What is the units digit of (71) 5(46) 3(103) 4 + (57)(1088) 3 ?

Question

What is the units digit of  (71)^{5}*(46)^{3}*(103)^{4} + (57)*(1088)^{3}  ?

A. 0
B. 1
C. 2
D. 3
E. 4

DesiGmat · Accepted Answer

Here we go....

Thumb Rule - Always pick the digit at the Unit place for such questions...

let's go step by step

(71)^5 ------> 1^5 ----- always result in a number that has 1 at it's unit place ---------- (1)

(46)^3 -------> 6^3 ------ like 1, 6 always result in a number that has 6 at it's unit place ---------- (2)

Check yourself 6*6 = 36*6 => 216*6 => 1296 and so on

(103)^4 -------> 3^4

Here is the pattern in case of 3 that should be considered

3 = 3
3*3 = 9 (3^2)
3*3*3 = 2(7) (3^3)
3*3*3*3 = 8(1) (3^4)
3*3*3*3*3 = last digit 3

so pattern order in case of number 3 is 4

back to our number in the question ---> (103)^4 => 3^4 => last digit would be 1 ---------------- (3)

From equations 1, 2, and 3

1*6*1 would result in 6

so from (71)^5∗(46)^3∗(103)^4 results in a number that has a last digit of 6 ------------------(a)

Apply the above principle to (57)∗(1088)^3

8 = 8
8*8 = 6(4)
8*8*8 = last digit would be (2)

the last digit of the product of (57)∗(1088)^3 ===> 7*2 => 14 => 4 (we are interested in the unit place) ----------(b)

Combine a and b

6 + 4 would result in 0 at the unit place....

Hence option A is correct

Consider Kudos for the post if it helped.

T700ISB · Answer

Could somebody explain,Please?

Shiv2016 · Answer

The question is asking for the unit's digit. So we will just consider the unit's digit of all the numbers because the unit's digit of a operation depends on the last digit only.
For example, 22*24 will end in 8 (2*4).

The other rule is to remember the cyclicity of nos. 
Cyclicity of 2= 4 (that means when 2 is squared, cubed, and so on the last digit start repeating after four i.e. 2,4,8.6)
Cyclicity of 3= 4 (3,9,7,1 - only the unit's digit)
Cyclicity of 4= 2 (4,6)
Cyclicity of 5= 1 (5)
Cyclicity of 6= 1 (6)
Cyclicity of 7= 4 (7,9,3,1)
Cyclicity of 8= 4 (8,4,2,6)
Cyclicity of 9= 2 (9,1)

Just write the unit's digit:
1*6*3^4 + 7*8^3
First let's determine 3^4 and 8^3
3^4 will end in 1 and 8^3 will end in 2

=6+4 (4 because 7*2=1 4 )
=10
The unit's digit is 0.

ScottTargetTestPrep · Answer

We need to determine the units digit of (71)^5 x (46)^3 x (103)^4 + (57) x (1088)^3. Since we only care about the units digits, we can rewrite the expression as:

What is the units digit of (1)^5 x (6)^3 x (3)^4 + (7) x (8)^3 ?

Since 1 raised to any power always has a units digit of 1, 1^5 will have a units digit of 1.

Since 6 raised to any power always has a units digit of 6, 6^3 will have a units digit of 6.

Since (3)^4 = 81, 3^4 has a units digit of 1.

7, of course, has a units digit of 7.

Since 8^3 = 512, 8^3 has a units digit of 2.

Let’s now plug all of this information into the expression:

1 x 6 x 1 + 7 x 2 = 6 + 14 = 20

Thus, the units digit is 0.

Answer: A

krishnav89 · Answer

(71)^{5}*(46)^{3}*(103)^{4} + (57)*(1088)^{3}

1 * 6 *1 + 7 * 2

6 + 4

0

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the units digit of (71) 5(46) 3(103) 4 + (57)(1088) 3 ?

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

What is the units digit of (71) 5(46) 3(103) 4 + (57)(1088) 3 ?

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