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28 Sep 2023, 08:15
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
74% (01:15) correct
26%
(01:13)
wrong
based on 46
sessions
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If x, y are positive integers, what is the unit digit of 2^(4x + 2) + y?
(1) x = 1
(2) y = 2
(1) x = 1
(2) y = 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
28 Sep 2023, 10:46
Kudos
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cyclicity of 2
2^1 = 2
2^2 = 4
2^3=8
2^4=6
2^5=2
so for 2^(4x + 2) the unit digit will always be 0
we need to determine value of y
#1
x=1
insufficient
#2
y=2
so unit digit of 2^(4x + 2) is 2
sufficient
option B
2^1 = 2
2^2 = 4
2^3=8
2^4=6
2^5=2
so for 2^(4x + 2) the unit digit will always be 0
we need to determine value of y
#1
x=1
insufficient
#2
y=2
so unit digit of 2^(4x + 2) is 2
sufficient
option B
Bunuel
28 Sep 2023, 17:44
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Bunuel
x and y are positive integers, and we need to answer the question:
units digit of [2^(4x + 2) + y] = ?
Notice that even without knowing the value of x, we could determine the units digit of the exponential term in the above sum. How? Because the remainder of the exponent after division by four is 2, we are at the second item in the four-item-long units digit cycle of powers of 2. Since the answer to the original question now hinges on only the units digit of y, we can rephrase the question as:
units digit of y = ?
Statement One Alone:
=> x = 1
We don’t have any information about the units digit of y.
Statement one is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:
=> y = 2
The units digit of y is 2. Statement two is sufficient.
Answer: B
