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If u > t, r > q, s > t, and t > r, which of the following

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If u > t, r > q, s > t, and t > r, which of the following [#permalink] New post 05 Feb 2012, 15:15
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A
B
C
D
E

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Question Stats:

87% (01:43) correct 12% (00:46) wrong based on 66 sessions
If u > t, r> q, s > t, and t > r, which of the following must be true?

I. u > s
II. s > q
III. u > r

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
[Reveal] Spoiler: OA

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Re: if u > t, r > q, s > t, and t > r, which of the following [#permalink] New post 05 Feb 2012, 15:31
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Expert's post
fiendex wrote:
If u > t, r > q, s > t, and t > r, which of the following must be true?

I. u > s
II. s > q
III. u > r

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III


Arrange so that you have a string: u>t, t>r, r>q and s>t (this one do not fit so far).

So we have that: u>t>r>q;

Next, as s>t, then s can be more as well as less than u, so the final ordering is either u>s>t>r>q or s>u>t>r>q

Hence, II and III are always true, but I may or may not be true.

Answer: E.

P.S. You can also use number line to mark the variables and visualize it.
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Re: if u > t, r > q, s > t, and t > r, which of the following [#permalink] New post 31 Oct 2012, 11:05
from the question we can establish
u - t > 0, r - q > 0, s - t > 0, and t - r > 0
(u - t) + (t -r ) >0 ==> u > r III holds
(r - q) +(t - r) > 0 ==> t > q Since s > t and t > q ==> s > q II holds
Brother Karamazov
Re: if u > t, r > q, s > t, and t > r, which of the following   [#permalink] 31 Oct 2012, 11:05
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