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Which is greater x^2+x+2/x or 2y^2+y+1/y
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02 Apr 2019, 09:40
02 Apr 2019, 09:40
Expert Reply
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Question Stats:
73% (01:02) correct
26% (01:01) wrong based on 63 sessions
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\(x = \frac{1}{y}\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\frac{x^2+x+2}{x}\) |
\(\frac{2y^2+y+1}{y}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: Which is greater x^2+x+2/x or 2y^2+y+1/y
[#permalink]
03 Apr 2019, 02:43
03 Apr 2019, 02:43
2
Expert Reply
First, let me break up each quantity:
Quantity A:
\(\frac{x^{2}}{x}+\frac{x}{x}+\frac{2}{x} = x+ 1 + \frac{2}{x}\)
Quantity B:
\(\frac{2y^{2}}{y}+\frac{y}{y}+\frac{1}{y} = 2y+1+ \frac{1}{y}\)
Okay, now let's plug \(\frac{1}{y}\) in for x in quantity A:
\(\frac{1}{y}+ 1 + \frac{2}{\frac{1}{y}} = \frac{1}{y} + 1 + 2y\)
And that's the same as quantity B. So both quantities are equal.
Quantity A:
\(\frac{x^{2}}{x}+\frac{x}{x}+\frac{2}{x} = x+ 1 + \frac{2}{x}\)
Quantity B:
\(\frac{2y^{2}}{y}+\frac{y}{y}+\frac{1}{y} = 2y+1+ \frac{1}{y}\)
Okay, now let's plug \(\frac{1}{y}\) in for x in quantity A:
\(\frac{1}{y}+ 1 + \frac{2}{\frac{1}{y}} = \frac{1}{y} + 1 + 2y\)
And that's the same as quantity B. So both quantities are equal.
gmatclubot
Re: Which is greater x^2+x+2/x or 2y^2+y+1/y [#permalink]
03 Apr 2019, 02:43
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