If x and y are primes, and x @ y = 1/x + 1/y, is x @ y (1) x = y (2) x + y = 4

Correct Answer is : Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

Either statement BY ITSELF is sufficient to answer the question.

Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

Correct Answer is : Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

Test Index

GMAT Quantitative Reasoning Practice Test 6

Question : 40 of 100

Marks: +1, -0

x

y

x @ y = \frac{1}{x} + \frac{1}{y}

x @ y < 1

x = y

x + y = 4

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
Either statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

Solution:

Since

x = y

and both are primes,

\frac{1}{x} + \frac{1}{y}

could equal

\frac{2}{3}

when

x = y = 3

, or equal 1 when

x = y = 2

. Therefore, the first statement is not sufficient to solve. According to the second statement,

x + y = 4

, the only primes to match are

x = y = 2

. Now we know that

\frac{1}{x} + \frac{1}{y} = 1

and the question is solved.

Go to Question:

Prev Question

Next Question