If 0

Question

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

Bunuel · Accepted Answer

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.

SD007 · Answer

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

Bunuel · Answer

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reto · Answer

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

King407 · Answer

0 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

OptimusPrepJanielle · Answer

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

Celestial09 · Answer

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

D3N0 · Answer

Ans: D Solution: given to us 01 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

KS15 · Answer

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

23a2012 · Answer

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

akhilbajaj · Answer

This was kind of intuitive for me. For all x such that 01 For all y>1, 0<1/y<1 Answer D.

ranaazad · Answer

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

Abhishek009 · Answer

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

bumpbot · Answer

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

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

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