(p q)^(r s) is worked out

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue May 26, 2009 2:29 am

What will be the digit at the unit’s place, when (p q)^(r s) is worked out?

(1) p^2 + q^2 = 41 and r s = 4 t for some positive integer t.

(2) p q = 20.

MBM

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

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Source: Beat The GMAT — Data Sufficiency | Tue May 26, 2009 2:29 am

ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Tue May 26, 2009 3:51 am

imo : c
coz if i take only B then its (20)^(rs), now rs can be 0 or non zero. so the unit's place differs in both the cases.
but when we take both the statements then pq = 20 and rs is a positive integer so that means that unit's place would alwways be 0.

hence C.. please correct me if i am missing something.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: (p q)^(r s) is worked out

by Brent@GMATPrepNow » Tue May 26, 2009 6:30 am

sanju09 wrote:What will be the digit at the unit’s place, when (p q)^(r s) is worked out?

(1) p^2 + q^2 = 41 and r s = 4 t for some positive integer t.

(2) p q = 20.
MBM

Can we assume that p, q, r and s are all integers?
If so, then (1) is sufficient since p^2 + q^2 = 41 tells us that (p,q) is either (4,5), (-4,-5), (4,-5), (5,-4), (-5,-4) and so on.
This means that pq = 20 or -20

"r s = 4 t for some positive integer t" tells us that rs is positive.

So, 20 (or -20) to the power of a positive integer will have zero as its units digit.

The answer is A (if p,q,r and s are integers).

Brent Hanneson - Creator of GMATPrepNow.com

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue May 26, 2009 6:35 am

Same question here Brent! Can we assume?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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