Quote:
*gotitright writes:*
Martin owns a pizza shop, and his only monthly expenses are rent and utilities. If his rent is $4,000 per month, was Martin’s profit greater than $1,500 in the month of June?
1) Martin’s profit in June was 1/4 of his revenue.
2) Martin’s utility expense in June was less than 1/3 of his profit.
ans: C
Hey, this question is from TTP practice tests. Can anyone help with this?
To determine if Martin’s profit was greater than $1,500 in June, we first need to establish the relationship between his variables.
The Setup:
* Expenses (E): Rent + Utilities. We know Rent = $4,000. So, E = 4,000 + U.
* Profit (P): Revenue (R) - Expenses (E).
* Equation: P = R - (4,000 + U).
* Goal: Is P > 1,500?
Evaluating Statement 1
1) Martin’s profit in June was 1/4 of his revenue.
* This gives us P = 0.25R, which also means R = 4P.
* Substitute this back into the profit equation: P = 4P - (4,000 + U).
* Rearranging gives: 3P = 4,000 + U, or P = (4,000 + U)/3
* We know U (utilities) must be a positive value (at least 0).
* If U = 0, then P = 4,000/3 ~ 1,333.33.
* If U is a large number, P could easily exceed 1,500.
* Since we don't know the value of U, we cannot definitively say if P > 1,500.
* Statement 1 is NOT SUFFICIENT.
Evaluating Statement 2
2) Martin’s utility expense in June was less than 1/3 of his profit.
* This gives us U < P/3.
* Without knowing the Revenue (R), we have no way to anchor the profit value. Martin could have had 10 in revenue or 1,000,000 in revenue.
* Statement 2 is NOT SUFFICIENT.
Combining Statements 1 & 2
From Statement 1, we have the relationship: 3P = 4,000 + U.
From Statement 2, we have the inequality: U < P/3
Let's substitute the upper limit of U into the Statement 1 equation to see the boundary for P:
* * Since U < P/3, then 3P < 4,000 + P/3
* Subtract P/3 from both sides: 8P/3 < 4,000
* Solve for P: P < 12000/8
* P < 1,500.
By combining both statements, we find that P must be less than 1,500.
The Answer is C.