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If x/y < 1, then which of the following must be true?
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Updated on: 06 Jul 2017, 09:02
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If \(\frac{x}{y} < 1\), then which of the following must be true? (I) \(\frac{x+1}{y+1}< 1\) (II)\(\frac{x^2+1}{y^2+1} < 1\) (III)\(\frac{x1}{y1} < 1\) A. I only B. II only C. III only D. I & II only E. II & III only
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Originally posted by aazt on 25 Jun 2017, 12:57.
Last edited by Bunuel on 06 Jul 2017, 09:02, edited 3 times in total.
Edited the question.




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Re: If x/y < 1, then which of the following must be true?
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25 Jun 2017, 14:13
I presume you meant \(\frac{x}{y} < 1\) So, either x and y could be both positive or both negative, x is negative, y positive or x is positive and y, negative.However it is clear that the magnitude of y will definitely be greater than x(it will be farther away from the origin) If x=1,y=3, the expression \(\frac{x+1}{y+1}\) has value 1, which is not lesser than 1. While evaluating condition II, x^2 and y^2 will both become positive and added to 1, will have a ratio similar to that of \(\frac{x}{y}\). If x=1,y=3, the expression \(\frac{x1}{y1}\) has value 1, which is not lesser than 1. Hence Option B(II only) is the only choice, for which the condition holds true.
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Re: If x/y < 1, then which of the following must be true?
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25 Jun 2017, 18:56
Thanks! Sorry, the gmatclub formatting makes it look weird. The question was actually x/y \(< 1\). I presume this changes things? aazt pushpitkc wrote: I presume you meant \(\frac{x}{y} < 1\) So, either x and y could be both positive or both negative, x is negative, y positive or x is positive and y, negative. However it is clear that the magnitude of y will definitely be greater than x(it will be farther away from the origin)
If x=1,y=3, the expression \(\frac{x+1}{y+1}\) has value 1, which is not lesser than 1. While evaluating condition II, x^2 and y^2 will both become positive and added to 1, will have a ratio similar to that of \(\frac{x}{y}\). If x=1,y=3, the expression \(\frac{x1}{y1}\) has value 1, which is not lesser than 1.
Hence Option B(II only) is the only choice, for which the condition holds true.



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Re: If x/y < 1, then which of the following must be true?
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07 Jul 2017, 19:13
If \(\frac{x}{y} < 1\), then which of the following must be true?
(I) \(\frac{x+1}{y+1}< 1\)
(II)\(\frac{x^2+1}{y^2+1} < 1\)
(III)\(\frac{x1}{y1} < 1\)
A. I only B. II only C. III only D. I & II only E. II & III only
Let's plug in numbers and work strategically
(1/2), (1,2), (1,2), (1, 2)...We need to consider all possibilities that satisfy the \(\frac{x}{y} < 1\)
Start with I, let's examine either (1/2) or (1, 2) (because by eyes, other pairs make fraction less than one: 0 < 1)
(1, 2): \(\frac{1+1}{2+1}< 1\).........\(\frac{2}{1}< 1\)..........Eliminate A & D
Let's check III as there is possibility to eliminate E and get II as only solution. let's examine either (1/2) or (1, 2) (because by eyes, other pairs make fraction less than one: 0 < 1)
(1/2): \(\frac{11}{21}< 1\).........\(\frac{2}{1}< 1\)..........Eliminate C & E
No need to check as we have only one answer left.
Answer: B



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Re: If x/y < 1, then which of the following must be true?
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13 Jul 2017, 10:18
Hi, Please help me understand.
Why can't we take x, y = 0 ??



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Re: If x/y < 1, then which of the following must be true?
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13 Jul 2017, 10:25
Prashant420 wrote: Hi, Please help me understand.
Why can't we take x, y = 0 ?? You can take x =0 and y anything except 0 because 0/0 is undefined value. You CAN NOt take x = any number and y =0 because Number/0 is undefined value. Please visit the below link for more info from Khan academy. https://www.khanacademy.org/math/algebr ... eterminate



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Re: If x/y < 1, then which of the following must be true?
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27 Aug 2018, 06:04
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Re: If x/y < 1, then which of the following must be true?
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