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21 Apr 2021, 03:30
Kudos
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A
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Difficulty:
55%
(hard)
Question Stats:
57% (02:07) correct
43%
(02:33)
wrong
based on 70
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a positive integer, does the remainder, when (3^x + 2) is divided by 100, have 1 as the units digit?
(1) x = 2(2n + 1), where n is a positive integer.
(2) 10 > x > 4
(1) x = 2(2n + 1), where n is a positive integer.
(2) 10 > x > 4
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
21 Apr 2021, 05:32
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Bunuel
This question can be simplified by analysing the question stem.
Remainder when divided by 100 would be last two digits.
So units digit of the remainder will be the units digit of \(3^x+2\), so \(3^x+2\) also has a units digit of 1.
This further tell us that \(3^x \) should have unit digit of x1-2 or 9.
The cyclicity of unit digit of successive powers of 3 is 3, 9, 7, 1, 3.....
So x has to be of the type 4K+2, where k is non negative integer.
The question, therefore, becomes: Is x of type 4K+2?
(1) x = 2(2n + 1), where n is a positive integer.
x=4n+2
Exactly what we were looking for.
Sufficient
(2) 10 > x > 4
If x is 6 or 4*1+2, then yes, otherwise no.
Insufficient
A
30 May 2023, 23:47
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