Lesson: Data Sufficiency Basic - 13t01

In-Format Practice

[Page 13 of 22]

Now let’s practice applying the Method to an in-format test question.

Use the CAT Method to select an answer, then click Continue.

If x is a prime number and 69 < x < 80, what is the value of x?

(1) x – 6 is a prime number

(2) 2x < 150

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient.
Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient.
Both statements TAKEN TOGETHER are sufficient, but NEITHER statement BY ITSELF is sufficient.
EACH statement BY ITSELF is sufficient.
The two statements TAKEN TOGETHER are NOT sufficient.

Countinue

Focus on the stem. This question stem provides a great deal of information. Begin by listing the prime numbers between 69 and 80. Your only possible choices are 71, 73, and 79. A sufficient statement would have to indicate one and only one of those three numbers.

Statement (2) is shorter, so begin there. If 2x < 150, then x < 75. So, x could be 73 or 71. Statement 2 is insufficient. Eliminate Choices (B) and (D).

Statement (1) tells you that x – 6 is prime. Subtract 6 from each of the three possible values of x.

71 – 6 = 65, but 65 is not prime.

73 – 6 = 67, which is prime.

79 – 6 = 73, which is prime.

You have two possible values for x, so Statement (1) is insufficient. Eliminate Choice (A).

Combine the statements.

x – 6 is a prime number and 2x < 150

Translation: x is less than 75 and yields a prime number when you subtract 6

Of the three numbers 71, 73, and 79, only one fits both criteria.

Therefore the value of x must be 73, the combined statements are sufficient, and the answer is Choice (C).

The information in each statement does not contradict the stem, nor do the statements contradict each other.

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