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

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Re: If 0 < st < 1 then which of the following can be true? [#permalink]
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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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Re: If 0 < st < 1 then which of the following can be true? [#permalink]
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? [#permalink]
They must have the same signs in order to be positive: leaves B and C
B: both smaller than -1 results in a positive number larger than 1 -> eliminate
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Re: If 0 < st < 1 then which of the following can be true? [#permalink]
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Re: If 0 < st < 1 then which of the following can be true? [#permalink]
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