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

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fiendex
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If u > t, r > q, s > t, and t > r, which of the following [#permalink] New post   05 Feb 2012, 16:15
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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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E
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Bunuel
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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, 16:31
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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.

Answer: E.

P.S. You can also use number line to mark the variables and visualize it.
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Ousmane
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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, 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
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dave13
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If u > t, r > q, s > t, and t > r, which of the following [#permalink] New post   23 Feb 2018, 11:33
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.

Answer: E.

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 :?
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Bunuel
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Re: If u > t, r > q, s > t, and t > r, which of the following [#permalink] New post   24 Feb 2018, 00:48
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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.

Answer: E.

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 \(s>u>t>r>q\)
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rishabhmishra
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Re: If u > t, r > q, s > t, and t > r, which of the following [#permalink] New post   26 Feb 2018, 22:22
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.
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volcanictempest78
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Re: If u > t, r > q, s > t, and t > r, which of the following [#permalink] New post   17 Jan 2022, 21:44
I used the number line approach..fit each variable in number line..leave space between each.....eg u>t...then see next equation with t or u and fit accordingly in the number line...
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Re: If u > t, r > q, s > t, and t > r, which of the following [#permalink] New post   27 Oct 2022, 04:10
Given that,
U>T
R>Q
S>T
T>R

Now, we can write the following:
T>R>Q

We do not know if U>S
But we can say II and III (option E).

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Re: If u > t, r > q, s > t, and t > r, which of the following [#permalink] New post   18 Dec 2023, 09:13
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Re: If u > t, r > q, s > t, and t > r, which of the following [#permalink]
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