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14 Jun 2013, 05:48
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The tip on Page 14 of GMAT Club Math Book, highlighted in bold, states:
"Even roots have only a positive value on GMAT".
Where did the above statement originate?
Solving Question 191 in GMAT Review 13th Edition requires:
\(x - 1 = \sqrt{400}\)
\(x = -19\)
The two sources appear to contradict each other. If I look closer, GMAT Club Math Book also gives conditions such as,
"When the GMAT provides the square root sign..."
In Q.191, the sign is added while solving the problem, so is exempt from the tip. I tentatively suggest that printing conditional tips introduces a risk rather than remove one.
"Even roots have only a positive value on GMAT".
Where did the above statement originate?
Solving Question 191 in GMAT Review 13th Edition requires:
\(x - 1 = \sqrt{400}\)
\(x = -19\)
The two sources appear to contradict each other. If I look closer, GMAT Club Math Book also gives conditions such as,
"When the GMAT provides the square root sign..."
In Q.191, the sign is added while solving the problem, so is exempt from the tip. I tentatively suggest that printing conditional tips introduces a risk rather than remove one.
arpanpatnaik
GMAT 1: 640 Q42 V37
Posts: 101
14 Jun 2013, 06:57
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The question actually states:
If \((x-1)^2 = 400\), what is the value of \((x-5)\)?
Now I understand the general idea is to take a square root of both sides, but that action isn't the right way to proceed. The approach should be:
\((x-1)^2 = 400\)
=> \((x-1)^2 - 20^2 = 0\)
=> \((x-1-20)(x-1+20) = 0\)
=> \((x+19)(x-21) = 0\)
Hence the value of x can be -19 or 21. Now, using the same x-5 can be -24 and 16. Out of the two only -24 is under the answer choices. Hence the answer is [C]. GMAT always considers the positive value of a square root i.e\(\sqrt{x^2} = |x|\) always. Please refer to the below threads if you have further queries:
https://gmatclub.com/forum/confusion-on-square-roots-127807.html
https://gmatclub.com/forum/a-square-root-has-only-one-value-134601.html
Hope the above explanation helps!
Regards,
A
If \((x-1)^2 = 400\), what is the value of \((x-5)\)?
Now I understand the general idea is to take a square root of both sides, but that action isn't the right way to proceed. The approach should be:
\((x-1)^2 = 400\)
=> \((x-1)^2 - 20^2 = 0\)
=> \((x-1-20)(x-1+20) = 0\)
=> \((x+19)(x-21) = 0\)
Hence the value of x can be -19 or 21. Now, using the same x-5 can be -24 and 16. Out of the two only -24 is under the answer choices. Hence the answer is [C]. GMAT always considers the positive value of a square root i.e\(\sqrt{x^2} = |x|\) always. Please refer to the below threads if you have further queries:
https://gmatclub.com/forum/confusion-on-square-roots-127807.html
https://gmatclub.com/forum/a-square-root-has-only-one-value-134601.html
Hope the above explanation helps!
Regards,
A
14 Jun 2013, 12:00
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Bookmarks
Thank you. I retract the word "requires" in my opening post.
How can you define which is the right way to proceed?
I always thought maths is maths: as long as it's done without error, there is no right or wrong approach. Using \(\sqrt{400} +1 = -19 or +21\) to derive the answer is the quickest and most direct approach (imho). I find that using roots is less prone to error because there are fewer steps and less to write down - but I doubt everyone is wired the same.
GMAT does not test approaches, only answers.
It seems to me the \(\sqrt{25} = +5\) is a house rule when writing questions, and I'm fine with any rules until those rules change without notice.
How can you define which is the right way to proceed?
I always thought maths is maths: as long as it's done without error, there is no right or wrong approach. Using \(\sqrt{400} +1 = -19 or +21\) to derive the answer is the quickest and most direct approach (imho). I find that using roots is less prone to error because there are fewer steps and less to write down - but I doubt everyone is wired the same.
GMAT does not test approaches, only answers.
It seems to me the \(\sqrt{25} = +5\) is a house rule when writing questions, and I'm fine with any rules until those rules change without notice.
