VJesus12 wrote:Is the price of an apple greater than that of an orange?
(1) The price of 10 apples and 15 oranges is $8.
(2) The price of 5 apples is $1.30 greater than the price of 6 oranges.
Let A = the price (in dollars) of ONE apple
Let O = the price (in dollars) of ONE orange
Target question: Is O < A?
Statement 1: The price of 10 apples and 15 oranges is $8
We can write: 10A + 15O = 8
This doesn't tell us the RELATIONSHIP between the two prices.
Here's what I mean...
There are several values of A and O that satisfy statement 1. Here are two:
Case a: A = $0.50 and O = $0.20. So, 10A + 15O = 8 becomes = 10(0.5) + 15(0.2) = 8 (which checks out). In this case,
O < A
Case b: A = $0.20 and O = $0.40. So, 10A + 15O = 8 becomes = 10(0.2) + 15(0.4) = 8 (which checks out). In this case,
O > A
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The price of 5 apples is $1.30 greater than the price of 6 oranges.
This tells us that the cost of 5 apples is GREATER THAN the cost of 6 oranges
We can write:
6O < 5A
IMPORTANT: We also know that the cost of 5 oranges is LESS THAN the cost of 6 oranges. So, we can write:
5O < 60
When we combine the two red inequalities, we get:
5O < 6O < 5A
From this, we can conclude that 5O < 5A
Divide both sides by 5 to get:
O < A (PERFECT!)
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
