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If 0 < x < 1 < y, which of the following must be true?

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Bunuel
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If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  14 May 2015, 04:55
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If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1

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Bunuel
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  18 May 2015, 07:17
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Bunuel wrote:
If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1

Kudos for a correct solution.


OFFICIAL SOLUTION:

Since 0 < x < 1, then 0 < 1 < 1/x (dividing by x) and since 0 < 1 < y, then 0 < 1/y < 1 (dividing by y).

So, we have that 0 < 1/y < 1 < 1/x.

Answer: D.
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  14 May 2015, 05:14
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Bunuel wrote:
If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1

Kudos for a correct solution.


Should be D IMHO.

1/x is a fraction between 0 and 1 its reciprocal will be the greatest
then value of Y can be an integer or a fraction with a numerator > denominator hence 1/Y = D>N hence between 0 and 1

Cheers !
S
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  14 May 2015, 05:28
Expert Reply
karthickhari wrote:
is OA D???


The OA will be automatically revealed on Sunday 17th of May 2015 04:55:59 AM Pacific Time Zone
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  14 May 2015, 06:33
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Bunuel wrote:
If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1

Kudos for a correct solution.


Variables in the answer choices? PLUG IN. Chose easy numbers like x = 0.5 and y = 2 which fits the condition of the question steam.
Now plug in the values in the Answer choices and POE like that:

A. 1 < 1/x < 1/y > eliminate because 1/x > 1/y
B. 1/x < 1 < 1/y > eliminate because 1/x > 1/y and > 1
C. 1/x < 1/y < 1 > eliminate because 1/x > 1/y
D. 1/y < 1 < 1/x That's the one!
E. 1/y < 1/x < 1 > eliminate because 1/x > 1

D. 1/2 < 1 < 1/(1/2)

D is the answer
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  14 May 2015, 10:01
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Bunuel wrote:
If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1

Kudos for a correct solution.



0<x<1<y. Let x=1/2 and y =2

Substituting values:

A. 1<2<1/2 --- Wrong
B. 2<1< 1/2 --- Wrong
C. 2<1/2<1 --- Wrong
D. 1/2<1<2 --- Correct
E. 1/2<2<1 --- Wrong

Hence answer is D

Mathematically, If y is a positive number greater than one, its reciprocal(1 over that no.) will always be smaller than 1 => 1 > 1/y (e.g. 2>1 but 1/2<1)
Also, If x is a positive fraction less than one, its reciprocal will always be greater than 1 => 1/x > 1 (e.g. 1/2 < 1 but 1/(1/2) = 2 > 1)

Only D satisfies both these conditions. Hence answer is D
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  14 May 2015, 10:27
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You can quickly solve this by choosing values for x and y. x can be 1/2 and y can be 2.
D is the only option that fits.
1/y < 1 < 1/x

1/2 < 1 < 1/ (1/2) or
1/2 < 1 < 2
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  14 May 2015, 12:41
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Hi,
IMO is should be D.
just checked... x has to be in decimals..hence 1/x is greater than 1 and same time greater than Y.

the only option was D.
please evaluate my approach...
thanks
celestial


kudos if its a correct solution
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  14 May 2015, 20:30
Bunuel wrote:
If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1


Ans: D

Solution: given to us 0<x<1 and option contains form of 1/x, which always will be >1
y>1 and option contain form of 1/y, which always will be <1
and comparison point here is 1.
now from this information we can say that for must be true; 1/y < 1 < 1/x
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  15 May 2015, 09:56
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Bunuel wrote:
If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1

Kudos for a correct solution.


Put x=1/2 and y=2

A. 1<2<1/2. False
B. 2<1<1/2 False
C. 2<1/2<1 False
D. 1/2<1<2. True
E. 1/2<2<1 False
Answer D
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  15 May 2015, 17:11
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the answer is D

when we put x=1/2 and y=2 the only option that match is the option D
1/2<1<2
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  16 May 2015, 00:51
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This was kind of intuitive for me.

For all x such that 0<x<1, 1/x>1
For all y>1, 0<1/y<1

Answer D.
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  25 Apr 2016, 01:01
Bunuel wrote:
If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1

Kudos for a correct solution.



We can multiply options by xy. D gives x < xy < y, which must be true according to the question stem. :)
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Re: If 0 < x < 1 < y, which of the following must be true? [#permalink] New post  25 Apr 2016, 01:36
ranaazad wrote:
Bunuel wrote:
If 0 < x < 1 < y, which of the following must be true?

A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1

Kudos for a correct solution.



We can multiply options by xy. D gives x < xy < y, which must be true according to the question stem. :)


You can solve GMAT questions using various approach , however for the sake of simplicity and reaching the answer in minimum time , IMHO King407 's approach is the best , just by plugging in some values of x and y you can solve the problem in less than 1 minute...

Abhishek
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