Data Sufficiency

Which of company X and company Y earned the greater gross profits last year ?


Statement I - last year the expenses of Company X were 5/6 of the expenses of company Y

Statement II - Last year the revenues of Company X were $6 million less than the revenues of Company Y

I got C as the answer. Is this correct?

Thanks.

didieravoaka wrote:Which of company X and company Y earned the greater gross profits last year ?


Statement I - last year the expenses of Company X were 5/6 of the expenses of company Y

Statement II - Last year the revenues of Company X were $6 million less than the revenues of Company Y

The following cases satisfy both statements.

Case 1:
Revenues for X = $10 million, expenses for X = $5 million, yielding a profit for X of $5 million.
Revenues for Y = $16 million, expenses for Y = $6 million, yielding a profit for Y of $10 million.
In this case, Y earns a greater profit than X.

Case 2:
Revenues for X = $60 million, expenses for X = $50 million, yielding a profit for X of $10 million.
Revenues for Y = $66 million, expenses for Y = $60 million, yielding a profit for Y of $6 million.
In this case, X earns a greater profit than Y.

Since in the first case Y>X, but in the second case X>Y, the two statements combined are INSUFFICIENT.

The correct answer is E.

didieravoaka wrote:Which of company X and company Y earned the greater gross profits last year ?


Statement I - last year the expenses of Company X were 5/6 of the expenses of company Y

Statement II - Last year the revenues of Company X were $6 million less than the revenues of Company Y

I got C as the answer. Is this correct?

Thanks.

Required: Which of X and Y earned greater profit
Profit = Revenue - Expenses

Statement 1: last year the expenses of Company X were 5/6 of the expenses of company Y
This statements just tells us about about the expenses.
Insufficient

Statement 2: Last year the revenues of Company X were $6 million less than the revenues of Company Y
This statement tells us just about the revenues but nothing about the expenses.
Insufficient

Combining both the statements:
From statement 1 - Assume the expenses of company X = 5E,
expenses of company Y = 6E
From statement 2 - Assume the revenue of company X = R
Revenues of company Y = R + 6

Profit of X = R - 5E
Profit of Y = R + 6 - 6E
Since we do not know the relation between R and E, we cannot calculate the relation between the profits.
Insufficient

Correct Option: E

Let's say X's expenses are a and its revenues are b. For Y, let's make those c and d.

S1:: a = (5/6)c
S2:: b = d - 6,000,000

The gross profits would be revenues - expenses, so our question is now

Is b - a > d - c ?

Is (d - 6,000,000) - (5/6)c > d - c ?

Is (1/6)c > 6,000,000 ?

Is c > 36,000,000 ?

But we don't know the value of c (Company Y's expenses), so we can't answer.