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OG16 - PS17

This topic has 3 expert replies and 1 member reply
amina.shaikh309 Senior | Next Rank: 100 Posts Default Avatar
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OG16 - PS17

Post Sun May 08, 2016 7:54 am
If k^2 = m^2, which of the following must be true?
A. k = m
B. k = -m
C. k = |m|
D. k = - |m|
E. |k| = |m|

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Post Wed May 11, 2016 11:58 pm
We could also do

k² - m² = 0

(k - m) * (k + m) = 0

If the first case is true, k = m.

If the second case is true, k = -m.

Only E covers both cases, so that's our answer!

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Post Mon May 09, 2016 10:39 am
amina.shaikh309 wrote:
If k^2 = m^2, which of the following must be true?
A. k = m
B. k = -m
C. k = |m|
D. k = - |m|
E. |k| = |m|
Solution:

We are given that k^2 = m^2, and we can start by simplifying the equation by taking the square root of both sides.

√k^2 = √m^2

When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:

√k^2 = √m^2 is |k| = |m|

Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.

Answer:E

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OptimusPrep Master | Next Rank: 500 Posts
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Post Sun May 08, 2016 9:28 pm
amina.shaikh309 wrote:
If k^2 = m^2, which of the following must be true?
A. k = m
B. k = -m
C. k = |m|
D. k = - |m|
E. |k| = |m|
k^2 = m^2.
Taking the square root on both sides,

Since square root of a number is always positive,

√x^2 = |x|
This means |k| = |m|

Correct Option: E

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Post Sun May 08, 2016 8:13 am
amina.shaikh309 wrote:
If k² = m², which of the following must be true?
A. k = m
B. k = -m
C. k = |m|
D. k = - |m|
E. |k| = |m|
The question asks us what MUST be true. So, if we can find a case where a statement is not true, we can eliminate that answer choice.

So, for example, one solution to the equation (k² = m²) is k = 1 and m = 1
Now let's check the answer choices.
A. k = m. Test: 1 = 1. Works. Keep A.
B. k = -m. Test: 1 = -1. DOESN'T WORK. ELIMINATE B.
C. k = |m|. Test: 1 = |1|. Works. Keep C.
D. k = - |m|. Test: 1 = -|1|. DOESN'T WORK. ELIMINATE D.
E. |k| = |m|. Test: |1| = |1|. Works. Keep E.

Okay, so the correct answer is A, C or E

Let's try another case. Another solution to the equation (k² = m²) is k = -1 and m = 1
Now let's check the remaining answer choices.
A. k = m. Test: -1 = 1. DOESN'T WORK. ELIMINATE A.
C. k = |m|. Test: -1 = |1|. DOESN'T WORK. ELIMINATE C.
E. |k| = |m|. Test: |-1| = |1|. Works. Keep E.

By the process of elimination, the correct answer is E

Cheers,
Brent

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