If x = m − 1, which of the following is true when m = 1/2?

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

by Gmat_mission » Fri May 25, 2018 12:52 am

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If x = m − 1, which of the following is true when m = 1/2?

(A) x^0 > x^2 > x^3 > x^1
(B) x^0 > x^2 > x^1 > x^3
(C) x^0 > x^1 > x^2 > x^3
(D) x^2 > x^0 > x^3 > x^1
(E) x^3 > x^2 > x^1 > x^0

[spoiler]OA=A[/spoiler].

Could someone explain to me how can I order these numbers? Please. Thanks in advance.

Source: Beat The GMAT — Problem Solving | Fri May 25, 2018 12:52 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri May 25, 2018 6:01 am

Gmat_mission wrote:If x = m − 1, which of the following is true when m = 1/2?

(A) x^0 > x^2 > x^3 > x^1
(B) x^0 > x^2 > x^1 > x^3
(C) x^0 > x^1 > x^2 > x^3
(D) x^2 > x^0 > x^3 > x^1
(E) x^3 > x^2 > x^1 > x^0

Given: x = m - 1
So, if m = 1/2, then x = 1/2 - 1 = -1/2
Or we can say that x = -0.5

So, x^0 = (-0.5)^0 = 1
x^1 = (-0.5)^1 = -0.5
x^2 = (-0.5)^2 = 0.25
x^3 = (-0.5)^3 = -0.125

The biggest value (1) is for x^0
The next biggest value (0.25) is for x^2
The next value (-0.125) is for x^3
The smallest value (-0.5) is for x^1

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Scott@TargetTestPrep » Tue May 29, 2018 8:34 am

Gmat_mission wrote:If x = m − 1, which of the following is true when m = 1/2?

(A) x^0 > x^2 > x^3 > x^1
(B) x^0 > x^2 > x^1 > x^3
(C) x^0 > x^1 > x^2 > x^3
(D) x^2 > x^0 > x^3 > x^1
(E) x^3 > x^2 > x^1 > x^0

Substituting m = 1/2 in x = 1 - m, x = 1/2 - 1 = -1/2. We see that x^0 = 1, x^1 = -1/2, x^2 = 1/4 and x^3 = -1/8. Ordering these fractions, we see that x^0 > x^2 > x^3 > x^1. So the answer is A.

Answer: A

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