How many integers x satisfy both 2<x 4 and 0 x 3 ?

1 We intersect the two ranges by taking the tighter lower and upper bounds that x must satisfy simultaneously. 2 < x 4 0 x 3 Combined: 2 < x 3 We list the integers in the combined range and count them. 2 < x 3 x is an integer x = 3 Count = 1

GMAT Number Properties: Integers x satisfy both 2<x 4 and 0

Question

How many integers x satisfy both 2 < x \leq 4 and 0 \leq x \leq 3 ?

Options:

A. $5$
B. $4$
C. $3$
D. $2$
E. $1$

inequalitiesnumber theorycounting evenly spaced integers

Steps

Explanation	Calculations	Help
$We intersect the two ranges by taking the tighter lower and upper bounds that x must satisfy simultaneously.$	$2 < x \leq 4 0 \leq x \leq 3 Combined: 2 < x \leq 3$
$We list the integers in the combined range and count them.$	$2 < x \leq 3 x is an integer x = 3 Count = 1$

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Final Answer

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