12 Days of Christmas GMAT Competition - Day 10: A bakery produces an : Two-part Analysis (TPA)

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27 Dec 2024, 09:31

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Bunuel

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A bakery produces an average of 170 cupcakes per day for 5 days and x cupcakes per day for the next y days. The bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period.

Select for x the value of x and for y the value of y that would be jointly consistent with the given information. Make only two selections, one in each column.

Total cupcakes produced = 170*5 + x*y = 200*(5 + y)

850 + xy = 1000 + 200y
(x - 200)y = 150

Checking options for x>200

x	y
215	10	Correct
250	3	Not possible

Hence, the correct value for (x, y) = (215, 10)

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27 Dec 2024, 09:32

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170 cupcakes per day for 5 days and x cupcakes per day for the next y days.
Total prodn = 170x5+xy

The bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period.
average production = 170x5+xy/5+y = 200
This gives us y(x-200)=150

Factorise 150 and look at the option that fit into this equation.
The only one that works is 10(215-200)=150

Hence the answer is *x=215 and y=10*

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27 Dec 2024, 09:50

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Average = 200

=> 170*5 + x*y = 200 * (y + 5)
=> 850 + xy = 200y + 1000
=> y(x-200) = 150

This means x > 200 for sure now from the options putting x = 215 we get y = 10
For x = 250 we get y = 3

Answer: (215, 10)

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27 Dec 2024, 10:00

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Writing equation for average:

(170*5+x*y)/(y+5) = 200

on simplification: (x-200)*y=150
Also, note that x should be > 200, only then the avg of 170 and x would be 200.

Testing 215, immediately we get y=10 ans

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27 Dec 2024, 10:02

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Bunuel

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Total cupcakes in the first 5 days: 170 cupcakes/day * 5 days = 850 cupcakes
Total cupcakes in the next y days: x cupcakes/day * y days = xy cupcakes
Total cupcakes over the entire period: 850 + xy
Total number of days: 5 + y
Overall average: (850 + xy) / (5 + y) = 200
Now we test the given options:
If y = 10: (850 + 10x) / (5 + 10) = 200 => 850 + 10x = 3000 => 10x = 2150 => x = 215. This works.
Let's check the other options for y to see if any others work just to be sure.
If y = 50: (850 + 50x) / (5 + 50) = 200 => 850 + 50x = 11000 => 50x = 10150 => x = 203. This is not an option.
Since we found a valid solution with y=10 and x=215, we don't need to test any further.
Answer: x = 215, y = 10

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27 Dec 2024, 10:04

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A bakery produces an average of 170 cupcakes per day for 5 days and x cupcakes per day for the next y days. The bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period.

Total cupcakes produced = 170*5 + xy = 850 + xy = 200(5+y) = 1000 + 200y
xy = 150 + 200y
y = 150/(x-200)
x>200
x & y are positive integers

x	215	250
y	10	3

Since y=3 is not possible
x = 215; y = 10

Select for x the value of x and for y the value of y that would be jointly consistent with the given information. Make only two selections, one in each column.

x	y
215	10

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27 Dec 2024, 10:08

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170*5+xy= 200(5+y)
Y(x-200)=150
X=215, y=10

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27 Dec 2024, 10:13

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A bakery produces an average of 170 cupcakes per day for 5 days and x cupcakes per day for the next y days. The bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period.

Analyze: (170 * 5 + xy) / (5+y) = 200

850 + xy = 1000 + 200y

xy - 200y = 150

y(x-200) = 150; from here we can say that x>200

Now check the options;
x = 250, then y would be 3, which is not an option.

x = 215, then y would be 10. bingo.

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27 Dec 2024, 10:24

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Bunuel

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Total cupcakes for first 5 days = 170 * 5 = 850
Total cupcakes for next y days = x*y
Average for 5+y days = (850 + xy)/(5 + y) = 200
=> 850 + xy = 1000 + 200y
xy = 150 + 200y
(x - 200)y = 150

Clearly x >= 200 from the above eq hence if x = 215 => y = 10
if x = 250 => y = 3

Therefore x = 215 and y = 10

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27 Dec 2024, 10:26

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27 Dec 2024, 10:30

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27 Dec 2024, 10:30

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The answer is 215 and 10.

Given 170 *5 +xy / 5+y = 200

solving this we get 850+xy = 1000+200y

x-200 = 150/y

Substituting value of y=10 we get x=215. Thus the answer.

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27 Dec 2024, 10:34

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Number	Average	Sum
5	170	850
y	x	xy

Overall avg = 200

850+xy = 200(5+y)
y= 150 /(x- 200)
both x and y have to be positive

x>200, checking with x= 215, y = 10

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27 Dec 2024, 10:57

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To solve the problem, let's set up the equation for the bakery's total cupcake production:

The total number of cupcakes produced over 5+y days is:

170*5 + x*y

The average production per day is given as 200 cupcakes, so:

Total cupcakes/total days = 200

Or, 170*5 + x*y / 5+y = 200

Or, 170⋅5+x⋅y=200⋅(5+y)

Or, 850+x⋅y=1000+200y

Or, x⋅y=200y+1000−850

Or, x⋅y=200y+150

Divide through by y (assuming y≠0):

x=200+150/y

Now, test values of y that result in an integer value for x.

Option that fits is

Y= 10 and X=215

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27 Dec 2024, 10:58

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Step 1: Key information
For the first 5 days: Average = 170 cupcakes/day
Total cupcakes produced:
1170×5 = 850

For the next y days:
Average = x cupcakes/day
Total cupcakes produced: x*y

Overall period:
5+y days with an average of 200 cupcakes/day
Total cupcakes produced over all days:
200×(5+y)=1000+200y

Step 2: Equation for total production
The total cupcakes produced over all days is the sum of cupcakes produced in the two periods:
850+x*y=1000+200y

Rearranging for x and y:
x*y=150+200y
x=200+ 150/y

Step 3: Test options
We need to select
x and y that satisfy this equation.

Option 1:
x=250,
y=10
Substitute y=10:
x=200+ 150/10 = 200+15 = 215 (NOT consistent with x=250).

Option 2: x=215, y=10
Substitute y=10:
x=200+ 150/10 = 200+15 = 215(CONSISTENT).

Option 3:
x=250, y=50
Substitute y=50:
(NOT consistent with x=250)
x= 200+ 150/50 =200+3=203(NOT consistent with x=250).

Final Answer:
x: 215
y: 10

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27 Dec 2024, 11:01

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Total number of cupcakes would be equal -

170*5 + x*y = 200 (5+y)
850 + xy = 1000 + 200y
y(x-200) = 150

Put in values,

x has to be greater than 200. so put in x = 215, we get,

15y = 150
y= 10.

Therefore,

x = 215, y = 10

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27 Dec 2024, 11:02

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For the first 5 days,
Average cupcakes = 170
Total cupcakes = 5 * 170 = 850

For the next y days,
Average cupcakes = x
Total cupcakes = x * y = xy

Overall average = 200 for 5 + y days

Overall average = Total cupcakes / Total days = 200
(850 + xy) / (5 + y) = 200

Solving,
y(x - 200) = 150

We know that x > y

Substituting from the given options,
x = 215
y(215 - 200) = 150
y = 10

Therefore, x = 215 and y = 10