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

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Manager
Joined: 01 Dec 2011
Posts: 67

Kudos [?]: 52 [1], given: 12

If u > t, r > q, s > t, and t > r, which of the following [#permalink]

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05 Feb 2012, 16:15
1
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1
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Difficulty:

5% (low)

Question Stats:

89% (00:54) correct 11% (01:15) wrong based on 333 sessions

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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

_________________

http://en.wikipedia.org/wiki/Kudos

Kudos [?]: 52 [1], given: 12

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132507 [1], given: 12323

Re: if u > t, r > q, s > t, and t > r, which of the following [#permalink]

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05 Feb 2012, 16:31
1
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Expert's post
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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.

P.S. You can also use number line to mark the variables and visualize it.
_________________

Kudos [?]: 132507 [1], given: 12323

Intern
Joined: 11 Jul 2012
Posts: 42

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

Re: if u > t, r > q, s > t, and t > r, which of the following [#permalink]

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31 Oct 2012, 12:05
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

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

Non-Human User
Joined: 09 Sep 2013
Posts: 15703

Kudos [?]: 281 [0], given: 0

Re: If u > t, r > q, s > t, and t > r, which of the following [#permalink]

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26 Dec 2015, 01:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Kudos [?]: 281 [0], given: 0

Re: If u > t, r > q, s > t, and t > r, which of the following   [#permalink] 26 Dec 2015, 01:14
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