The units digit of (44^91)*(73^37) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
OA A
Source: Magoosh
The units digit of (44^91)*(73^37) is:
This topic has expert replies

 Moderator
 Posts: 6010
 Joined: 07 Sep 2017
 Followed by:20 members
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 3008
 Joined: 22 Aug 2016
 Location: Grand Central / New York
 Thanked: 470 times
 Followed by:32 members
To know the units digit of (44^91)*(73^37), we must the units digit of (4^91)*(3^37).BTGmoderatorDC wrote: ↑Tue Jul 14, 2020 7:30 pmThe units digit of (44^91)*(73^37) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
OA A
Source: Magoosh
Let's understand the power cycle of 4 and 3.
4:
• 4^1 = 4 => unit digit = 4;
• 4^2 = 16 => unit digit = 6;
• 4^3 = 64 => unit digit = 4;
• 4^4 = 216 => unit digit = 6;
You will note that if the exponent of 4 is odd, the unit digit is 4 and if the exponent is even, the unit digit is 6.
Thus, the unit digit if (44)^91 = 4.
3:
• 3^1 = 3 => unit digit = 3;
• 3^2 = 9 => unit digit = 9;
• 3^3 = 27 => unit digit = 7;
• 3^4 = 81 => unit digit = 1;
• 3^5 = 243 => unit digit = 3;
You will note that after every 4 consecutive exponents, the units digit of the exponent of 3 repeats. They are in order 3, 9, 7 and 1.
Let's find out the units digit of 3^37.
3^37 can be written as 3^(36 + 1) = 3^(4*9 + 1)
So, the units digit of 3^37 = the units digit of 3^1 = 3
Thus, the units digit of (44^91)*(73^37) = units digit of 4*3 = units digit of 12 = 2.
Correct answer: A
Hope this helps!
Jay
_________________
Manhattan Review GMAT Prep
Locations: Manhattan TOEFL  IELTS Practice Questions  GMAT Practice Test  ACT Info  and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 6362
 Joined: 25 Apr 2015
 Location: Los Angeles, CA
 Thanked: 43 times
 Followed by:26 members
Solution:BTGmoderatorDC wrote: ↑Tue Jul 14, 2020 7:30 pmThe units digit of (44^91)*(73^37) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
OA A
Let’s first determine the units digit of 44^91. Since we only care about units digits, we can rewrite the expression as:
4^91
Now we can evaluate the pattern of the units digits of 4^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 4. When writing out the pattern, notice that we are ONLY concerned with the units digit of 4 raised to each power.
4^1 = 4
4^2 = 6
4^3 = 4
The pattern of the units digit of powers of 4 repeats every 2 exponents. The pattern is 4–6. In this pattern, all positive exponents that are odd will produce 4 as its units digit, and all positive exponents that are even will produce 6 as its units digit. Since 91 is odd, the units digit of 4^91 (which is equal to the units digit of 44^91) is 4.
Next, let’s determine the units digit of 73^37 using a similar approach. Since we only care about units digits, we can rewrite the expression as:
3^37
Now we can evaluate the pattern of the units digits of 3^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 3. When writing out the pattern, notice that we are ONLY concerned with the units digit of 3 raised to each power.
3^1 = 3
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3
The pattern of the units digit of powers of 3 repeats every 4 exponents. The pattern is 3–9–7–1. In this pattern, all positive exponents that are multiples of 4 will produce 1 as its units digit. Thus:
3^26 has a units digit of 1, and so 3^37 has a units digit of 3.
Since the units digit of 44^91 is 4 and the units digit of 73^37 is 3, the units digit of (44^91)*(73^37) is equal to the units digit of 4 * 3 = 12, which is 2.
Answer: A
Scott WoodburyStewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews