Digits, power

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ru2008: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Tue Aug 26, 2008 9:42 am

Digits, power

by ru2008 » Tue Aug 31, 2010 7:11 am

If (243)x(463)y = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

Please explain the answer

Source: Manhattan Gmat

OA is A

Last edited by ru2008 on Tue Aug 31, 2010 7:50 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Tue Aug 31, 2010 7:11 am

kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 am; Location: London; Thanked: 70 times; Followed by:3 members

by kmittal82 » Tue Aug 31, 2010 7:38 am

Assuming here the question means multiplication, we know that
.....9 * xy = n (9 will be the units digit when 243 is multiplied with 463)

(1)

Not enough, since x = 6 y = 1 will result in a unit digit of 4 (...9 x 6), and x = 4 y = 3 will result in a units digit of 8 (...9 x 12)

(2)

Not enough

x = 4 reduces the question further to ....6*y = n
Depending on y, n could take any units digit.

Combining (1) and (2), we know that x = 4, y = 3
Question reduces to ...9 x 12, so n will have a units digit of 8.

(C) should be the answer. OA please?

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 am; Thanked: 32 times; Followed by:3 members

by Gurpinder » Tue Aug 31, 2010 8:53 am

Not sure about OA or whether I am wrong but IMO (C).

243*463 = units digit = 9.

so 9*xy=n

(1) x+y=7

there are so many combination's of x+y that can give you 7. and if we take each of those values and multiply it with 9, we get different answers.

Insufficient.

(2) x=4

so 9*y*4

then we have 6*y

Now y could be anything. therefore, this one is also insufficient.

Together:

4+y=7

x=4
y=3

9*4*3

8 is the units digit.

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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uwhusky: Legendary Member; Posts: 1172; Joined: Wed Apr 28, 2010 6:20 pm; Thanked: 74 times; Followed by:4 members

by uwhusky » Tue Aug 31, 2010 8:58 am

The question is copied incorrectly.

https://www.beatthegmat.com/exponent-pro ... 24675.html

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 am; Thanked: 32 times; Followed by:3 members

by Gurpinder » Tue Aug 31, 2010 8:59 am

uwhusky wrote:The question is copied incorrectly.

https://www.beatthegmat.com/exponent-pro ... 24675.html

No wonder!

Thanks!

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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beatthegmatinsept: Master | Next Rank: 500 Posts; Posts: 422; Joined: Mon Aug 09, 2010 11:47 am; Thanked: 22 times; Followed by:1 members; GMAT Score:680

by beatthegmatinsept » Tue Aug 31, 2010 9:08 am

Gurpinder wrote:
uwhusky wrote:The question is copied incorrectly.

https://www.beatthegmat.com/exponent-pro ... 24675.html
No wonder!

Thanks!

That explains.. BTW, I got C too for the 'modified' question posted above.

Being defeated is often only a temporary condition. Giving up is what makes it permanent.

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uwhusky: Legendary Member; Posts: 1172; Joined: Wed Apr 28, 2010 6:20 pm; Thanked: 74 times; Followed by:4 members

by uwhusky » Tue Aug 31, 2010 9:14 am

You can simply pretend they have the same base, since we are only concerned with the unit digit.

So even though it's 243^x * 463^y, you can simplify it down to 3^x * 3^y. We know that when two exponents have the same base multiplying, we simply add them together: 3^(x+y).

Answer is A.

Hope I am clear on this one.

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 am; Thanked: 32 times; Followed by:3 members

by Gurpinder » Tue Aug 31, 2010 9:18 am

uwhusky wrote:You can simply pretend they have the same base, since we are only concerned with the unit digit.

So even though it's 243^x * 463^y, you can simplify it down to 3^x * 3^y. We know that when two exponents have the same base multiplying, we simply add them together: 3^(x+y).

Answer is A.

Hope I am clear on this one.

Yes you are,

I was about the write the same thing.

Since we are ONLY dealing with units digits we simply need to be worried about the units digit.

so the question becomes 3^x * 3^y as you pointed out. And modifying this > 3^7

So stmt 1 is sufficient.

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.