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04 Feb 2019, 00:47
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D
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Difficulty:
65%
(hard)
Question Stats:
49% (01:38) correct
51%
(01:18)
wrong
based on 119
sessions
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What is the units digit of \((2x)^8\)?
(1) The unit's digit of \(x^2\) is 9.
(2) The unit's digit of \(x^3\) is 7.
(1) The unit's digit of \(x^2\) is 9.
(2) The unit's digit of \(x^3\) is 7.
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:
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04 Feb 2019, 01:09
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chetan2u
From 1:- x can be 7 or 3 but unit digit of \(x^8\) will always be one(\(x^2\) 4 times or check for both 7 and 3).
so we can find single solution.
From 3:- x can only be 7. so sufficient
Option D
04 Feb 2019, 01:26
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chetan2u
IMO D
\((2x)^8 = 2^8*x^8\)
The unit digits of \(2^n\) cycle as 2, 4, 6, 8, 0
The 8th power will have unit digit as 6.
Statement 1:
Unit digit of \(x^2\) is 9.
This means the unit digits of \(x^n\) cycle as 3, 9, 7, 1.
Therefore, the 8th power will have unit digit as 1. Multiplying 8th power of x to 8th power of 2 will give unit digit as 6.
Sufficient.
Statement 2:
Unit digit of \(x^3\) is 7.
From this again we can derive the unit digits of \(x^n\) cycle as 3, 9, 7, 1.
And again the unit digit of product of 8th power of x and 2 is 6.
Sufficient.
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