Official Guide Explanation:
Data Sufficiency #D26

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Solution and Metadata

Question: D26
Page: 24
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: Statement (1) is insufficient. If 2, 3, and 5 must all be a factor of p, we can eliminate some possible values (7, for example), and establish that some numbers, such as 30, could be the value of p. But since all we know are some of the factors, we don't know the precise number. Every multiple of 30 is a possible value.

Statement (2) is also insufficient. By the same reasoning as in (1), those factors establish that p must be 70 or a multiple of 70.

Taken together, the statements are still insufficient. The smallest possible value of p is 210 (the product of 2, 3, 5, and 7), but p could also be any multiple of 210. Choice (E) is correct.

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