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Which of the following equations has a graph that can pass t

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by Max@Math Revolution » Tue Jul 03, 2018 12:43 am
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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=√2*x+1
C. y= 1/x^2 - 1
D. y=1/x^3
E. y=(-1/x)+1
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Which of the following equations has a graph that can pass t

by Shahrukh_mbabreakspace » Tue Jul 03, 2018 1:09 am
In option B, When Sqrt 2 is multiplied with x, and x is a non-zero integer then sqrt2*x will be an irrational number and even after adding 1 to it, it remains irrational.
So, it can never be equal to an integer unless x will be 0. So, it has only only both integer solution
Last edited by Shahrukh_mbabreakspace on Tue Jul 03, 2018 3:41 am, edited 1 time in total.
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by GMATGuruNY » Tue Jul 03, 2018 3:10 am
Max@Math Revolution 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=√2*x+1
C. y= 1/x^2 - 1
D. y=1/x^3
E. y=(-1/x)+1
Eliminate the four answer choices with MORE THAN ONE coordinate pair (x, y ) such that x and y are integers.
If x=1, integer values for y are yielded by A, C, D and E.
If x=-1, integer values for y are yielded by A, C, D and E.
Since each of these options has more than one coordinate pair (x, y ) such that x and y are integers, eliminate A, C, D and E,

The correct answer is B.

In B, only x=0 will yield an integer value for y.
Thus, B has only one coordinate pair (x, y) such that x and y are integers.
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by Max@Math Revolution » Wed Jul 04, 2018 11:35 pm
=>

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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