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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
(x - 5)² > (1 - x)²
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15 Jun 2022, 07:21
15 Jun 2022, 07:21
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Question Stats:
61% (01:05) correct
38% (01:15) wrong based on 21 sessions
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(x - 5)² > (1 - x)²
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
x |
3 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: (x - 5)² > (1 - x)²
[#permalink]
16 Jun 2022, 08:40
16 Jun 2022, 08:40
3
GreenlightTestPrep wrote:
(x - 5)² > (1 - x)²
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
x |
3 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Note: I created this question to see if anyone falls for the trap of taking the square root of both sides to get: x - 5 > 1 - x
If you fall for this trap, you will incorrectly conclude that x > 3, when, in actuality, we should get x < 3
Here's an example of why we should avoid taking the square root of both sides:
If k is a negative value, and we square it, and then take the square root, we get a positive value.
For example, if x = -5, then x² = (-5)² = 25, which means √x = √25 = 5, which is not the same value we started with.
Here's how we should tackle the question....
Given: (x - 5)² > (1 - x)²
Expand and simplify both sides to get: x² - 10x + 25 > 1 - 2x + x²
Subtract x² from both sides: -10x + 25 > 1 - 2x
Add 10x to both sides: 25 > 1 + 8x
Subtract 1 from both sides: 24 > 8x
Divide both sides by 8 to get: 3 > x
If x is less than 3, the correct answer is B
