=waWVH6zPj-4

We know that at least 10 units were bought from each supplier. 
Cost of first 10 units from X = 100 + 20*10 = 300
Cost of first 10 units from Y = 150 + 15*10 = 300

So on average cost of first 20 units was $30 per unit. Now additional units are bought at cheaper price of $5 per unit or $10 per unit. The average price of all these additional units would be between $5 and $10 say it is $n. But the overall average is $20 which is closer to the $30 price. Hence number of additional units bought must be less than 20.

Of the given options, there are only 2 possible options - 15 and 20 (additional units 15) or 15 and 22 (additional units 17). In all other cases, additional units will be more than 20 which is not acceptable. We will check for one of them. If that doesn't work, we know that the other one will.

Try additional units 15. Then the weights are 15 and 20 which means that

\frac{3}{4} = \frac{(30 - 20)}{(20 - n)} 
 x = $\frac{20}{3}

This is the average of $5 and $10.

\frac{w1}{w2} = \frac{(10 - 20/3)}{(20/3 - 5)} = 2:1

Hence 10 additional units were bought at $5 and 5 additional units were bought at $10. So 20 units were bought from X and 15 were bought from Y.

ANSWER: 20 from X and 15 from Y

Note that the solution looks long with multiple calculations but while solving it, you can do it directly on a single number line (using scale method). It happens much faster (shown in the video)

For scale method of weighted averages, check:

https://www.youtube.com/watch?v=_GOAU7moZ2Q

Oppenheimer1945 · Answer

A: 100+200+5(a-10)=5a+250
B: 150+150+10(b-10)=10b+200

Avg=0.5(5a+10b+450)
equals
20(a+b)

20(a+b)=5a+10b+450
=>15a+10b=450
=>3a+2b=90

Options-10: 5,10,12,15,17,20
a=20, b=15

jaky_nguyen · Answer

Cost X = 100 + 20x10 + 5 (X-10)

Cost Y = 150 + 10x10 + 10 (Y-10)

Average = (Cost X + Cost Y)/ (X+Y) = 20
450 + 5X + 10Y = 20X + 20Y
3X + 2Y = 90
X +2/3*Y = 30 
=> Y must be divisible by 3 = 15, 27, 30

Y= 15; X = 20

ShubhamSS28 · Answer

There can be an alternate method which i used :

For supplier X : 100 (fixed) + 20 (10) + x = 100 + 200 + y = 300 + x
For Y : 150 (fixed) + 15 (10) + y = 150 + 150 + y = 300 + y

Now we know average unit price is 20 $ i.e, 300 + x + 300 + y / no. of items = 20
This also gives an estimation that total qty. combining x and y should be greater than 30.
I started to look for combination of 35 and just verified where i can get 20$ unit price.

Prepared additional table for additional prices (beyond 10 qty.) below

300 + (50) + 300 + (50) / 15 + 20 = 700/35 = 20

P.S : This method can be inefficient if table have more fields but considering the current question, using above it can be solved in lesser time.

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colfer · Answer

3x+2y=40 where x and y are the excess units of X and Y
x = (40-2y)/3

Is x is an integer, 40-2y should be a multiple of 3..

y=5, x=10 ; total 15, 20
y=8, x= 8 ; total 18 ,26
y=11, x=6.. you get the pattern.. y=5,8,11,14.. x=10,8,6,4,2...

Can,Will · Answer

Dear experts  gmatophobia   Bunuel   KarishmaB  
It is given, the combined average is 20. when we talk about "combine avg" then it means we are taking the avg of a gp in which elements are avg itself. But here, we are taking avg of total cost for X and Y as 20, instead avg cost per item of X and avg cost per item of Y as 20 ??

kindly clear my doubt.

KarishmaB · Answer

We are given "... the combined average cost for the units was $20 per unit." We are given that the average of the cost per item is $20. The individual costs are $5, $10 and $30 per item. We have taken them in quantities such that the average per item comes out to be $20. Does that clear your doubt? I have discussed the weighted args approach using a scale for this question here: https://youtu.be/waWVH6zPj-4

D3N0 · Answer

The highlighted should be 10x15

ZeroSquare · Answer

In your solution, for eq 2, shouldn't it have been 10x15?

egmat · Answer

Hi ZeroSquare,

Good catch, you're reading the problem correctly.

You're looking at Garvesh's equation   for Supplier Y:

Cost = 150 +  10×10  + 10(Y-10)

The stem says Supplier Y charged  $15 per unit for each of the first 10 units  (the $10 rate is only for units  beyond  the first 10). So that middle term should indeed be  15 × 10 = 150 , not 10 × 10. What's written there is a typo.

The correct setup for Y is:

- Fixed cost:  150 
- First  10  units:  15 × 10 = 150 
- Excess units:  10 × (Y - 10) 
- Total: 150 + 150 + 10(Y - 10) =  200 + 10Y

Here's the reassuring part:  even though the posted line shows  10×10 , the final equation Garvesh landed on -  3X + 2Y = 90  - is the one you get from the  correct  $15 value. If you actually used  10×10 , you'd get a total of  400 + 5X + 10Y , which leads to  3X + 2Y = 80 , not  90 . So the written term is just a slip; the real value $15 was used to reach the answer.

Let me confirm the full correct system:

- Supplier X: 100 +  20×10  + 5(X - 10) =  250 + 5X 
- Supplier Y: 150 +  15×10  + 10(Y - 10) =  200 + 10Y 
- Average = $20:  450 + 5X + 10Y = 20(X + Y)  -  therefore90 = 3X + 2Y

Plug in  X = 20 :  60  + 2Y =  90  -  henceY = 15 . Both are on the option list, so Supplier X =  20 , Supplier Y =  15 .

So trust your instinct - it's  15×10  for Y's first  10  units.

Answer: Column 1 = 20; Column 2 = 15

A company purchased at least 10 units of a certain product from each

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Number of units purchased from Supplier X	Number of units purchased from Supplier Y
		15
		20
		22
		25
		27
		30

GMAT Two-part Analysis (TPA) Questions

A company purchased at least 10 units of a certain product from each

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My Rewards