GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2019, 16:22 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a^b = c, what is the units digit of c?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59622
If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 59% (01:06) correct 41% (00:54) wrong based on 41 sessions

### HideShow timer Statistics

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

_________________
Director  P
Joined: 18 May 2019
Posts: 534
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
1
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.

Senior Manager  P
Joined: 07 Mar 2019
Posts: 442
Location: India
GMAT 1: 580 Q43 V27 WE: Sales (Energy and Utilities)
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

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.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Senior Manager  P
Joined: 01 Mar 2019
Posts: 336
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
(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

Posted from my mobile device
Manager  S
Joined: 05 Aug 2018
Posts: 72
Location: Thailand
Concentration: Finance, Entrepreneurship
GPA: 3.68
WE: Business Development (Energy and Utilities)
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
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
SVP  D
Joined: 03 Jun 2019
Posts: 1880
Location: India
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
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
VP  D
Joined: 20 Jul 2017
Posts: 1143
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
(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
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5466
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
#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
Director  P
Joined: 24 Nov 2016
Posts: 935
Location: United States
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
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.
$$b≠0,a=(6,-6):(6,-6)^{≠0} = c…units=6$$

Senior Manager  G
Joined: 25 Jul 2018
Posts: 395
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
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

Posted from my mobile device
Senior Manager  P
Joined: 10 Apr 2018
Posts: 281
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34 GPA: 3.3
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
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.
Manager  G
Joined: 17 Mar 2019
Posts: 105
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

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
Manager  P
Joined: 07 Apr 2018
Posts: 101
Re: If a^b = c, what is the units digit of c?  [#permalink]

### Show Tags

1
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.

a) + b) => cyclicity of 6 is 1 and b is positive integer.
so, unit digit of c is 6. Re: If a^b = c, what is the units digit of c?   [#permalink] 22 Oct 2019, 11:28
Display posts from previous: Sort by

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