Bunuel wrote:
A certain jewelry store sells gold necklaces in 18-inch and 28-inch lengths, and all necklaces of the same length sell for the same price per necklace regardless of the number of necklaces purchased. What is the price of a 28-inch necklace at this jewelry store?
(1) The total price of an 18-inch and a 28-inch gold necklace is $68.
(2) The total price of two 18-inch necklaces and one 28-inch necklace is $96.
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:Question Type: What Is the Value? This question asks you for a specific value for the price of the longer (28 inch) necklace.
Given information from the question stem: Necklaces come in two lengths and there is no “volume discount” since all necklaces of the same length sell for the same price regardless of number purchased.
Statement 1: Translated this becomes “x + y = $68” where x is 18 inch and y is 28 inch. This is two variables and just one equation. There is no way to distribute the $68 total. This is not sufficient. Eliminate choices A and D.
Statement 2: Translated this becomes “2x + y = $96.” This is just like Statement 1 in that you have two variables and only one equation. This, too, is not sufficient. Eliminate choice B.
Together: Taken together the statements give you two linear equations with the same two variables. As long as these equations are distinct this will be sufficient.
To ensure you come to an answer, you can use the Elimination Method for multiple variables, subtracting Statement 1’s equations from Statement 2’s:
2x + y = 96
-x – y = -68
x = 28, and you can plug that in to the first equation to solve for y. If 28 + y = 68, then y = 40. These statements together allow you to solve for y, the price in question, so
the correct answer is C.
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