If x is an integer where 2 --x 3- 2, how many values of x are possible?a)0b)1c)2d)A finite number greater than 2e)An infinite number of values are possibleCorrect answer is option 'E'. Can you explain this answer?

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GMAT Exam > GMAT Questions > If x is an integer where 2 -|x – 3| ...

If x is an integer where 2 -|x – 3| < 2, how many values of x are possible?

a)
0
b)
1
c)
2
d)
A finite number greater than 2
e)
An infinite number of values are possible

Correct answer is option 'E'. Can you explain this answer?

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Verified Answer

If x is an integer where 2 -|x – 3| < 2, how many values of ...

Step 1: Question statement and Inferences

Given the inequality and that x is an integer, x may have a limited number of possibilities:

2 - |x - 3| < 2

Step 2 & 3: Simplifying the fraction and calculating the final answer

Find out by simplifying the inequality. Start by subtracting 2 from both sides:

- |x - 3| < 0

Multiply both sides by –1 so the absolute value expression becomes positive, which also switches the inequality:

|x - 3| > 0

Any value of x other than 3 results in a number inside the absolute value bars, the absolute value of which is greater than zero. x can be any number other than 3, so the number of values is infinite.

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If x is an integer where 2 -|x – 3| < 2, how many values of x are possible?a)0b)1c)2d)A finite number greater than 2e)An infinite number of values are possibleCorrect answer is option 'E'. Can you explain this answer?

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