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A pizza place sells vegetarian pizza for a certain price and

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A pizza place sells vegetarian pizza for a certain price and

by BTGmoderatorLU » Thu Jun 14, 2018 2:23 pm

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A pizza place sells vegetarian pizza for a certain price and meat pizza for a certain price. If Dana, Alex, and Tim bought pizza from this store, How much did Dana Pay for 2 vegetarian pizzas?

(1) Tim bought 1 meat pizza and one vegetarian pizza for $18.80.
(2) Alex bought 2 meat pizzas and 2 vegetarian pizzas for $37.60.

The OA is E.

Please, can anyone assist me with this DS question? I'm not sure because Tim bought 2 pizzas for $18.80 and Alex bought 4 pizzas for twice the price than Tim, $37.60.
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by Jake@ThePrincetonReview » Thu Jun 14, 2018 2:40 pm

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This is a simultaneous equations question demonstrating the common trap of showing two equations that are not distinct and thus not solvable for the individual variables.

It doesn't matter who buys the pizzas - the prices of the pizzas are all we care about.

Given: V = price of a veggie pizza. M = price of a meat pizza. What is 2V? (so basically, solve for V)

Statement 1: M + V = 18.80. Clearly insufficient on its own.
Statement 2: 2M + 2V = 37.60. Also clearly insufficient on its own.

Statements 1 and 2 together: Since Statement 2 is not giving us any new information, just a multiple of the equation in Statement 1, the statements together are insufficient.

In other words, any numbers that fit into statement 1 will also fit into statement 2.
For example, meat pizzas could cost 18.80 each and veggie pizzas could cost 0. Or meat pizzas could cost 0 and veggie pizzas could cost 18.80 each. Since more than one answer is possible even with the 2 statements, the answer is E.

Usually, the GMAT will do a better job of hiding that the two equations are not distinct, such as by changing the ordering of the terms or by making one equation something like 1.2 times the other one. When they're in the same order and one equation is simply doubling the other, it's very easy to spot this common trap. (The trap is some students may choose C on this question, thinking the equations are distinct and thus solvable as a system of equations.)
Jake Schiff
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