A budget of $100,000 is allocated for the purpose of purchasing comput

Question

A budget of $100,000 is allocated for the purpose of purchasing computers, both desktop computers and laptops. The price of a desktop and a laptop is $200 and $650, respectively. The retailer has agreed to reduce the price of computers depending on the size of the order according to the following formula:

If x and y are the number of units of desktops and laptops ordered, the price of individual units is 200 - (x/10), and 650 - (y/10), respectively.

In the table given below, determine the number of desktop computers and laptops the company will be able to purchase using $100,000 completely.   Make only two selections, one in each column.

sagarkacha · Accepted Answer

My approach was to use elimination before doing any algebra.

The laptop price is 650−y/10
 ​
Even with the maximum discount available from the answer choices, the laptop price remains above $625.

If y=200, the laptop cost would be 630, so:

200×630=126,000

which already exceeds the $100,000 budget. Therefore, y=200 and y=250 can be eliminated immediately.

Similarly,

150×635=95,250

leaving less than $5,000 for desktops, which is impossible given the total number of computers required.

Thus, only y=50 or y=100 remain as viable laptop choices. From there, I checked the corresponding desktop options and found the combination that exactly satisfies the $100,000 budget.

This reduced the problem to testing only a couple of cases instead of solving the full equation upfront.

Amity007 · Answer

https://gmatclub.com/forum/download/file.php?id=88089 GMAT-Club-Forum-gz5l40t6.png

egmat · Answer

Hi there,

Great question! Let me walk you through this step by step.

The Setup: 
We have  $100,000  to spend on x desktops and y laptops. Due to the  bulk discount formula :
- Cost per desktop = ( 200  - x/ 10 ), so total desktop spend = x × ( 200  - x/ 10 )
- Cost per laptop = ( 650  - y/ 10 ), so total laptop spend = y × ( 650  - y/ 10 )

We need: Desktop Spend + Laptop Spend =  $100,000

The Strategy: 
Since both x and y must come from the same set of  5  choices, let's compute the total spend for each possible value.

Desktop spend for each x: 
- x =  50 :  50  × ( 200  -  5 ) =  50  ×  195  =  $9,750 
- x =  100 :  100  × ( 200  -  10 ) =  100  ×  190  =  $19,000 
- x =  150 :  150  × ( 200  -  15 ) =  150  ×  185  =  $27,750 
- x =  200 :  200  × ( 200  -  20 ) =  200  ×  180  =  $36,000 
- x =  250 :  250  × ( 200  -  25 ) =  250  ×  175  =  $43,750

Laptop spend for each y: 
- y =  50 :  50  × ( 650  -  5 ) =  50  ×  645  =  $32,250 
- y =  100 :  100  × ( 650  -  10 ) =  100  ×  640  =  $64,000 
- y =  150 :  150  × ( 650  -  15 ) =  150  ×  635  =  $95,250 
- y =  200  and y =  250  already exceed  $100,000  on their own, so we can ignore these.

Now Find the Pair That Sums to $100,000: 
We check which desktop spend + laptop spend =  $100,000 .

$36,000  (x =  200 ) +  $64,000  (y =  100 ) =  $100,000  ✓

No other combination from these lists adds up to exactly  $100,000 .

So the answer is: Desktop Computers =  200  (Row  4 ) and Laptops =  100  (Row  2 ).

Answer: Row 4 for Column A (Desktop), Row 2 for Column B (Laptop)

Key Insight:  The key trick here is to not get intimidated by the discount formula. Just compute the total spend for each option separately, then find the pair that hits the budget exactly.

Vivek1707 · Answer

***  In TPA questions in which there are  budgets  given and you have to choose between alternative options, one approach you can follow is to  ELIMINATE the options  which  exceed the budget

Trail and error is often faster than algebra in such TPA questions

We know that the budget is 100,000

Now if we have 250 units for the price of 650 ---> this would exceed the 100,000 mark 
Cause 600 x 200 is 120,000 hence 625 x 250 will be anyways more

So since 650 is a  large amount  compared with 200,  assign the lowest units  to this i.e. 50 
So we have 645 x 50 giving us 32,250

Now if we assign  250 units  to the price of 200 we get  175 x 250  which is  43,750 
Hence the total would be  32,250 + 43,750 This is < 100,000  |  *** Note don't waste precious time calculating the exact amounts ---> By looking at it you ll know this is less than 100k

Now since we have already maximized the units for price of 200, we can  increase the units  for the  price of 650 .  Try 100 , You ll get  640 x 100  which is  64,000 , now given the total of 43,570 for the price of 200  this would exceed  the  total of 100k.

Hence  reduce  the  qty for price of 200 units.

We try 200 units ----> we get 180 x 200 = 36,000

So 36,000 + 64,000 = 100, 000  exact match So answer is 200 and 50

A budget of $100,000 is allocated for the purpose of purchasing comput

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