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04 Jan 2021, 09:52
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D
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Difficulty:
15%
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Question Stats:
74% (00:47) correct
26%
(00:59)
wrong
based on 100
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What is the units' digit of 76^k, where k is an integer ?
(1) k is a prime number
(2) k is greater than 2
(1) k is a prime number
(2) k is greater than 2
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
04 Jan 2021, 10:04
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6 raise to any power will always end with 6 in the units digit.
Thus whether (1) k is prime or (2) k > 2 the units digit will be 6
As long as k is an integral value the units digit will always be 6
Answer: D
Posted from my mobile device
Thus whether (1) k is prime or (2) k > 2 the units digit will be 6
As long as k is an integral value the units digit will always be 6
Answer: D
Posted from my mobile device
Ekland
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04 Jan 2021, 16:36
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Bunuel
ANSWER: D
This question tests knowledge of number properties.
the units digit of a non-decimal number is the right-most digit of a number before you get to the decimal point.
since k is an integer, units digit of 76^k could be 0, 1, or 6 depending on whether k is negative, 0, or postive respectively.
1: any prime number is positive number, hence we can tell with certainty that the unit digit is 6. you can try multiplying 76 by itself as much as u can and you find out the unit digit doesnt change. in the exam it's easy to recall that 6 to any positive index yields a unit digit of 6. 6*6 = 36 etc..
So 1 is SUFFICIENT
2: k being greater than 2 means that unit digit of 76^k is 6; if you follow the logic given above. So 2 is also SUFFICIENT. Each of 1 and 2 is SUFFICIENT.
