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If p,q,r, and s are nonzero numbers, is (p – 1)(q - 2)

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Senior Manager
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If p,q,r, and s are nonzero numbers, is (p – 1)(q - 2) [#permalink] New post 11 Aug 2009, 11:45
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

63% (01:37) correct 38% (00:29) wrong based on 6 sessions
This is a DS 1000 series question(section 5 problem 22)
I couldn't understand the symbol ≧ and assumed as not equal to

If p,q,r, and s are nonzero numbers, is
(p – 1)(q - 2)2(r – 3)3(s – 4)4 ≧ 0?
(1) q > 2 and s > 4
(2) p > 1 and r > 3
[Reveal] Spoiler:
OA is B - I think it should be C


What does this ≧ represent?
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Re: ≧ [#permalink] New post 11 Aug 2009, 12:23
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≧ means greater than or equal to.
(p – 1)(q - 2)2(r – 3)3(s – 4)4 ≧ 0
For the above expression to be true, we must know the if (p-1), (r-3) are greater than or equal to zero
as (q-2)^2, (s-4)^4 will always be ≧ 0
from option 2, p>1, r>3
so (p-1)(r-3)^3 ≧0
So option 2 alone is sufficient and answer is B
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Re: ≧ [#permalink] New post 12 Aug 2009, 08:15
If p,q,r, and s are nonzero numbers, is
(p – 1)(q - 2)2(r – 3)3(s – 4)4 ≧ 0?
(1) q > 2 and s > 4
(2) p > 1 and r > 3


With the question worded like above the correct OA would be C. However as Aleehsgonji correctly deduced the numbers outside the brackets are exponents.
Since a number with an even exponent will always be positive we only care about p and r

OA - B
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Re: ≧ [#permalink] New post 12 Aug 2009, 08:20
When you post your question....please use the 'm' to correctly format.

I read the question as

If p,q,r, and s are nonzero numbers, is
(p – 1)(q - 2) * 2(r – 3) * 3(s – 4) *4 ≧ 0? (Multiplication)
in whcih case the OA must be C.

But if the question is with exponents

(p-1)(q-2)^2(r-3)^3(s-4)^4 ≧ 0?

, then the OA is B.
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Re: ≧ [#permalink] New post 12 Aug 2009, 11:12
If p,q,r, and s are nonzero numbers, is
(p – 1)(q - 2)^2(r – 3)^3(s – 4)^4 ≧ 0?
(1) q > 2 and s > 4
(2) p > 1 and r > 3

the question is asking whether (r-3), (p-1) have the same sign or any of the brackits = 0

from 1

no info about r,p however (q-2),(s-4) not = 0...insuff

from 2
both (p-1),(r-3) are +ve thus suff

B
Re: ≧   [#permalink] 12 Aug 2009, 11:12
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