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TheUltimateWinner
Joined: 23 Feb 2015
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Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Posts: 2,465
04 Apr 2020, 08:40
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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:
5%
(low)
Question Stats:
100% (00:53) correct
0%
(00:00)
wrong
based on 154
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x\) and \(y\) are integers between 0 and 9, inclusive, and the units digit of \(x^y \)is 5, what are the possible values of \(x\) and \(y\)?
A) \(x = 2\); \(1 ≤ y ≤ 9\)
B) \(x = 3\); \(1 ≤ y ≤ 9\)
C) \(x = 4\); \(1 ≤ y ≤ 9\)
D) \(x = 5\); \(1 ≤ y ≤ 9\)
E) \(x = 6\); \(1 ≤ y ≤ 9\)
A) \(x = 2\); \(1 ≤ y ≤ 9\)
B) \(x = 3\); \(1 ≤ y ≤ 9\)
C) \(x = 4\); \(1 ≤ y ≤ 9\)
D) \(x = 5\); \(1 ≤ y ≤ 9\)
E) \(x = 6\); \(1 ≤ y ≤ 9\)
04 Apr 2020, 11:25
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Solution
Given
In this question, we are given that
- • The integers x and y are in between 0 and 9, inclusive
• Units digit of \(x^y\) is 5
To find
We need to determine
- • The possible values of x and y
Approach and Working
From the concepts of units digit, we know that,
- • If a number is ending with 0, 1, 5 or 6, then the units digit remains same when the number is raised to a positive integer
• As \(x^y\) is ending with 5, x must also end with 5, and y can be any positive integer within the given range
• Therefore, x = 5, and 1 ≤ y ≤ 9
Thus, option D is the correct answer.
Correct Answer: Option D
