Which of the following equations has only one integer pair as solution

Question

Which of the following equations has only one integer pair as solution?

A.  y = 2x

B.  y = \frac{x}{2}

C.  y =\sqrt{5}*x

D.  y=x+1

E.  y=\frac{1}{x}

Source: Math Revolution

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler

gautamK0206 · Answer

By looking all the options and taking cases:
A. y= 2x, is valid for all the integer values for x
B. y = x/2, is valid for all the even integer values for x
C. y = √5*x, is valid integer value of y for x having a √5 as a multiple, therefore (0,0) is the only integral solution possible here.
D. y = x + 1, is valid for all the integer values for x
E. y = 1/x, is a valid integral pair for x = 1 or -1
Therefore, the correct answer is  C. y = √5*x

dhart · Answer

So may be we can ve 0,0 as a solution to C

dhart · Answer

So may be we can ve 0,0 as a solution to C

counterclash1 · Answer

Correct Answer: C

TESTING OPTIONS FOR INTEGER PAIRS (x, y):

- Option A: y = 2x
 x = 0 => y = 0
 x = 1 => y = 2
 Infinite integer pairs.

- Option B: y = x / 2
 x = 0 => y = 0
 x = 2 => y = 1
 Infinite integer pairs.

- Option C: y =  \sqrt{5} * x 
 x = 0 => y = 0 -> Pair (0,0)  
 For any x != 0, y is irrational (not an integer).
 EXACTLY 1 integer pair solution: (0,0).

- Option D: y = x + 1
 x = 0 => y = 1
 x = 1 => y = 2
 Infinite integer pairs.

- Option E: y = 1 / x
 x = 1 => y = 1 -> Pair (1,1)
 x = -1 => y = -1 -> Pair (-1,-1)
 EXACTLY 2 integer pair solutions.

Conclusion: Answer Choice C.

Which of the following equations has only one integer pair as solution

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following equations has only one integer pair as solution

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards