A company produces three types of electronic components: X, Y, and Z.

Question

A company produces three types of electronic components: X, Y, and Z. The production cost per unit of X is half that of Y, and the production cost per unit of Z is twice that of Y. The company sells all produced units each month. Did the company make a profit last month?

(1) The total revenue from component X was equal to the total revenue from component Y, and the total revenue from component Z was equal to the total production cost of Y.

(2) The number of units of X produced was twice the number of units of Y, while the number of units of Z produced was half the number of units of Y. The selling price per unit of X was 1.5 times its production cost, the selling price per unit of Y was equal to its production cost, and the selling price per unit of Z was 1.2 times its production cost.

Gmat750aspirant · Answer

Let: 
- Cost per unit of Y = C 
- Cost per unit of X = C/2 
- Cost per unit of Z = 2C

Statement (1): 
- Total revenue from X = Total revenue from Y → (Price of X * Quantity of X) = (Price of Y * Quantity of Y) 
- Total revenue from Z = Total production cost of Y → (Price of Z * Quantity of Z) = (C * Quantity of Y)

This gives relationships between revenues and costs but does not determine if total revenue exceeds total cost. 
Statement (1) alone is insufficient.

Statement (2): 
- Quantity of X = 2 * Quantity of Y 
- Quantity of Z = 0.5 * Quantity of Y 
- Selling price per unit: 
 - X = 1.5 * (C/2) = 0.75C 
 - Y = C 
 - Z = 1.2 * (2C) = 2.4C

Revenue calculations: 
- Revenue from X = 0.75C * (2Y) = 1.5CY 
- Revenue from Y = CY 
- Revenue from Z = 2.4C * (0.5Y) = 1.2CY

Total Revenue = 1.5CY + CY + 1.2CY = 3.7CY

Cost calculations: 
- Cost of X = (C/2) * (2Y) = CY 
- Cost of Y = CY 
- Cost of Z = 2C * (0.5Y) = CY

Total Cost = CY + CY + CY = 3CY

Since Total Revenue (3.7CY) > Total Cost (3CY), the company made a profit. 
Statement (2) alone is sufficient.

Combining (1) and (2) is unnecessary as (2) alone is sufficient.

Answer: B

rerumconsectetur · Answer

can we more rapidly tell that (from statement 2) being costs below prices (apart from Y that is equal) we can say that profit is positive?

luisdicampo · Answer

Deconstructing the Question

We need to determine whether total revenue exceeded total production cost.

Let the production cost per unit of Y be   c  .

Then the unit costs are

X=\frac{c}{2}, \quad Y=c, \quad Z=2c

We must determine whether the company made an overall profit.

Step-by-step

Statement (1): Total revenue from X equals total revenue from Y, and total revenue from Z equals total production cost of Y.

So

R_X=R_Y

and

R_Z=C_Y

Thus total revenue is

R_X+R_Y+R_Z=2R_Y+C_Y

But we still do not know total costs of X and Z, nor whether total revenue exceeds total cost.

Statement (1):  Insufficient

Statement (2): Let the number of Y units be   n  .

Then

q_X=2n,\quad q_Y=n,\quad q_Z=\frac{n}{2}

Selling price per unit of X is   1.5   times its cost, so

p_X=1.5\cdot \frac{c}{2}=\frac{3c}{4}

Selling price per unit of Y equals its cost, so

p_Y=c

Selling price per unit of Z is   1.2   times its cost, so

p_Z=1.2\cdot 2c=2.4c

Now compute total revenue and cost.

For X:

R_X=2n\cdot \frac{3c}{4}=\frac{3nc}{2}

C_X=2n\cdot \frac{c}{2}=nc

Profit from X:

\frac{3nc}{2}-nc=\frac{nc}{2}

For Y:

R_Y=nc,\quad C_Y=nc

Profit from Y:

0

For Z:

R_Z=\frac{n}{2}\cdot 2.4c=1.2nc

C_Z=\frac{n}{2}\cdot 2c=nc

Profit from Z:

1.2nc-nc=0.2nc

Total profit is

\frac{nc}{2}+0+0.2nc=0.7nc

which is positive.

Statement (2):  Sufficient

Answer: B

SaveSilk · Answer

I actually feel like this could be a viable thing, did you get any answer for this? I am also curious

Jash1666 · Answer

This is yes or no type question, and it doesn’t want us to compare like is profit more than 10k so just by knowing cost and sp we can conclude, as it says all what is produced is being sold so I thinks we should save time by not doing Calculation.

MrMaxMan · Answer

I solved this one by thinking about what information I need to solve rather than doing the math.
We know all the costs relative to one of the items from the prompt.

Statement 1 Gives us only revenues which we cannot all relate back to a cost, thus introducing unknowns.  No sufficient. 
Statement 2: Gives us sale price info for all items which can be used to calculate revenues and then have cost subtracted. This means we theoretically could solve the problem if we wanted.  Sufficient.

A company produces three types of electronic components: X, Y, and Z.

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A company produces three types of electronic components: X, Y, and Z.

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