SAT Mathematics Practice Test 2

Question : 41 of 58

Marks: +1, -0

A project manager estimates that a project will take

x

hours to complete, where

x > 100

. The goal is for the estimate to be within 10 hours of the time it will actually take to complete the project. If the manager meets the goal and it takes y hours to complete the project, which of the following inequalitiesrepresents the relationship between the estimated time and the actual completion time?

$x+y < 10$
y > x+10
$y < x-10$
$-10 < y-x < 10$

Validate

Solution:

The difference between the number of hours the project takes, y, and the number of hours the project was estimated to take, x, is

|y−x|

. If the goal is met, the difference is less than 10, which can be represented as

|y−x| < 10

−10 < y−x < 10.

Choice A is incorrect. This inequality states that the estimated number of hours plus the actual number of hours is less than 10, which cannot be true because the estimate is greater than 100. Choice B is incorrect. This inequality states that the actual number of hours is greater than the estimated number of hours plus 10, which could be true only if the goal of being within 10 hours of the estimate were not met. Choice C is incorrect. This inequality states that the actual number of hours is less than the estimated number of hours minus 10, which could be true only if the goal of being within 10 hours of the estimate were not met.

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