If t and x are integers, what is the value of...

### Related Test

If t and x are integers, what is the value of x?
(1) x2 / t2 = 4 / 9
(2) x > 0 and t > 0
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

In all of my classes and tutoring sessions, I emphasize how important it is to “spot the con” and to critically analyze your decision-making process when working through GMAT problems. This frequently missed question is a wonderful example of what happens when you don’t remain critical. In statement (1), you are given a piece of information that the test writers purposefully want you to determine is insufficient. You look at statement (1), glance at statement (2), and immediately realize that x and t could be positive or negative in statement (1) alone, making it insufficient. People feel good about themselves for identifying this fact and quickly pick (C), since adding statement (2) seems to guarantee that x and t are positive 2 and positive 3, respectively.
Anytime the test writers can create a scenario in which you have a dopamine response and feel good about finding a trap, you are likely to stop being critical. The positive/negative issues present in this question are a shiny penny—so many people pick (C) because they only focus on the positive/negative ambiguity in statement (1), and statement (2) guarantees they are positive. However, when taken together, all that statements (1) and (2) tell you is that the ratio of x:t must be 2:3 and x and t must be positive. This still leaves an infinite number of possibilities for the two values: 2 and 3, 4 and 6, 6 and 9, 8 and 12, etc. Since the value for x cannot be determined, the correct answer is (E).
If both statements together still result in an infinite number of possibilities for the value of x, why do a majority of high-performing students still pick (C), thinking x must be 2? Because they don’t understand the con and they let their guard down! Just because you find one “con” in a question (in this example, the positive/negative issue), does not mean there aren’t others still present!

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