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# If 0 < st < 1 then which of the following can be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 51035
If 0 < st < 1 then which of the following can be true?  [#permalink]

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17 May 2018, 04:01
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Difficulty:

45% (medium)

Question Stats:

64% (01:38) correct 36% (01:48) wrong based on 131 sessions

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If $$0 < st < 1$$, then which of the following can be true?

(A) s < -1 and t > 0

(B) s < -1 and t < — 1

(C) s > - 1 and t < - 1

(D) s > 1 and t < —1

(E) s > 1 and t > 1

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Joined: 11 Sep 2015
Posts: 3222
Re: If 0 < st < 1 then which of the following can be true?  [#permalink]

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17 May 2018, 07:08
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Top Contributor
Bunuel wrote:
If $$0 < st < 1$$, then which of the following can be true?

(A) s < -1 and t > 0

(B) s < -1 and t < -1

(C) s > - 1 and t < -1

(D) s > 1 and t < -1

(E) s > 1 and t > 1

(A) s < -1 and t > 0
This tells us that s is NEGATIVE and t is POSITIVE, which means the product st must be NEGATIVE
We're told that 0 < st < 1, which means st is POSITIVE

(B) s < -1 and t < -1
This tells us that s is NEGATIVE and t is NEGATIVE , which means the product st must be POSITIVE
We're told that 0 < st < 1, which means st is POSITIVE (so far good!)
However, if s < -1 and t < -1, the product st will be GREATER THAN 1, and we're told that st is LESS THAN 1

(C) s > - 1 and t < -1
So, it COULD be the case that s = -0.5 and t = -1.2, in which case st = (-0.5)(-1.2) = 0.6
Perfect! [since it is true that 0 < 0.6 < 1]

Cheers,
Brent
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Joined: 28 Jul 2016
Posts: 134
Re: If 0 < st < 1 then which of the following can be true?  [#permalink]

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07 Jul 2018, 10:16
1
1
If 0<st<10<st<1, then which of the following can be true?

(A) s < -1 and t > 0 --- s*t = negative, so eliminate
(B) s < -1 and t < — 1 --- st > 1, so eliminate
(C) s > - 1 and t < - 1 , looks good, s = -0,2; t = -2, so s*t = +0,4
(D) s > 1 and t < —1 --- s*t = negative, so eliminate
(E) s > 1 and t > 1 --- st > 1, so eliminate
Director
Joined: 14 Dec 2017
Posts: 519
Location: India
Re: If 0 < st < 1 then which of the following can be true?  [#permalink]

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07 Jul 2018, 10:50
Bunuel wrote:
If $$0 < st < 1$$, then which of the following can be true?

(A) s < -1 and t > 0

(B) s < -1 and t < — 1

(C) s > - 1 and t < - 1

(D) s > 1 and t < —1

(E) s > 1 and t > 1

Given 0 < st < 1,

we have s*t > 0, so s & t both have the same sign

s*t < 1, so either s or t or both are between 0 & 1 or both are between -1 & 0

(A) s < -1 and t > 0 gives opposite signs to s & t, hence not possible. s = -2 , t = 1 , s*t = - 2 < 0

(B) s < -1 and t < — 1 both are less than -1, hence not possible. s = -2, t = -1.5, s*t = 3 > 1

(C) s > - 1 and t < - 1 both can be of same sign & s can be more than -1 but less than 0. Possible. s = -0.5, t = - 1.2, s*t = 0.6 < 1

(D) s > 1 and t < —1 gives opposite signs to s & t, hence not possible. s = 2, t = -2, s*t = -4 < 0

(E) s > 1 and t > 1 both are more than 1, hence not possible. s = 1.2, t = 1.2, s*t = 1.44 > 1

Thanks,
GyM
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Joined: 02 Aug 2009
Posts: 7095
Re: If 0 < st < 1 then which of the following can be true?  [#permalink]

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07 Jul 2018, 11:05
Bunuel wrote:
If $$0 < st < 1$$, then which of the following can be true?

(A) s < -1 and t > 0

(B) s < -1 and t < — 1

(C) s > - 1 and t < - 1

(D) s > 1 and t < —1

(E) s > 1 and t > 1

TIP
0<st<1..... So atleast one of s or t should be a fraction between -1 and 1..
Both have to be of same sign to give it's product as positive..
Remember it is CAN be true

Eliminate A as s is negative and t is positive, so st<0

In remaining , only C gives s>-1, so possibility of it to be a fraction
S can be -1/4 and t can be -2, st=1/2

C
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Re: If 0 < st < 1 then which of the following can be true? &nbs [#permalink] 07 Jul 2018, 11:05
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