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# is m, p, and t are positive integers and m (1) t-p=p-m (2)

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Manager
Joined: 27 Jul 2003
Posts: 124
Location: Singapore
Followers: 1

Kudos [?]: 10 [0], given: 0

is m, p, and t are positive integers and m (1) t-p=p-m (2) [#permalink]  05 Oct 2003, 22:47
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0% (00:00) correct 0% (00:00) wrong based on 0 sessions
is m, p, and t are positive integers and m
(1) t-p=p-m
(2) t-m=16

if ab=a, what is the value of (axb) (ayb)?
(1) ax=by=2
(2) 2xy=4
Intern
Joined: 13 Sep 2003
Posts: 43
Location: US
Followers: 0

Kudos [?]: 7 [0], given: 0

How did you get C for the second one?please explain.
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

Since ab = a b = 1
from condition 1 by = 2 so y = 2
from condition 2 2xy = 4 so x = 1
going back to condition 1 ax = by = 2 since x = 1 a = 2
we know a,b,x and y
Director
Joined: 14 Oct 2003
Posts: 589
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 8 [0], given: 0

I agree with C and anandak's explanation.
Senior Manager
Joined: 05 May 2003
Posts: 427
Location: Aus
Followers: 2

Kudos [?]: 5 [0], given: 0

I was not questioning his explanation. I didn't understand it at the first sight. Now, I see b = 1 from the given the problem. So, the answer should be C.
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
Followers: 1

Kudos [?]: 0 [0], given: 0

Friends, I would agree with the answer but a little different opinion on the explanation.
Given,

ab = a => ab - a = 0 => a(b-1) = 0

=> a = 0 & b <> 1
OR
a = 0 & b = 1
OR
a <> 0 & b = 1

(Here <> stands for "not equal to")

What do we need to find? (axb) (ayb)

Since ab = a, this can be simplified to (ax) (ay) = (a^2)xy = ?

Statement 1:

ax=by=2 => Since ax = 2, a can NOT be 0. So the only possibility is the third one above (in bold). That is b = 1 => y = 2. This does not help us find the value of (a^2)xy.

Statement 2:

2xy = 4 => xy = 2 => This information along with the possible values of a and b above (in bold) will not help us find the value of (a^2)xy

TOGETHER

ax = 2
by = 2
xy = 2
=> (2/a) (2/b) = 2 => 4/ab = 2 => ab = 2 => a = 2 (because ab = a is given)

So we have value of a and xy hence,we can find out (a^2)xy
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