GMAT Question of the Day – 16/12/2020

QUESTION

Fred goes to a seafood market to purchase lobsters. All the lobsters he buys cost either $4 or $5. If he buys a total of 25 lobsters, and spends $112, what fraction of the lobsters that he purchased cost $5?

ANSWER SELECTION

(A) ¹²⁄₂₅  (THIS IS CORRECT!)

(B) ¹³⁄₂₅

(C) ¹⁴⁄₂₅

(D) ³⁄₅

(E) ¹⁶⁄₂₅

ANSWER EXPLANATION

Let x represent the number of lobsters purchased at $4 each, and let y represent the number of lobsters purchased at $5 each So the total cost of the lobsters, $112, is equal to x($4 per lobster) + y($5 per lobster). So we have the equation 112 = 4x +5y. Now, also know that 25 lobsters are purchased. So the sum of the number of lobsters purchased at $4 each and the number of lobsters purchased at $5 each is equal to 25; thus 25 = x + y. So we have two equations, 112 = 4x + 5y and 25 = x + y.

Now, let’s take the second equation, 25 = x + y, and solve for x in terms of y. Subtracting y from both sides, we find that 25 –y = x. Substituting 25 –y for x into the first equation, 112 = 4x + 5y, we have 112 = 4(25 –y) + 5y. Now let’s solve this equation for y. Then 112 = 100 – 4y + 5y, 112 = 100 + y, and 12 = y. So 12 lobsters were purchases at the price of $5 per lobster. Thus, the fraction of the lobsters purchased that cost $5 is ¹²⁄₂₅. The correct answer is choice (A).

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