Which of the following points is closest to line $y=x?$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Wed Sep 23, 2020 5:43 am

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Which of the following points is closest to line $y=x?$

A. $(2, -1)$
B. $(2, 4)$
C. $(-1, 1)$
D. $(2, 1)$
E. $(-2, 0)$

Answer: D

Source: GMAT Club Tests

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Source: Beat The GMAT — Problem Solving | Wed Sep 23, 2020 5:43 am

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Re: Which of the following points is closest to line $y=x?$

by Scott@TargetTestPrep » Mon Sep 28, 2020 12:31 pm

Gmat_mission wrote: ↑
Wed Sep 23, 2020 5:43 am
Which of the following points is closest to line $y=x?$

A. $(2, -1)$
B. $(2, 4)$
C. $(-1, 1)$
D. $(2, 1)$
E. $(-2, 0)$

Answer: D

Source: GMAT Club Tests

Solution:

The best way to solve this problem is to draw the graph:

Clearly, we see that (2, 1) is closest to the line y = x.

Alternate Solution:

Every ordered pair (x, y) on the line y = x has the difference |y - x| as 0. For example, the ordered pair (6, 6) is on the line y = x, and the difference |y - x| = |6 - 6| = 0.

For the given ordered pairs, the point with the smallest difference of |y - x| will be closest to the line y = x. We see that the point (2, 1) has a difference of |1 - 2| = |-1| = 1, and all the other ordered pairs have differences whose absolute values are greater than 1.

Answer: D

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