A construction company was paid a total of $500,000 for a construction

Cost(C) = Labor(L) + Materials(M)
Profit(P) = 500,000-C
is 500,000 - C > 150,000?
is C < 350,000

(1) C = 3M
C = 3M = L + M, L = 2M

(2) P > L
Substitute 2M for L
P > 2M
multiply both sides by 3/2
(3/2)P > 3M
Substitute C for 3M
(3/2)P > C
plug 150,000 in for P
(3/2)(150,000) > C
225,000 > C

So, C < 350,000 and the answer is yes, so then (1) and (2) together are sufficient

wow, that was fast, I was just typing my explanation, but yours looks much simpler. thanks

My solution:

1) Total cost = 3M, Labor = 2M, NS

2) Profit >= Labor, NS

1) and 2) Profit >= 2M, therefore profit must be at least 2M/(2M+M+2M)*$500,000 = 2/5*$500,000, therefore profit >= $200,000. Sufficient.

Could you please explain why profit must be at least 2M/(2M+M+2M)*500,000?

Gladly.

Since from:

1) we know that Labor (L) = 2 * Materials (M), and
2) we know that Profit (P) >= L
1) and 2) combined show that P >= 2M

There are only three components of the $500,000: P, L and M, so P+L+M = $500,000. The minimum amount of P is the case that P = L = 2M. In order to find what fraction P is of P+L+M we simply take \(P/(P+M+L) = 2M/(2M+M+2M) = 2M/5M = 2/5\). Now that we know what fraction of the $500,000 is P, we simply multiply 2/5 * $500,000 to get $200,000. Sufficient.

Total budget = 500

Is profit > 150

Or is expenditure < 350

1) Total cost = Material+Labor
T = M+L
T = 3M
3M = M+L
2M = L

Labor cost is twice that of material.

If M=1, L=2; T=3. Expenditure < 350. Yes
M=150; L=300; T=450; Expenditure > 350. No.
Not sufficient.

2) Company's Profit P>L
M=0; L=249; P=251. Expenditure <350. Yes
M=399; L=1; P=100. Expenditure <350. No.
Not sufficient.

Combining 1 and 2;
T=M+L=L/2+L
T=(3/2)L
P=500-T=500-(3/2)L
P=500-(3/2)L
P>L
500-(3/2)L>L
500>(5/2)L
(5/2)L<500
L<200
Since M is half L. M should be <100
Even if we consider maximum of these;
Total maximum expenditure = 200+100=300<350.
Thus profit will always be >150.

Ans: "C"

when you combine
TC (total cost)= 3m (material)
TC= L (labor) + m = 3m so L=2M

500-TC>2m (aka L)
500>5m
m<100

500 - less then 300= greater then 200k

C

Rephrase: 500K - [L+M] >= 150K
L+M <= 350K?

1. L+M = 3M => L = 2M. No info on M or L values, insuff.
2. L < 150K. M=? insuff

Together, L<150K, which means M<75K, which implies that the labor cost is 3M<3x75K=225K. Obviously, this means that profit > 150K. Suff.

Hi all. Bumping this topic because I didn't find an adequate answer explanation.

Here's mine:

Given :

Profit = 500,000 - TC

TC = L + M

St. 1: (N.S.)

TC = 3M
3M = L + M
2M = L

St. 2: (N.S.)

P > L , since L = 2M , Profit > 2M

Both Statements:

P = 500,000 - 3M [TC = 3M from st. 1]
2M = 500,000 - 3M [P > L , P > 2M ] . Substitute 2M into the profit formula, knowing that the Profit number must be greater than 2M.

solve for M: ... M = $100,000. Plug into profit formula :

2($100,000) = $500,000 - 3($100,000)

Profit > $200,000

Answer choice C.

Hi all. I’m not very good at mathy explanations (more of a verbal guy), but I got this question right first time in about 2 minutes. Here is my logic to it:

The question stem tells us that the company was paid $500k for the project, and states that only labor and material are the costs. It then asks if the company’s profit is greater than 150k. Another way of thinking of that is asking if the costs were greater than $350k. (Since $500k payment – $350k cost = $150k profit)

Statement 1 tells us that the ratio of total cost to cost of material is 3 to 1. Because the question stem states the only other cost is labor, we know that the ratio of labor cost to material cost is 2:1. For every dollar of material there is 2 dollars of labor. Not sufficient on its own.

Statement 2 tells us the company profit is greater than its cost of labor. An important part of that is that it means profit is indeed a positive number! Not sufficient on its own.

With the statements combined we know that profit is greater than labor, and the ratio of labor to material is 2:1.
The limit ends up being $200k profit, $200k labor, and $100k materials. The company’s actual costs have to be lower than this limit. Even the limit only has $300k of cost, which is much lower than $350k as asked in the question stem.

Answer is C.

Converting the question into equations is the key to solving this question under two mins.

What does the question stem say -> Cost (C) = Labour ( L ) + Material ( M )

Cost = 500 ( dividing by 1000, makes the calculations appear less daunting )

Is Profit > 150 ?

What is profit ? -> Money Earned - Money Spent

Money Earned is -> 500

So Profit ( P) = 500 - C

Now, Rephrasing the question stem,
Is 500 - C > 150
which means, Is C < 350 ?

Now, lets look at both the options.

A) C=3M

No numerical given, so there is no way to ascertain the answer to our main question.

B) Profit is > Cost of Labour -- Which in mathematical terms, means the following

500 - C > L

now as we already know that C= L + M, L= C -M

Substituting,

500 -C > C - M ,

500 > 2C - M ( Again no numerical value available to prove C< 350 )

Now , Lets combine A and B

500 >2C - M and C= 3M,

Lets get everything in terms of C as our main question is in terms of C.

500 > 2C - C/3 ,

This gives us -- > C < 300 , which is sufficient to answer our main question , Is C< 350 .

Answer is C.

(1) The company's total cost was three times its cost for materials.
P = 500 - C
C = m + l
C = 3m
We can deduce that l = 2m, but still have no value for P = 500 - 3m
Not sufficient

(2) The company's profit was greater than its cost for labor
P > l
Not sufficient

Together, We know P > l and that l = 2m
So P > 2m
We can use this (remembering that LHS is greater) 2m > 500 - 3m
5m > 500
m > 100
Since we know P > 2m, P > 200 so we can say yes to the question P>150?

here is a wonderfull explanation:

https://www.manhattanprep.com/gmat/foru ... t2638.html

Total cost =C
Material cost = M
Labor cost = M
C=L+M
1st statement
The company's total cost was three times its cost for materials.
C=3M
L = C-M= 3M-M = 2M
not sufficient

2nd statement
The company's profit was greater than its cost for labor
P>L
No information about cost for material
not sufficient

Both statements combined
P=500-C=500-3M
P>L => P>2M
multiple 3/2 on both sides
3/2P>3M
3/2(500-C)>C
1500-3C>2C
1500>5C
300>C
Hence total cost is less than 300, so profit is more than 200
Sufficient

Hope it is helpful

Thank you

Aryan Chandel
8169397962

then
2m < 200
so p can be
2m < p < 150 < 200 or 2m < 150 < p < 200

how is this sufficient ? i dont get it

I have edited the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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