M7MBA wrote: ↑

Fri Dec 11, 2020 2:48 am

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Which of the following equations is sufficient to determine which of the five distinct integers represented on the number line above is closest to zero, given that the distance between every two adjacent integers is not shown to scale?

A. \(b + d = 2c\)

B. \(d = -a\)

C. \(c < -e\)

D. \(b = -d\)

E. \(a + b = -d - e\)

Answer: D

Solution:

We need to establish a relationship such that one of the integers is positive and one is negative; in this way, we can have an interval that includes 0 in it. Choices B and D are the most promising ones, as in both choices one of the integers is positive and the other one is negative. However, we can easily eliminate answer choice B as there are two integers between a and d (which are b and c). Since the number line is not drawn to scale, it is impossible for us to determine which one of b or c is closer to 0. . Thus, let’s analyze answer choice D in greater detail.

Since b = -d, we see that d must be positive and b must be its opposite. So b and d are both equidistant from 0. However, since c is somewhere between b and d, so c is even closer to 0 than either b or d (despite the distance between two adjacent integers is not drawn to scale). Therefore, c is the closest to 0 when we know b = -d.

Answer: D