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03 Apr 2023, 09:00
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:17) correct
30%
(02:22)
wrong
based on 33
sessions
History
Date
Time
Result
Not Attempted Yet
What is the units digit of 9^x where x is a nonnegative integer?
(1) x is even.
(2) \(\sqrt{x−3}\) is odd.
(1) x is even.
(2) \(\sqrt{x−3}\) is odd.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
03 Apr 2023, 09:10
Kudos
Bookmarks
Bunuel
Question: Unit digit of 9^x = ?
CONCEPT: if x is non-negative
i) for even value of x, 9^x leaves unit digit = 1
ii) for odd value of x, 9^x leaves unit digit = 9
i) for even value of x, 9^x leaves unit digit = 1
ii) for odd value of x, 9^x leaves unit digit = 9
Statement 1:x is even
i.e. 9^x will always render unit digit = 1 hence
SUFFICIENT
Statement 2: \(\sqrt{x−3}\) is odd
i.e. (x-3) = odd^2 = odd
i.e. x = odd+3 = even
and 9^x will always render unit digit = 1 for even value of x hence hence
SUFFICIENT
Answer: Option D
04 Apr 2023, 00:31
Kudos
Bookmarks
Bunuel
Solution:
Pre Analysis:
- We are asked the unit digit of \(9^x\) where x is non negative integer
- We know cyclicity of 9 is 2
- So, we just need to know the even-odd nature of x to answer the question
Statement 1: x is even
- Gives us what we want
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: \(\sqrt{x−3}\) is odd
\(⇒x-3=odd^2\)
\(⇒x-3=odd\)
\(⇒x=odd+3\)
\(⇒x=even\)
- Gives us what we want
- Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
