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Intern  Joined: 06 Oct 2010
Posts: 25
What is the units digit of 13^4*17^2*29^3?  [#permalink]

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Difficulty:   15% (low)

Question Stats: 75% (00:55) correct 25% (01:03) wrong based on 286 sessions

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What is the units digit of $$13^4*17^2*29^3$$?

(A) 9
(B) 7
(C) 5
(D) 3
(E) 1

Originally posted by niheil on 17 Oct 2010, 12:50.
Last edited by stonecold on 24 Jan 2017, 12:43, edited 2 times in total.
Edited.
Manager  Joined: 03 Sep 2010
Posts: 61
Location: Israel
GMAT 1: 660 Q47 V34 GMAT 2: 670 Q48 V34 GPA: 3.2
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Re: What is the units digit of 13^4*17^2*29^3?  [#permalink]

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4
1
I think that the fastest and more important, the safest way to solve this is:
First brake the problem to three multiplication problems:
1. 13*13*13*13
2. 17*17
3. 29*29*29
In all of the problems we don't have to multiply by the whole number, but only by the last digit (because that is what we are asked about).
Second, simply multiply: 13*13*13*13. It is actually 3*3*3*3 (we are interested in the last digit). Thus - 3*3=9, 9*3=7(the last digit), 7*3=1 (the last digit).
17*17 is actually 7*7 = 9 (the last digit).
29*29*29 is actually -9*9*9- that can be interpreted into 9*9=1 (the last digit) and 1*9=9.
So eventually we will have- 9 (29^3) * 9 (17^2) * 1 (13^4). Therefore - 9*9=1(the last digit), 1*1=1

So the correct answer is E -1.
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GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: What is the units digit of 13^4*17^2*29^3?  [#permalink]

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2
General rule :

To find the unit's digit- find the remainder when divided by 10.

to find the last two digits - find the remainder when divided by 100.

....and so on.

For advance theory of remainders check the Math book of gmat Club.
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Re: What is the units digit of 13^4*17^2*29^3?  [#permalink]

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1
just need unit digit of every component and multipy them

3^1=3
3^2=9
3^3=7
3^4=1, it is first digit

7^2=9, it is second digit

9^3=9, it is third digit

1*9*9=1

E
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Re: What is the units digit of 13^4*17^2*29^3?  [#permalink]

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niheil wrote:
What is the units digit of 13^4*17^2*29^3?

(A) 9
(B) 7
(C) 5
(D) 3
(E) 1

Units digit of $$13^4$$ will be 1
Units digit of $$17^2$$ will be 9
Units digit of $$29^3$$will be 9

So, Units digit of $$13^4*17^2*29^3$$ will be 1 * 9 * 9 => 1

Answer will be option (E) 1 _________________
Thanks and Regards

Abhishek....

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Intern  B
Joined: 07 Oct 2018
Posts: 2
Re: What is the units digit of 13^4*17^2*29^3?  [#permalink]

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Here's how you do this in under 1:30:

Step 1: Rephrase the question to --- (3^4) * (7^2) * (9^3)
Step 2: Apply unit digit power rules (ANEI = A number ending in) = (ANEI 1) * (ANEI 9) * (ANEI 9)
Step 3: Multiply the ends of numbers (i.e. units digits) = 1*9*9 = 81 = units digit of 1.
e-GMAT Representative V
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Posts: 3074
Re: What is the units digit of 13^4*17^2*29^3?  [#permalink]

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Solution

Approach and Working:

The units digit of $$13^4∗17^2∗29^3$$ will be same as the units digit of $$3^4 * 7^2* 9^3$$.
• Units digit of $$3^4 * 7^2* 9^3$$= Units digit of ($$3^4$$)* Units digit of ($$7^2$$) * Units digit of ($$9^3$$)
• = 1* 9*9= 1
Hence, the correct answer is option E.

_________________ Re: What is the units digit of 13^4*17^2*29^3?   [#permalink] 14 Oct 2018, 17:12
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