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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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.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|
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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k^2 = m^2.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|
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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Solution: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|
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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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!
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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Hi All,
We're told that K^2 = M^2. We're asked which of the following MUST be true. This essentially means "which of the following is ALWAYS true no matter how many different examples we can come up with?" These types of questions often require a bit more 'thoroughness' than normal - so you might have to do a bit more work than you initially think you will have to.
When dealing with squared terms, you should be prepared to look for multiple answers (for example X^2 = 4 has TWO solutions: +2 and -2). Here, we have a squared term equal to ANOTHER squared term, so there will be FOUR possible outcomes. Here's how you can use TEST IT to quickly 'map' those options out:
K=3, M=3
K=3, M= -3
K= -3, M=3
K= -3, M= -3
Thus, we could have two positives, two negatives or one of each. Using these 4 options, you can quickly run through the answer choices and eliminate any answer that does NOT account for all 4 options. For example, Answer A can be eliminated because K=3, M=-3 is not a solution to that equation. You'll find that only one answer covers all 4 options...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
We're told that K^2 = M^2. We're asked which of the following MUST be true. This essentially means "which of the following is ALWAYS true no matter how many different examples we can come up with?" These types of questions often require a bit more 'thoroughness' than normal - so you might have to do a bit more work than you initially think you will have to.
When dealing with squared terms, you should be prepared to look for multiple answers (for example X^2 = 4 has TWO solutions: +2 and -2). Here, we have a squared term equal to ANOTHER squared term, so there will be FOUR possible outcomes. Here's how you can use TEST IT to quickly 'map' those options out:
K=3, M=3
K=3, M= -3
K= -3, M=3
K= -3, M= -3
Thus, we could have two positives, two negatives or one of each. Using these 4 options, you can quickly run through the answer choices and eliminate any answer that does NOT account for all 4 options. For example, Answer A can be eliminated because K=3, M=-3 is not a solution to that equation. You'll find that only one answer covers all 4 options...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich