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Which of the following equations has a graph that ca

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Math Revolution GMAT Instructor
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Which of the following equations has a graph that ca  [#permalink]

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New post 03 Jul 2018, 01:52
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

40% (01:31) correct 60% (00:57) wrong based on 43 sessions

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[GMAT math practice question]

Which of the following equations has a graph that can pass through only one coordinate (\(x,y\)) in which both \(x\) and \(y\) are integers?

\(A. y=2x\)
\(B. y=\sqrt{2}*x+1\)
\(C. y= \frac{1}{x^2} - 1\)
\(D. y=\frac{1}{x^3}\)
\(E. y=(\frac{-1}{x})+1\)

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Re: Which of the following equations has a graph that ca  [#permalink]

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New post 03 Jul 2018, 05:20
1
MathRevolution wrote:
[GMAT math practice question]

Which of the following equations has a graph that can pass through only one coordinate (\(x,y\)) in which both \(x\) and \(y\) are integers?

\(A. y=2x\)
\(B. y=\sqrt{2}*x+1\)
\(C. y= \frac{1}{x^2} - 1\)
\(D. y=\frac{1}{x^3}\)
\(E. y=(\frac{-1}{x})+1\)


If you look at the choices, all are with power of x, and these can take values of 1 and -1 and still give integer value for y....
but \(y=\sqrt{2}*x+1.......\).. y can be integer only when \(\sqrt{2}*x]\) is integer and it cannot be integer when x is integer except when x =0..
so our answer
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Which of the following equations has a graph that ca  [#permalink]

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New post 05 Jul 2018, 00:50
=>

A. \(x = 1, y = 2\) and \(x = 2, y = 4\) lie on this graph.
B. Since \(√2\) is irrational, the only point on this graph with integer coordinates is \(x = 0, y = 1\).
C. \(x = 1, y = 0\) and \(x = -1, y = 0\) lie on this graph.
D. \(x = 1, y = 1\) and \(x = -1, y = -1\) lie on this graph.
E. \(x = 1, y = 0\) and \(x = -1, y = 2\) lie on this graph.


Therefore, the answer is B.
Answer: B
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Re: Which of the following equations has a graph that ca &nbs [#permalink] 05 Jul 2018, 00:50
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