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555-605 Level|   Math Related|         
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 28 Dec 2024, 00:33
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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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The bakery produces 170 cupcakes per day for 5 days, so the total number of cupcakes produced in the first 5 days is: 170 * 5 = 850 cupcakes.
For the next y days, the bakery produces x cupcakes per day, so the total number of cupcakes for these y days is: x * y.
The overall average production is 200 cupcakes per day for the entire (5 + y) days, so the total number of cupcakes for (5 + y) days is: 200 * (5 + y).
Now we can set up the equation: 850 + x * y = 200 * (5 + y).
Expanding the right side: 850 + x * y = 1000 + 200y.
Subtract 850 from both sides: x * y = 150 + 200y.
Now let’s test the values for x and y.
If x = 250: 250 * y = 150 + 200y. 50 * y = 150. y = 3.
If we substitute y = 3, we get: x * 3 = 150 + 200 * 3. x * 3 = 150 + 600. x * 3 = 750. x = 250.
Thus, the correct answer is: x = 250 y = 50.
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From the provided info, we have the equation:

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

So y >0 and x>200. From the provided selections, only x = 215 and y = 10 satisfy.
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Explanation:

  1. The total cupcakes over 5 + y days is:
    (170 × 5) + (x × y).
  2. The average over these 5 + y days is 200 cupcakes/day, so:
    (850 + x × y)/5 + y = 200.
  3. Multiply both sides by (5 + y):
    850 + x × y = 200 × (5 + y) = 1000 + 200y.
    Hence,
    x × y = 150 + 200y.
  4. Check the possible values for x and y from the answer choices.
    • If y = 10, then
      x × 10 = 150 + 200 × 10 = 15 0+ 2000 = 2150 ⇒ x = 215.
    • x = 215 is one of the given options, so (x,y) = (215 ,10) works.
Thus, the consistent pair is:
x = 215 and y = 10.
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Framing the equation we get 200(5+y) = 170*5 + xy
therefore y(x-200) =150 => x=215,y=10
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Hi everyone :)
Last day!

We are dealing here with a statistic (average) problem.

5 Days = 170 cakes/day
_ Days = ___ cakes/day
In order to get an average of 200 cakes/day.

Straight forward.
1) because the difference between 200 and 170 is 30
2) and since we have 2 larger answer choices than 200: 215 and 250.
3) We will test these 2 answer choices, starting with 215:

The difference between 200 and 215 is 15. (Half of 30).
Thus, we need a doubled quantity of 215 than 170, resulting in 10 days (5*2).
Do we have 10 days in our "y" answers? YES.

This is our answer. x=215 y=10


We can check that if someone wants to be sure.
(5*170+10*215)/15 = 200 ?
(850+2150)/15 => 3000/15 = 200 !
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12 Days of Christmas GMAT Competition - Day 10: A bakery produces an 28 Dec 2024, 04:35
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170*5+xy=200(5+y)
850+xy=1,000+200y
y(x-200)=150
y=150/(x-200)

Checking the values, x=215 and y=10
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Avg=200 per day

Number of days= 5+y

Total= 1000+200y

170*5+XY=1000+200Y

XY-200Y=150
Y(X-200)= 150

Check options, If Y=15, X-200 MUST BE 10, X=210 > NOT AN OPTION
Y=10, X=215

Ans X=215, 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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New average = (170*5+x*y)/(5+y)= 200

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

If y=10, x=215
If y=50, x=203: the value of x is not in the options
If y=75, x=202: the value of x is not in the options

Answers x=215, 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.
xy
10
50
75
215
250


As per the given constraints,

170 cupcakes per day for 5 days;.............................................................................................................(1)
and
x cupcakes per day for the next y days. .............................................................................................................(2)

bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period........................(3)

So, we get

170 * 5 + x*y = 200 (5+y)
(x-200) * y = 1000 - 850
(x-200) * y = 150............................(4)

Putting x = 215, and y = 10..................Equation (4) is satisfied


x = 215,
y = 10; is the CORRECT 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.

Solution: (170*5+xy)/(5+y)=200.---> y(x-200)=150.
Pick the numbers: y=10, ---> x=215. Other numbers are not here as a coulpe.
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avg =170
5 days
170*5=850

x cupcakes for y days = xy

average for the entire period is 200 per day



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

both x and y must be integers that's why I solved in this way.
Try values:
x = 10 then y <0 not possible
x = 50 then y<0
x = 215 then y =10 possible. Select
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According to the given info, the total production= 5(170)+y(x)

Avg= [5(170)+ y(x)]/(5+y)= 200
=> 850+ yx= 1000+200y
=> yx= 200y+ 150
=> x= 200+ 150/y

for x to be an integer, 150/y should also be an integer.

So, values of y can be= 10,50,75 (according to the listed values in question)

So, values of x accordingly would be=

At y= 10, x=215
at y= 50, x=203
at y= 75, x=202.

ANs- x= 215, 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.

Let’s assume,

Bakery produces 215 cupcakes per day for the next 10 days after the initial 5 days.

Since our average should be 200, additional cupcakes will be produced, 15x10=150. We can decide these cupcakes equally among the initial 5 days, 150/5=30. Then the initial 5 days will also have, 170+30= 200 cupcakes per day.

Answer: x=215, y= 10
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Key equation is 170*5 = 850 total cupcakes for first 5 days
xy total cupcakes for the following y days

total over the period 850 + xy
total n of days = 5+y

avg of all period = (850 + xy)/(5+y) = 200 cupcakes a day

simplifying we get that

150 = (x - 200)y

x > 200 so that the relationship is positive, since y must be integer and > 0 too

try first with 215 = x
then 150 = 15*y and y = 10 which is a combination among the answers. Correct
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Average = Total / Number of units
200 = ((170*5)+ xy) / (5+y)
1000 + 200y = 850 + xy

Substituting options we get -
When x = 215
1000 + 200y = 850 + 215y
150 = 15 y
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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(170*5 + xy)/(5 + y) = 200;
(850 + xy)/ (5 + y) = 200;
850 + xy = 200(5 + y);
850 + xy = 1000 + 200y;
xy - 200y = 150;

(x - 200)y = 150; - (1)

Now plug in x, such that x must be greater than 200.
Apply x = 215;
15y = 150;
y = 10; - Option A
Therefore x = 215 - Option D
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For the first 5 days, the bakery produces 170*5=850 cupcakes in total.
For the next y days, the bakery produces x*y cupcakes in total.

the total number of cupcakes produced in 5+y days is:
Total cupcakes=850 + x*y

Total cupcakes=200*(5+y)
Equating and resolving we get
y(x−200)=150

Try different values of x from the options and solve for y
x=215 and y=10 satisfy the equations

I have tried all the other options, they do not satisy


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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 = 850 total cupcakes produced in 5 days

therefore x*y gives total cupcakes produced in y days
therefore 200 = (850 + x*y)/(5+y)

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

plugging x=215 and y=10 satisfies the equation

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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