Find the ones digit of 73^350

Question

A) 3
B) 5
C) 6
D) 7
E) 9

My answer was A, but it turned out incorrect. Can someone help understand why.

SOURH7WK · Accepted Answer

Cyclicity of 3 is 3,9,7,1 & after 4 multiplication again the cycle repeats. 
So divide 350 by 4 and we get 87 as quotient and 2 as remainder. So cycle will run for 87 times and then 2 times more. So pick up the 2nd item from the cycle.

Hence Answer E.

Bunuel · Answer

The GMAT wording would be: What is the units digit of 73^350? The units digit of 73^350 will be the same as the units digit of 3^350. 3^1=3 --> the units digit is 3; 3^2=9 --> the units digit is 9; 3^3=27 --> the units digit is 7; 3^4=81 --> the units digit is 1; 3^5=243 --> the units digit is 3 AGAIN; ... So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 350=348+ 2 =(multiple of 4)+2, then the units digit of 3^350 will be the second number in the pattern thus 9. Answer: E. For more please check Number Theory chapter of Math Book: math-number-theory-88376.html Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html (Please pay attention to the rule #3).

Bunuel · Answer

Bumping for review and further discussion.

For more on this kind of questions check  Units digits, exponents, remainders problems collection .

rohitrawat9990 · Answer

3,9,7,1 repeats after every four times

therefore 350/4 = 87 + 2 remainder

9 is the ones digit

so E is coorect

Sent from my iPhone using  GMAT Club Forum mobile app

sashiim20 · Answer

To find unit digit of  73^{350}  , we need to find unit digit of  3^{350}

Power of  3  has cyclicity of  4   (3,9,7,1) .  \frac{350}{4}  gives remainder of  2 .

Therefore new power will be  3^2 . And Unit digit of  3^2 = 9

Therefore Unit digit of  73^{350} = 9

Answer (E)...

pushkarajnjadhav · Answer

The unit digit of 73^350 is same as that of 3^350.
Power of 3 has cyclicity of 4. That means set of 4 values repeats {3,9,7,1}.
3^1=3 (3)
3^2=9 (9)
3^3=27 (7)
3^4=81 (1)
3^5=243 (3)
and cycle continues.

Hence 3^350= 3^348 * 3^2
 =3^2
 =9.

Hence Option E.

Kudos if it helps.

JeffTargetTestPrep · Answer

Since we only care about units digits, we really are determining the units digit of 3^350.

Let’s evaluate the units digit 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 a power.
 
3^1 = 3 
 
3^2 = 9 
 
3^3 = 7 
 
3^4 = 1 
 
3^5 = 3
 
The pattern of the units digits 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 a 1 as the units digit. Thus:
 
3^348 has a units digit of 1 and 3^349 has a units digit of 3, and thus 3^350 has a units digit of 9.

Answer: E

js17 · Answer

3,9,7,1 will keep repeating

So, 350/4 = 87 + 2 remainder

9 is the ones digit

Ans->E

v12345 · Answer

For unit digit, let see only 3^350 last digit.
Unit digit 3^1 = 3
Unit digit 3^2 = 9
Unit digit 3^3 = 7
Unit digit 3^4 = 1
And then it repeats, i.e after four intervals.

350 = 87*4 + 2
For 3^350, unit digit = 9 (as 2 is left after dividing by 4)

Hence, OA is (E).

MathRevolution · Answer

73^{350} = 3^ {350}

=>  3^ {4 * 87} * 3^ {2}

=> unit digit =  3^{2} = 9

Answer E

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=RSWx-abm2QA

We need to find the units digit of  73^{350}

Units digit of  73^{350}  will be same as units digit of  3^{350}

Lets start by finding the cyclicity of units' digit in powers of 3

3^1  units’ digit is 3
 3^2  units’ digit is 9 
 3^3  units’ digit is 7 
 3^4  units’ digit is 1
 3^5  units’ digit is 3

That means that units digit of power of 3 has a cycle of 4

=> We need to divide the power (350) by 4 and check what is the remainder
350 divided by 4 gives 2 remainder

=> Units digit of  73^{350}  = Units digit of  3^2  = 9

So,  Answer will be E 
Hope it helps!

Watch this video to    MASTER how to find Units digit of Power of 3

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Find the ones digit of 73^350

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Find the ones digit of 73^350

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards