[GMAT math practice question]
(Number Properties) P is a positive integer greater than 3. Is P + 1 a multiple of 6?
1) Both P and P+2 are prime numbers.
2) P is a multiple of 5.
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Since we have 1 variable (P) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.
Let’s look at condition 1). It tells us that P + 1 is a multiple of 6.
Since P is a prime number, P can’t have a remainder of 0, 2, 3, or 4 when P is divided by 6.
Since P + 2 is a prime number, P + 2 can’t have a remainder 0, 2, 3, or 4 when P + 2 is divided by 6, which means P can’t have a remainder of 0, 1, 2, or 4.
Then, the possible remainder of P when divided by 6 is only 5.
Thus, P + 1 has a remainder of 0 when divided by 6, and P + 1 is a multiple of 6.
The answer is unique, yes, and the answer is sufficient according to Common Mistake Type 2, which states that the answer must be a unique yes or no.
Let’s look at condition 2). It tells us that we don’t have a unique solution.
If P = 5, then P + 1 = 6 and P + 1 is a multiple of 6 and the answer is ‘yes’.
If P = 10, then P + 1 = 11 and P + 1 is not a multiple of 6 and the answer is ‘no’.
The answer is not unique, yes and no, so the condition is not sufficient, according to Common Mistake Type 2, which states that if we get both yes and no as an answer, it is not sufficient.
Condition 1) ALONE is sufficient.
Therefore, A is the correct answer.
Answer: A
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.
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