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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: 63
If u > t, r > q, s > t, and t > r, which of the following  [#permalink]

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05 Feb 2012, 15:15
3
5
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:19) correct 11% (01:47) wrong based on 440 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

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Math Expert
Joined: 02 Sep 2009
Posts: 51121
Re: if u > t, r > q, s > t, and t > r, which of the following  [#permalink]

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05 Feb 2012, 15:31
2
1
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.
_________________
Intern
Joined: 11 Jul 2012
Posts: 40
Re: if u > t, r > q, s > t, and t > r, which of the following  [#permalink]

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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
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Joined: 09 Mar 2016
Posts: 1214
If u > t, r > q, s > t, and t > r, which of the following  [#permalink]

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23 Feb 2018, 10:33
Bunuel wrote:
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.

hello Bunuel i have a question

if $$u>s>t>r>q$$

let u = 5; s = 4 ; t = 3; r = 2; q =1

then why option 2 is not correct ? $$s > q$$ --> $$4>1$$ isnt it
Math Expert
Joined: 02 Sep 2009
Posts: 51121
Re: If u > t, r > q, s > t, and t > r, which of the following  [#permalink]

### Show Tags

23 Feb 2018, 23:48
1
dave13 wrote:
Bunuel wrote:
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.

hello Bunuel i have a question

if $$u>s>t>r>q$$

let u = 5; s = 4 ; t = 3; r = 2; q =1

then why option 2 is not correct ? $$s > q$$ --> $$4>1$$ isnt it

You did not read the solution you quote carefully.

The final ordering is either $$u>s>t>r>q$$ OR $$s>u>t>r>q$$
_________________
Manager
Joined: 23 Sep 2016
Posts: 217
Re: If u > t, r > q, s > t, and t > r, which of the following  [#permalink]

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26 Feb 2018, 21:22
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

put the question in single line and it will be easy for you from above statement we can say u,s>t>r>q accordingly 1st statement maybe true or may be not as we don't have any exact information about. So answer is E 2 and 3 statement is true.
Re: If u > t, r > q, s > t, and t > r, which of the following &nbs [#permalink] 26 Feb 2018, 21:22
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