Question

The numbers represented by variables w and y on the number line are integers.

If w < x < y, under which of the following conditions could the expression x > 2 be true? Select TWO that apply.
A
when y = 6 and w = 2
B
when y = 4 and w = –1
C
when y = 2 and w = 0
D
when y = 0 and w = –2
E
when y = –1 and w = –4

Answer 1

Option A) when y=6 and w= 2, Option B) when y=4 and w=-1 are the TWO correct choices.

Explanation:

The given inequality is w<x<y and x>2.

step 1: let us assume that x=3, since it is given that x>2.

step 2: substitute the value of x=3 and each options in the inequality

step 3: option A) w=2, y=6. Then w<x<y = 2<3<6 (the condition satisfies).

option B) w= -1, y=4. Then w<x<y = -1<3<4 (the condition satisfies).

option C) w= 0, y=2. then w<x<y ≠ 0<2<2 (does not satisfies).

option D) w= -2, y=0. then w<x<y ≠ -2<2<0 (does not satisfies).

option E) w= -4, y= -1. then w<x<y ≠ -4<2<-1 (does not satisfies).