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 \(\frac{p}{q}= \frac{7}{3}\)

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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