What is the remainder when 3^32 is divided by 82?
A) 0
B) 1
C) 8
D) 9
E ) 81
Answer: B
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What is the remainder when 3^32 is divided by 82?
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Brent@GMATPrepNow
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Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
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Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
If we recognize that 82 is 1 greater than 81 (aka 3^4), then we might see that 82 is a divisor of 3^32 - 1Brent@GMATPrepNow wrote: ↑Sun Feb 23, 2020 8:51 amWhat is the remainder when 3^32 is divided by 82?
A) 0
B) 1
C) 8
D) 9
E ) 81
Answer: B
Source: www.gmatprepnow.com
Here's why:
3^32 - 1 = (3^16 + 1)(3^16 - 1)
= (3^16 + 1)(3^8 + 1)(3^8 - 1)
= (3^16} + 1)(3^8 + 1)(3^4 - 1)(3^4 + 1)
= (3^16 + 1)(3^8 + 1)(3^4 - 1)(82)
This tells us that (3^32 - 1) is a multiple of 82...
...and this means 3^32 is 1 greater than a multiple of 82, which means we'll get a remainder of 1 when we divide 3^32 by 82
Answer: B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
