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If x and y are positive integers, what is the unit digit of the expression \(6^{x+2} + y^6?\)
(1) x=6
(2) y=7
(1) x=6
(2) y=7
25 Feb 2020, 23:45
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kapil1
If x and y are positive integers, what is the unit digit of the expression \(6^{x+2} + y^6?\)
(1) x=6
(2) y=7
(1) x=6
(2) y=7
Question: what is the unit digit of the expression \(6^{x+2} + y^6?\)
We know that cyclicity of Unit digit of
Number ending with {2, 3, 7, 8} = 4
Number ending with {0, 1, 5, 6} = 1
Number ending with {4, 9} = 2
So, we need only unit digit of y to answer the question because \(6^{x+2}\) will always have unit digit 6 irrespective of the value of x
Statement 1: x=6
NOT SUFFICIENT
Statement 2: y=7
Unit digit of \(6^{x+2} + y^6?\) = Unit digit of \(6+7^6\) = Unit digit of \(6+7^2\)= Unit digit of \(6+9\) = 5
SUFFICIENT
Answer: Option B
26 Feb 2020, 06:19
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kapil1
If x and y are positive integers, what is the unit digit of the expression \(6^{x+2} + y^6?\)
(1) x=6
(2) y=7
(1) x=6
(2) y=7
Solution
Step 1: Analyse Question Stem
- • x and y are positive integers.
• We need to find the unit digit of expression \(6^{x+2} + y^6\)
- o Or, we need to find the value of (unit’s digit of \(6^{x+2} \)+ unit’s digit of \(y^6\))
- We know that cyclicity of powers of 6 is 1.
So, irrespective of value of x, unit’s digit of \(6^{x+2} = 6\)
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: \(x = 6\)
• We are not getting the value of y.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.
Statement 2: \(y = 7\)
• Here we get the value of y ,i.e. \(y = 7\)
Hence, statement 2 is sufficient.
Thus, the correct answer is Option B
