GMAT Math : DSQ: Solving linear equations with two unknowns

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #911 : Data Sufficiency Questions

A toy store sells dolls for \(\displaystyle 14\) dollars each and trucks for \(\displaystyle 17\) dollars each. How many dolls did the store sell last week?

(1) Last week, the store sold twice as many trucks as dolls.

(2) Last week, the store made \(\displaystyle 24\),\(\displaystyle 000\) dollars from selling trucks and dolls.

Possible Answers:

B: Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient

C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

D: EACH statement ALONE is sufficient

 

A: Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient

 

E: Statements (1) and (2) TOGETHER are not sufficient

Correct answer:

C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

Explanation:

Let:

t: the number of trucks sold last week

d: the number of dolls sold last week - d is the value we are looking to find

To evaluate the statements, we translate the word problems into equations

(1): \(\displaystyle t = 2d\) or \(\displaystyle d = 0.5 t\)

(2): \(\displaystyle 14d + 17t = 24,000\)

Each statement provides a single equation with two unknowns which is unsolvable, so each statement alone is not enough.

The two statements taken together give us a system of two equations with two unknowns, which we can solve.

Therefore the right answer is C.

 

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