GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
What is the units digit of (3^{50})(7^{52})?
[#permalink]
27 Nov 2021, 08:17
27 Nov 2021, 08:17
1
Bookmarks
00:00
Question Stats:
100% (00:26) correct
0% (00:00) wrong based on 2 sessions
Hide Show timer Statistics
What is the units digit of \((3^{50})(7^{52})\)?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Challenge: Can you solve the question in your head?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Challenge: Can you solve the question in your head?
Re: What is the units digit of (3^{50})(7^{52})?
[#permalink]
28 Nov 2021, 00:30
28 Nov 2021, 00:30
=(3*7)^50 * 7^2
=(21 ^50) *49
=1 in units * 49
Therefore 9 in units
=(21 ^50) *49
=1 in units * 49
Therefore 9 in units
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the units digit of (3^{50})(7^{52})?
[#permalink]
28 Nov 2021, 06:19
28 Nov 2021, 06:19
1
GreenlightTestPrep wrote:
What is the units digit of \((3^{50})(7^{52})\)?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Challenge: Can you solve the question in your head?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Challenge: Can you solve the question in your head?
Useful property: \((x^k)(y^k) = (xy)^k\)
First rewrite the given expression as follows: \((3^{50})(7^{52})=(3^{50})(7^{50})(7^{2})\)
Apply the property to get: \((3^{50})(7^{50})(7^{2}) = (3 \times 7)^{50}(7^{2}) \)
Evaluate: : \((3 \times 7)^{50}(7^{2})=(21)^{50}(7^{2}) \)
Since \(21^n\) has units digit \(1\) for ANY positive integer \(n\) we can write: \((21)^{50}(7^{2}) = (????1)(49) =\) ?????9
Answer: E
