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Set A is given as {1, 2, 3, … , n} and n is a positive integer. What is the value of n?

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Set A is given as {1, 2, 3, … , n} and n is a positive integer. What is the value of n?

by Max@Math Revolution » Tue Jul 07, 2020 2:12 am

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[GMAT math practice question]

Set A is given as {1, 2, 3, … , n} and n is a positive integer. What is the value of n?

1) The number of subsets of A containing both 1 and n is 16.
2) n is less than 8.
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Source: — Data Sufficiency |
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Re: Set A is given as {1, 2, 3, … , n} and n is a positive integer. What is the value of n?

by Max@Math Revolution » Thu Jul 09, 2020 2:17 am

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Since we have 1 variable (n) 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 set A has four elements.

Remember that the number of subsets of a set with n elements is 2n.
Since 2n = 24 = 16, we have n = 4.

The answer is unique, and the condition is sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.

Let’s look at condition 2). It tells us that we don’t have a unique solution since n = 6 and n = 7 are possible values.

The answer is not unique, and the condition is not sufficient, according to Common Mistake Type 2, which states that the number of answers must be only one.

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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