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Bunuel
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For all numbers p and q (where p 0 ), the operation $ is defined as 24 Jun 2022, 09:30
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Difficulty:

55% (hard)

Question Stats:

49% (01:04) correct 51% (01:10) wrong based on 87 sessions

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For all numbers p and q (where p ≠ 0 ), the operation $ is defined as \(p \$ q = (p-1)^{(q-1)}\). What is the value of \((p +1) \$ (q +1)\)?

(1) p =1

(2) q = 0
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D
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gmatophobia
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For all numbers p and q (where p 0 ), the operation $ is defined as 17 Sep 2023, 18:31
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RenB
For all numbers p and q (where \(p \neq 0\)), the operation $ is defined as p $ q = \((p-1)^{(q-1)}\). What is the value of (p +1) $ (q +1)

(1) \(p =1\)

(2) \(q = 0\)

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Given:

p $ q = \((p-1)^{(q-1)}\)

Statement 1

(1) \(p =1\)

\(p + 1 = 1 + 1 = 2\)

(p +1) $ (q +1) \(= (2 - 1) ^{(q + 1 - 1)} = 1^{q} = 1 \)

The statement alone is sufficient. We can eliminate B, C, and E.

Statement 2

(2) \(q = 0\)

\(q + 1 = 0 + 1 = 1\)

(p +1) $ (q +1) \(= (p + 1 - 1) ^{(1 - 1)} = p^{0} = 1 \)

The statement alone is sufficient.

Option D
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