If x and y are positive integers, what is the unit digit of the

Question

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​

GMATinsight · Answer

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

GMATWhizTeam · Answer

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     
Thus, we only need to find the value of y.

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

TestPrepUnlimited · Answer

Note a positive power of 6 will always have a unit digit of 6, this is because  6 * 6 = 36  so no matter how many 6's you multiply together you always end with a last digit of 6. 
Hence we should pay attention to the  y^6  part, as  6^{x+2}  always has a unit digit of 6.

Statement 1:  Don't know y, insufficient.
 Statement 2:  Gives y, sufficient.

Ans: B

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. 6^x has a unit digit 6 whatever x is. Thus 6^x+2 + y^6 relies on the variable y only. Thus, condition 2) is sufficient. Therefore, B is the answer.

If x and y are positive integers, what is the unit digit of the

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GMAT Data Sufficiency (DS) Questions

If x and y are positive integers, what is the unit digit of the

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