Fahim22 wrote:
For positive number p and q, \(\frac{(p+q)}{p}= \frac{10}{7}\)
Quantity A |
Quantity B |
\(\frac{p-q}{q}\) |
\(\frac{5}{3}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Here are two often-tested fraction properties: \(\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\) and \(\frac{a-b}{c}=\frac{a}{c}-\frac{b}{c}\)GIVEN: \(\frac{(p+q)}{p}= \frac{10}{7}\)
Use property to rewrite left side as: \(\frac{p}{p}+\frac{q}{p}= \frac{10}{7}\)
Simplify: \(1+\frac{q}{p}= \frac{10}{7}\)
Subtract 1 from both sides to get: \(\frac{q}{p}= \frac{3}{7}\)
NOTE: If \(\frac{q}{p}= \frac{3}{7}\), then
\(\frac{p}{q}= \frac{7}{3}\)-----------------------------------------------------------
Now let's deal with the two quantities:
Quantity A: \(\frac{p-q}{q}\)
Quantity B: \(\frac{5}{3}\)
Use property to rewrite Quantity A as:
Quantity A: \(\frac{p}{q}-\frac{q}{q}\)
Quantity B: \(\frac{5}{3}\)
Simplify Quantity A:
Quantity A: \(\frac{p}{q}-1\)
Quantity B: \(\frac{5}{3}\)
Now that we know \(\frac{p}{q}= \frac{7}{3}\), we can rewrite Quantity A as follows:
Quantity A: \(\frac{7}{3}-1\)
Quantity B: \(\frac{5}{3}\)
Evaluate Quantity A :
Quantity A: \(\frac{4}{3}\)
Quantity B: \(\frac{5}{3}\)
Answer: B
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep