unit digit problem

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rkiran9: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Mon Nov 05, 2012 2:11 am

by rkiran9 » Tue Dec 18, 2012 2:27 am

If n=(33)^43 + (43)^33 wat is the unit digit??

The approach which i followed was lyk i multiplied 33*33=1089,43*43 =...9

9+9=18,unit digit 8 but its wrong:(:(

is there any other easy approach??????

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Source: Beat The GMAT — Problem Solving | Tue Dec 18, 2012 2:27 am

aman88: Master | Next Rank: 500 Posts; Posts: 142; Joined: Sat Oct 20, 2012 3:31 amFollowed by: 3 members; Location: New Delhi; Thanked: 20 times

by aman88 » Tue Dec 18, 2012 3:24 am

IMO 0

Please me know the OA.
Thanks.

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Anindya Madhudor: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Mon Nov 12, 2012 11:12 amFollowed by: 2 members; Thanked: 8 times

by Anindya Madhudor » Tue Dec 18, 2012 7:45 am

You need to find the pattern in the exponential.

When the last digit of any number is 3, you have the pattern 3, 9, 7, 1 for powers of 1, 2 ,3,4. This pattern repeats. So, it will be same for powers of 5, 6, 7, 9.

You divide the power by 4 and find the remainder.

43 divided by 4 leaves 3 as remainder. So, the unit digit will be 7.
33 divided by 4 leaves 1 as remainder. So, the unit digit will be 3.

Add the two units digit. Units digit of of n is 0.

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GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Sat Dec 22, 2012 2:45 pm

Anindya is correct, you want to look for patterns in the units digits.

I just wanted to mention one more thing... whenever you see something like 33^43, which would be impossible to compute in 10 minutes, let alone 2 minutes, don't do any computation! Ask yourself - what is the shortcut here? There must be one. The GMAT never intends for you to do long multiplication or long division, so try to think about the concepts rather than computing.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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