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12 Mar 2023, 07:59
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A
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Difficulty:
45%
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58% (01:54) correct
42%
(02:21)
wrong
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If a and b are positive integers, what is the digit at the unit's place of 18^(2a + 5b)?
(1) a is even, b is a multiple of four.
(2) b = 12
(1) a is even, b is a multiple of four.
(2) b = 12
12 Mar 2023, 13:41
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Statement 1
(1) a is even, b is a multiple of four
a = 2; b = 4
18(4 + 20) = 18 * 24 ⇒ Unit Digits = 2
a = 4; b = 4
18(8 + 20) = 18 * 28 ⇒ Unit Digits = 4
Statement 1 is not sufficient.
Statement 2
(2) b=12
a = 2; b = 12
18(4 + 60) = 18 * 64 ⇒ Unit Digits = 2
a = 4; b = 60
18(8 + 60) = 18 * 28 ⇒ Unit Digits = 4
Statement 2 is not sufficient.
Combined
The statements combined won't help either, as both the cases of Statement 2 hold true.
Option E
Either the question or the option is incorrect.
Moderator Note: The question has been updated
Updated Question: If a and b are positive integers, what is the digit at the unit's place of \(18^{(2a + 5b)}?\)
Updated Question: If a and b are positive integers, what is the digit at the unit's place of \(18^{(2a + 5b)}?\)
Statement 1
(1) a is even, b is a multiple of four
We can represent a and b as
a = 2*x ; x is a constant
b = 4*y ; y is a constant
So \(18^{(2a + 5b)}?\) can now be represented as
\(18^{(2(2x) + 5(4y))}?\)
\(18^{4 (x + 5y)}?\)
The cyclicity of 8 is 4, hence \(18^{4 (x + 5y)}?\) will always end in 6.
The statement is sufficient and we can eliminate B, C ,and E.
Statement 2
(2) b=12
The information is not sufficient as we don't know the value of a.
Hence, the statement alone is not sufficient.
Option A
