If x is a positive integer such that the units digit of x^3 is 3, what

Question

If x is a positive integer such that the units digit of x^3 is 3, what is the units digit of x^15 ?

A. 1 
B. 3 
C. 5 
D. 7 
E. 9

NandishSS · Answer

Only possible x^3 is 7^3=343

Cycle of 7 is 4 When you divide 15/4 remainder is 3 so 7^3 is again 3

Hence B

MikeScarn · Answer

The only units digit that has  3  as the units digit when it is cubed is 7. So possible answers for x are 7, 17, 27, etc.

We know that 7 has a cyclicity of 4, so we should divide 15 by 4. This gives a remainder of 3. So the units digit will be the same as  x^3

Answer: B. 3

Abhishek009 · Answer

Break it down to pieces and solve

So, x = 7

7^1 = 7 
 7^2 = 9 
 7^3 = 3 
 7^4 = 1

So,  x^{15} = 7^{4*3 + 3}

7^{12 } will have units digit as  1  and  7^3  will have units digit as  3 , Thus answer must be (B) 3

CAMANISHPARMAR · Answer

The units digit of x has to be 7 to satisfy the conditions given in question stem.

The answer would be determined by pattern recognition.  7^x  follows a pattern.

.  Units Digit 
1) 7^1 = 7 
2)  7^2 = 9 
3)  7^3 = 3 
4)  7^4 = 1 
5)  7^5 = 7 
so on...

so the pattern repeats after an interval of 4 rounds. 
Since it is asked that what is the units digit of x^15 i.e. 7^15 we need to identify that when 15 is divided by 4 it leaves a remainder 3. Hence in the pattern we have already found that x^15 will have a units corresponding to the third item in the pattern, i.e. units digit of 3 .

Hence the answer is (B)

Jayiet89 · Answer

Value of x can only be 7,and cyclicity of 7 is 7,9,3,1.Therefore x^15 is x^4*3+3 = 3

SistaSuvarna · Answer

A faster method below ; can somebody please confirm if it is correct?

X^15 = (x^3)^5

We know that the units digit of x^3 = 3
so units digit of x^15 = units digit of 3^5

Cyclicity of 3 is 4 (Ending in 3,9,7,1)
Thus units digit of x^15= 3

Answer : B

CAMANISHPARMAR · Answer

I think your method is better

.... good job!!

ScottTargetTestPrep · Answer

If the units digit of x^3 is 3, then x must have a units digit of 7. We see that 7 repeats in a pattern of 7-9-3-1, so a units digit of 7, when raised to any exponent that is a multiple of 4, will have a units digit of 1.

Thus, x^16 has a units digit of 1, and x^15 has a units digit of 3.

Alternate solution:

Since the units digit of x^3 is 3 and x^15 = (x^3)^5, the units digit of x^15 must be the same as the units digit of 3^5. Since the units digit of powers of 3 are:

3^1 = 3, 3^2 = 9, 3^3 = 7, 3^4 = 1, and 3^5 = 3, 
then the units digit of x^15 is 3.

Answer: B

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If x is a positive integer such that the units digit of x^3 is 3, what

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If x is a positive integer such that the units digit of x^3 is 3, what

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