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555-605 (Medium)|   Math Related|         
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 11:05
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Total production for the first 5 days: 5 * 170 = 850

For the next y days, the bakery produces x cupcakes per day, total production for y days = x*y

Total production for 5 + y days = 850 + x*y

The overall average production for 5+y days is 200 cupcakes per day.

Total production for 5 + y days = 200 * (5+y)

850 + x*y = 200 * (5+y)

y*(x−200) = 150

Now, testing answer choices,

if x = 215, y = 10. We have both the options in answer choices, no need to test further.

Answer 215 and 10
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For the first 5 days, the total number of cupcakes produced is:170×5=850 cupcakes
For the next y days, the bakery produces x cupcakes per day, so the total number of cupcakes x×y cupcakes

Thus, the total number of cupcakes produced in 5+y days is: 850+x×y cupcakes

Given the average for all the days is 200 so, (800+(xy))/(5+y)= 200. solve the equation to get

Y=150/(x-200)

Now try the options as X-200 must divide 150. X=215 will give Y=10
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 11:44
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Average = ( 170*5 + x*y)/(5+y) = 200

after solving we get

850 + xy = 1000 + 200y

y(x - 200) = 150

Hence from the options

x = 215 and y = 10
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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.
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 11:49
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If we try to solve this question mentally, we see that for first 5 days the avg cupcake made was 170.
For next y days how many cupcakes at an average should be made to get to an combined average of 200.

To average to 200, we need (200-170) * 5, cupcakes extra made in the next y days along with 200 cupcakes daily.

So, 150 cupcakes + 200* y cupcakes needs to be made in the next y days.

Now looking at the option, we see that if 215 cakes will be made for next 10 days then the extra cake made will be 200*10 + 150 cupcakes

So 10 & 215 is the answer.
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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.
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Given

170*5 = 850 Cupcakes in first 5 days
x*y = Cupcakes in next y days

Total cupcakes / total days = 200

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

Further solving the equation we get x*y = 150 + 200y

From here on I started to test each pair of values from the option for x and y to find a consistent solution.

x = 250 , y = 10 is the only possible combination that satisfy the equation
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 12:18
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170*5=850, if x=215,y=10,
then, 215*10+820=3000/10+5=200
therefore, x=215 and y=10.
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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.
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 12:19
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  • x=215
  • y=10


To determine the values of x and y that are consistent with the given information, we need to set up and solve the equation for the overall average production of cupcakes.

Given Information:
  • The bakery produces an average of 170 cupcakes per day for 5 days.
  • The bakery produces xx cupcakes per day for the next y days.
  • The overall average production is 200 cupcakes per day for the entire 5+y day period.

Now, the value of X can only be 215 or 250 because anything below 200 won't satisfy the condition for average being 200

  1. Total Production for the First 5 Days:
    Total production for 5 days=170×5=850 cupcakes
  2. Total Production for the Next [size=100]y Days:[/size]
    Total production for y days=x×y
  3. Overall Average Production:
    Overall average production=200 cupcakes per day
    Total production for (5+y) days=200×(5+y)
  4. Setting Up the Equation:
    Total production for 5 days+Total production for y days=Total production for (5+y) days
    850+xy=200×(5+y)
  5. Solving the Equation:
    y(x−200)=150
Finding Consistent Values for x and y:
We need to find values of x and y from the given options that satisfy the equation y(x−200)=150
Checking the Given Options for X as only 2 are valid

[*]X=215 solves and Y =10
10(215−200)=150
Conclusion:
The only consistent values for x and y that satisfy the equation are:
  • x=215
  • y=10
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From the information provided we can derive that 170x5 + xy = 200(5+y)
850+xy=1000+200x
xy-200y=150
Y(X-200)=150
Testing the option the only valid options is Y=10 and x= 215 cupcakes per day
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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.
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 14:02
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(170*5)+xy=200(y+5)
y(x-200)=150

if x=215, y=10 ..satisfies
if x=250, y=3..y not available in option

Answer 215 & 10
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 14:50
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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.
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170*5 + xy = 200 (5+y)

xy - 200y = 150

y(x-200) = 150

Let's start with the first value, assume that y = 10

10(x-200) = 150
x - 200 = 15
x = 215

Matches.

x = 215
y = 10
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 16:50
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170 cupcakes/day for 5 days: 170 * 5 = 850 cupcakes.
Overall average of 200 cupcakes/day for 5 + y days: 200 * (5 + y).

For the next y days, x cupcakes/day are produced, so total production for those days is x * y.

--> 850 + x * y = 200 * (5 + y)
--> x * y = 150 + 200y
--> y(x - 200) = 150
--> x - 200 = 150/y


Since x > 170 (due to the overall average being higher than 170), trying x = 215 gives y = 10 (Valid combination)

Final Answer: x = 215; y = 10
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 20:35
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To calculate the total number of cupcakes,

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

Here the total number of cupcakes produced are average production of cupcakes for the entire 5+y day period.

Hence (x-200)*y=1000-850
(x-200)*y=150
X needs to be a value greater than 200 hence if we select x to be 215
(215-200)*y=150
Y=150/15
Y=10

Hence the correct answer is:
X:215
Y:10
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 20:58
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Overall average production: 200 per day for (5+y) days
Therefore: total cupcakes = 200 * (5+y)
Total cupcakes = 170*5 + xy
Therefore: 170*5 + xy = 200 * (5+y)
y * (x - 200) = 150
From this equation: x > 200. We only have 2 values of x greater than 200: 215 and 250
x = 215: y = 10
x = 250: y = 3 (no value 3 in answers)
Therefore: x = 215; y = 10
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.
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 27 Dec 2024, 23:22
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Please find the solution attached
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170 cupcakes for first 5 days = 170*5 = 850
x cupcakes for next y days = xy
total production x+y = (850+xy)/(5+y) = 200
by solving, xy = 150+20y
from option) substitute x=250 and y=50
250*50 = 150+200*50
12500 = 12500

Therefore, x = 250 and y = 50
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x = 215 and y = 10

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

Of the options we're given, it must be that x>200, so we can test x = 215 and x = 250.
If x = 215, then y = 10, which is an option.
If x = 250, then y = 3, which isn't an option.
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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.
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  1. Average production for the first 5 days: 170 cupcakes/day.
    • Total production for the first 5 days = 5×170= 850
  2. Average production over 5+y days: 200 cupcakes/day.
    • Total production over 5+y days = 200×(5+y)
  3. Production during the next y days: x cupcakes/day.
    • Total production for these y days = xy.

The total production over 5+y days can also be expressed as:
Total production=Production for first 5 days + Production for next y days.
Substitute the values:
200×(5+y)=850+xy
Simplify:
1000+200y=850+xy
Rearrange:
xy-200y=150
y(x-200)=150

Now x>200 for the equation to be positive overall, since y, i.e., number of days will always be positive
Lets try the options
when x=215, y=10
when x=250, y=3 (however, 3 is not an option choice)

Therefore, x=215, y=10 is the correct solution
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Total cupcakes for the first 5 days = 170*5=850
Total cupcakes for the next year days = xy
As per given, we have:
(850+xy)/5+y = 200
=> xy-200y = 150
=> y(x-200) = 150
=> y = 150/(x-200)
As y is the number of days, it cannot be minus => x-200>0 =>x>200
* if x = 215 => y=10 (matching with the options given)
* if x = 250 => y = 3 (we don't have y=3 in the options)
=> IMO, x=215; y=10
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|---5 days---|------y days-----|
|Avg: 170 c | Avg: x cupcakes |
|Total: 850c. | Total: yx cupcakes|

200 = (850 + yx)/(5+y)
=> x = 215, y =10
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 28 Dec 2024, 00:21
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simple wt avg concept,

170*5+x*y
___________ = 200,
5+y

This will give us an Equation of x and y,
now we have to put the values according to options,
on keeping y=10 we are getting x=215 and yeah both are in the options so these are the right answers.
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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.
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