12 Days of Christmas GMAT Competition - Day 3: Mary sells both cookies

SP of Cookie $ 1.5
SP of cake $ 2.5
let cookies sold be x and cakes be y
x+y= 580
Cost of cookie $0.7 & that of cake $ 1.2
Proft = SP-CP
target
x * ( 1.5-0.7)+ y*(2.5-1.2) >600
x * ( 0.8) + y * 1.3>600

#1
She sold 30 more cakes than cookies.

x+30= y
x+y= 580
we get x = 275 , y = 305
275 * ( 0.8 ) + 305 * 1.3 = 616.5
sufficient

#2
She sold more cakes than cookies
y>x
it has to be integer value as cookies / cake cannot be fraction
least value of x is 1 and y is max 579
1* 0.8 + 579 *1.3 ; 753.7
max value of x 289 ; y least 291
289 * 0.8 + 291 * 1.3 ; 609.5

sufficient

OPTION D is correct

option a will give exact number. No issue there.
for option b, consider same number of cake and cookies sold and profit comes out as more than 600. As cake has higher profit per unit, any increase in unit of cake sold will increase the profit.

Mary sells both cookies and cakes at her bakery. She sells each cookie for $1.5 and each cake for $2.5. In the month of May, she sold a total of 580 cookies and cakes. If the cost of making one cookie and one cake is $0.7 and $1.2 respectively, did Mary make a profit of more than $600?

(1) She sold 30 more cakes than cookies.
(2) She sold more cakes than cookies.


Here, profit/cookie = 1.5 - 0.7 = 0.8
profit/cake = 2.5 - 1.2 = 1.3

(1) She sold 30 more cakes than cookies.

Let cookies = a ; then cakes = a + 30
thus, 2a + 30 = 580

So, cookies = 275 ;
cakes = 275 + 30 = 305

Total profit = 275*0.8 + 305*1.3 = 616.5 > 600
So, YES is the answer

(2) She sold more cakes than cookies.

Maximum value for cookies = 289
Minimum value for higher profit item ie, cakes = 291

Total profit = 289*0.8 + 291*1.3 = 609.5 > 600
also, All other values will be greater than 609.5

So, YES is the answer

Since, both the options independently give a unique answer
(D) is the correct answer

Cookie
Sp=1.5$
Cp=0.7$
Profit=0.8$
Let no of cookie be x
Cake
SP=2.5$
CP=1.2$
Profit=1.3$
No of cake be 580-x
0.8x+1.3(580-x)>600
x<308 (need to check this)
St1 .
cake=30+cookie
30+cookie+cookie=580
cookie=275
cake=305
can be ans by st 1

St2 She sold more cakes than cookies.
cant be answered

oa:A

First of all from the information:
profit per cookie- 1.5-0.7 = 0.8$ (lets assume a)
profit per cake- 2.5-1.2 = 1.3$ (lets assume b)
Total quantity of cookie and cake sold- 580

We need to find out if Mary made a profit over 600$

a+b= 580
0.8a + 1.3b = 600 ?

(1) She sold 30 more cakes than cookies.

b = 30 + a
a+b=580
a+30+a=580
2a=550
a=275
b= 305

0.8(275) + 1.3(305) = 220 + 396.5 = 616
Which is greater than 600
Sufficient


(2) She sold more cakes than cookies.

b>a

We know the profit margin of b is more than that of a, therefore to maximizing/minimizing the profit we need to maximize/minimize b.
Minimum possible value of b while being greater than a would be:
b=291
a=289

0.8(289) + 1.3(291) = 609, greater than 600

Since the minimum value of b gives us a profit of over a 600, all other possible values of b must give us a profit more than 600.

Therefore B is also sufficient, answer D

Let no of cookies be 'a' and no of cakes be 'b'.
Total no of cookies and cakes
a + b = 580
Profit from sale of one cookie = $(1.5-0.7) = $0.8
Profit from sale of one cake= $(2.5-1.2) = $1.3

Therefore total profit: 0.8a + 1.3b

From statement A
b = a + 30
Now a + b =580
=> 2a + 30 = 580
=> 2a = 550 => a = 275 and b = 305
Substituting in profit eqn: 0.8(275) + 1.3(305) > 600
Hence A is sufficient

From statement B
Mary sells more cakes then cookies. Since the profit earned on sale of each cookie is lower than the profit earned on sale of each cake, we need to find out boundary conditions on which the profit will be greater than $600. If the no of cookies sold is very less, then automatically the profit will skyrocket(i.e Profit >$600). For e.g if a = 5 and b = 575 then P: 0.8(5) + 1.3( 575) = $751.5>$600
So let us check the boundary condition i.e b is marginally greater than a
For this b can be 291 and a can be 289.
Therefore P: 0.8(289) + 1.3(291) = 231.2 + 378.3 = 609.5 > $600.
Hence B is sufficient

IMO D is the asnwer

Let c be the number of cookies and k be number of cakes.

c+k = 580

Is 1.5c+ 2.5k - 0.7c-1.2k > 600

Condition (1):

k - c = 30

so, 2k = 610.
k= 305.
c = 275.

Condition (1) alone is sufficient as we can find the value of (1.5c+ 2.5k - 0.7c-1.2k) and verify it is greater than 600 or not.

So keep A and D.


Condition (2):

k > c

so k is atleast k>= 291 and c<= 289

Assuming extreme edge case, k=291 and c= 289:

1.5c+ 2.5k - 0.7c-1.2k = 1.5(289)+2.5(291) - 0.7(289) - 1.2(291) = 0.8(289) + 1.3(291) = 609.5

The amount is greater than 600.

The next extreme case is k =579 and c= 1.


1.5c+ 2.5k - 0.7c-1.2k = 1.5(1)+2.5(579) - 0.7(1) - 1.2(579) = 0.8(1) + 1.3(579) = 675.5

The amount is always greater than 600.

Edge cases prove that the amount of profit is always greater than 600.

So Condition (2) alone is sufficient.

So Eliminate choice A.


Hence D is the correct answer choice.

Solution Total 580 cookies and cakes , benefit is $0.8 on one cookie and $1.3 on one cake.

1. 30 cakes more than cookies. it means 580-30= 550, 550/2= 225 cookies and 225+30= 255 cakes
by simple multiplication its is clear that cookies profit is = 225*0.8=180 and profit on cakes is = 255*1.3= 331
hence profit is lower than $600 (Sufficient to answer)

2. sold more cakes than cookies - not specific number is mention , it means she might have sold one cookie or 100 cookies or 239 cookies and 241 cakes. hence , in different scenarios profit is sometimes over 600$ and sometimes lower than $600. Hence not clear, not sufficient.

answer is A.

Mary sells both cookies and cakes at her bakery. She sells each cookie for $1.5 and each cake for $2.5. In the month of May, she sold a total of 580 cookies and cakes. If the cost of making one cookie and one cake is $0.7 and $1.2 respectively, did Mary make a profit of more than $600?

(1) She sold 30 more cakes than cookies.
(2) She sold more cakes than cookies.


Here, profit/cookie = 1.5 - 0.7 = 0.8
profit/cake = 2.5 - 1.2 = 1.3

(1) She sold 30 more cakes than cookies.

gain per cookie = 0.8 & gain per cake = 1.3

30 more cakes than cookies. --> cakes = 305 & cookies = 275

Total gain of $ 616.50 , which is greater than 600

Answer can be uniquely determined as Yes

(2) She sold more cakes than cookies.

For cookies = cakes = 290

Total gain of @ 609

If cakes (ie, greater profit item) are further increased , gain will further increase in excess of $ 609

Here, also Answer can be uniquely determined as Yes

Thus, we get the answer as

option D

(1) She sold 30 more cakes than cookies.

Cookies + cakes = 580
cakes = cookies + 30
cakes = 305; cookies = 275
Now, we will definitely get a Yes/No answer here. No need to calculate the sum.
Sufficient

(2) She sold more cakes than cookies.

This doesn't tell us anything.
If cakes sold are 500 and cookies sold are 80 then profit exceeds 600. YES
But if cakes are 305, and cookies are 275 the profit will be under 600. NO
Insufficient

Ans A

Let the number of cookies Mary sold be x
Let the number of cakes Mary sold be y

Given: x+y= 580
1.5x-0.7x= 0.8x= profit on cookies
2.5y-1.2y= 1.3y= profit on cakes

Statement (1):
x+30=y
x+y= 580

Sufficient to calculate the value of x and y and hence the profit.

Statement (2)
y>x
Let's take 2 scenarios to see if profit is more than $600 or not.

Scenario 1: x=1, y=579
0.8*1+1.3*579= 753.2

Scenario 2: x=289, y=291
0.8*289+1.3*291=609.5

Since the profit is always greater than $600, this statement is sufficient.

(D) is the answer

Let number of cookies = x, number of cakes = y
Given:
x+y = 580
Profit = # units sold (Selling Price - Cost) = (1.5-0.7)x + (2.5-1.2)y = 0.8x + 1.3y

Question: Is Profit > $600? or Is 0.8x + 1.3y > 600? or Is 8x + 13 y > 6000? (removed decimals to avoid errors)
Replace x with 580-y (easier to deal with multiplication with 8 than with 13) in profit equation: 8(580-y) + 13y > 6000?
Is 5y > 1360? Is y > 272?

(1) She sold 30 more cakes than cookies.
y = x + 30
Solve x+y = 580
2y - 30 = 580 --> 2y = 610 --> y = 305
y>272. Sufficient.

(2) She sold more cakes than cookies.
y > x
If y = x, then y = x = 580/2 = 290
y > 272
Sufficient.

Answer: D

Note: Attempted this as a part of the Christmas challenge (answers not revealed yet). Let me know if there is an error.

Cookies = x; Cakes = y => x+y=580
Price of cookies = 1.5x; Cost of cookies =0.7x. Then profit is: 1.5x-0.7x=0.8x
Price of cakes =2.5y; Cost of cakes = 1.2y. Profit is: 2.5y-1.2y=1.3y

The question is whether P(profit)>$600 or 0.8x+1.3y>600?
We need to find the number of cookies or cakes sold in a month to answer the given question. This means knowing only x or y will be enough.

(1) She sold 30 more cakes than cookies.
St (1) tells us that y=x-30 is the number of cakes in a month.
x+x-30=580 This is enough to find x so the statement is SUFFICIENT
x=305; y=275
$0.8*305+$1.3*275>600
601.5>600

(2) x<y
Let's see minimum and maximum possibilities that y can take. y(min)=291 y(max)=579
It is obvious that with the maximum number of cakes, that is 579, the profit(579*$1.3) is greater than $600.

y=291 x=289
$0.8*289+$1.3*291>600
609.5>600
Since with the minimum number of cakes the profit is greater than $600 that means the statement is SUFFICIENT

Answer D

Correct Answer: A

We have all the information for analysing the question in the passage. The final question is whether Profit> $600.

Statement 1: Gives the relationship between cookies and cake sold which help to get the answer of Profit value from per piece. Multiply with the quantity ans Profit is less than 600. Hence, A is enough.

Statement 2: This does not give any relationship of quantity hence, alone not enough to answer the question.

Eliminate choice D and A is the answer.

Mary sells both cookies and cakes at her bakery. She sells each cookie for $1.5 and each cake for $2.5. In the month of May, she sold a total of 580 cookies and cakes. If the cost of making one cookie and one cake is $0.7 and $1.2 respectively, did Mary make a profit of more than $600?

(1) She sold 30 more cakes than cookies.
(2) She sold more cakes than cookies.

Profit per cake = $1.3
Profit per cookie = $0.8

1.
Sufficient
No of cakes = 305
Cookies = 275

We can calculate the profit and determine if it is greater than 600

2.
Sufficient
No of cakes = 291
No of cookies = 289

Profit = 291*1.3+289*.8 > 600

Answer - D

case 1 :- She sold 30 more cakes than cookies. --> sufficient

case2:- She sold more cakes than cookies. --> sufficient
consider the worst case cookies 289 & cake 291. still profit is more than $600

ans D

First, profit per cookie= 1.5-0.7=$0.8
profit per cake= 2.5-1.2=$1.3

Let, number of cookies be x and number of cakes be 580-x.

To make a profit of more than $600,
0.8x + 1.3(580-x) >600
Solving, x<308

Now,
Statement I: 580-x-x=30
x=275
Since 275<308, This statement is enough to determine whether profit will be greater than $600.

Statement II: She sold more cakes than cookies,
First, x(cookies)=0 , cakes=580 - In this case, profit is greater than 600 since x<308 and cakes are more than cookies.
Second, x(cookies)=307, cakes=173 - In this case, profit is again greater than 600 since x<308 and cakes are less than cookies.
Hence, this statement is not enough.

So, answer will be A.