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If a^b = c, what is the units digit of c?
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21 Oct 2019, 21:28
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Competition Mode Question If a^b = c, what is the units digit of c? (1) a^2 – 36 = 0 (2) b is a positive integer
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Re: If a^b = c, what is the units digit of c?
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21 Oct 2019, 21:58
Given a^b=c, we are to determine the unit digits of c.
Statement 1: a^2  36=0 This implies a=6 or a=6 No information is available on the values of b or c. Hence we cannot determine the unit digit of c. Much as it is tempting to assume that b=2 and c=36, such an assumption is not erroneous. if b=0, then c=1, and its unit digit is 1. However when b=1, c=6 with a unit digit of 6. Statement 1 is insufficient.
Statement 2: b is a positive integer. Not sufficient. b can take infinite values. In addition, no information is provided on the possible value of a to enable us to determine the value of c leading to the determination of the unit digits of c. Statement 2 is insufficient.
1+2 a=6 or 6 and b is a positive integer. both statements taken together is sufficient. This is because when b=1, the unit digit of c(6)=6. When b=2, the unit digit of c(36) = 6. The unit digit of the positive integer powers of 6 is 6.
The answer is therefore C.



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Re: If a^b = c, what is the units digit of c?
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21 Oct 2019, 22:12
If \(a^b = c\), what is the units digit of c? (1) \(a^2 – 36 = 0\) \(a^2 – 6^2 = 0\) \((a  6) * (a + 6) = 0\) a = 6 or 6. Since either of 6 or 6 raised to any power would always give unit digit as 6, unit digit of c is always 6. SUFFICIENT. (2) b is a positive integer Nothing concrete about both a and b is given so. INSUFFICIENT. IMO Answer A.
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Re: If a^b = c, what is the units digit of c?
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21 Oct 2019, 22:19
(1) a^2 – 36 = 0 Then a^2=36...I.e a=6.... If b is positive... Units digit of a^b will be 6 always If b is 0 Units digit of a^b will be 1 If b is negative Units digit of a^b will be different So A is insufficient
(2) b is a positive integer Clearly insuff...Without the value of a
CombiNing both will get units digit as 6
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Re: If a^b = c, what is the units digit of c?
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21 Oct 2019, 22:25
If a^b = c, what is the units digit of c?
(1) a^2 – 36 = 0 a = 6, 6 but we do not know anything about b. If b =1, unit of c (if a =6, a = 6) will be 6 However, if b = 0, unit of c = 1 INSUFFICIENT
(2) b is a positive integer we do not know anything about a.  insufficient
taken (1) + (2): we now know that b is always positive so either a = 6, 6 unit of c will be 6.
Therefore, C is the correct answer



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Re: If a^b = c, what is the units digit of c?
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21 Oct 2019, 23:12
If a^b = c, what is the units digit of c?
(1) a^2 – 36 = 0 a = {6,6} Since value of b is unknown NOT SUFFICIENT
(2) b is a positive integer Since value of a is unknown NOT SUFFICIENT
(1) + (2) (1) a^2 – 36 = 0 a = {6,6} (2) b is a positive integer Unit digit of c will be 6 SUFFICIENT
IMO C



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Re: If a^b = c, what is the units digit of c?
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21 Oct 2019, 23:12
(1) a^2 – 36 = 0 > a = ±6 But we do not know whether b is an integer or a fraction So, we cannot have a definite unit digit > Insufficient
(2) b is a positive integer Does not talk anything about 'a' > Insufficient
Combining (1) & (2), Since Cyclicity of 6 is 1 and b is a positive integer > a^b will have end in 6 > Unit digit of a^b = c is 6 > Sufficient
IMO Option C



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Re: If a^b = c, what is the units digit of c?
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22 Oct 2019, 03:01
#1 a^2 – 36 = 0 a=+/6 so any power of b except 0 will give unit digit of c as 6; but b is not know it can be 0 at which c =1 insufficient #2 b is a positive integer insufficent a not know from 1 &2 b>0 and a = +/6 ; unit digit of c = 6 always IMO C
If a^b = c, what is the units digit of c?
(1) a^2 – 36 = 0 (2) b is a positive integer



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Re: If a^b = c, what is the units digit of c?
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22 Oct 2019, 04:51
Quote: If a^b = c, what is the units digit of c?
(1) a^2 – 36 = 0 (2) b is a positive integer (1) a^2 – 36 = 0 insufic.\(a^2 – 36 = 0…a^2=36…a=(6,6)\) \(b=0:a^0 = c…units=1\) \(b≠0:(6,6)^b = c…units=6\) (2) b is a positive integer insufic.(1 & 2) sufic.\(b≠0,a=(6,6):(6,6)^{≠0} = c…units=6\) Answer (C)



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Re: If a^b = c, what is the units digit of c?
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22 Oct 2019, 05:29
a^{b} = c—> what is the units digit of c?
(Statement1): a^{2}—36=0 (a—6)(a+6)= 0 a= 6, a=—6 But no info about what b is. —> if b=0, then 6^{0}=1 and (—6)^{0}= 1 —> units digit of c is equal to 1
—> if b = 2, then 6^{2}=36 and (—6)^{2}= 36 —> units digit of c is equal to 6
Insufficient
(Statement2) b is a positive integer. No info about what a is. Clearly insufficient.
Taken together 1&2, —> 6 or (—6) to the power of any positive integer end with ...6 .
Units digit of c is equal to 6 Sufficient
The answer is C
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Re: If a^b = c, what is the units digit of c?
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22 Oct 2019, 10:39
Quote: If \(a^b\) = c, what is the units digit of c?
(1) \(a^2\) – 36 = 0 (2) b is a positive integer (1) \(a^2\)=36 =>a=+6 or 6 From this we don't get a unique value of unit digit of \(a^b\) because for a=6 and b=2, \(a^b\)=\(2^6\)=36, but for a=6 and b=1/2, \(a^b=6^{1/2}\)=2.45 Therefore, insufficient. (2) No information about value of a, so we don't get a unique value of \(a^b\). Therefore, insufficient. From (1) and (2), we get that a=+6 or 6 and that b is a positive integer. So, for all the above values of a and b, \(a^b\) will have 6 as unit digit, for example, \(6^2=36, 6^3=216\), and so on. Thus, sufficient. Therefore, the correct answer is option C.



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Re: If a^b = c, what is the units digit of c?
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22 Oct 2019, 11:08
If a^b = c, what is the units digit of c?
(1) a^2 – 36 = 0 (2) b is a positive integer
Statement 1: a^2=36, a=+6 or 6. if a^2=36 units digit is 6.
If a^3= units digit is 2. Hence cannot determine.
Statement 2: b is positive. It could be any number 1 to 3 hence we cannot determine.
when combining statements 1 and 2 still even if b is positive we cannot determine exactly the units digit.
IMO E



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Re: If a^b = c, what is the units digit of c?
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22 Oct 2019, 11:28
Given: a^b= c a) a^2  36= 0 => a= 6, a= 6
No info about b. so, Insufficient
b) b is a positive integer. no info about a. Insufficient
a) + b) => cyclicity of 6 is 1 and b is positive integer. so, unit digit of c is 6.
Correct answer: C




Re: If a^b = c, what is the units digit of c?
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