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Joined: 07 Jul 2018
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Re: Square Root = Always Positive?
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 14 Jan 2019, 05:40
Bunuel wrote: MartinSC wrote: I was counting on that, but what about this one:
If (x-1)^2=400, which of the following could be the value of ?
(A) 15
(B) 14
(C) –24
(D) –25
(E) –26
I thought "16" applying the "always positive" mantra, but the explanation goes as follows:
"Work the problem by taking the square root of both sides and solving for x.
Thus,
(x-1)^2=400
x-1= +/-20 (wait, I was not expecting to see the negative root!!)
So x= -19 or x=21 and
x-5=-24 or x-5=16" (which is not even an option).
Seeing that 16 was not among the choices, I could have picked (C)-24, which would have been correct, but it goes against the theory of the positive root...so I was left scratching my head.
Anyone has an idea?
Thks! When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is: \(\sqrt{9} = 3\), NOT +3 or -3; \(\sqrt[4]{16} = 2\), NOT +2 or -2; Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).\(p^2 = (q+1)^2\) Now according to you, this should give 2 solutions. But If I square root this, then it should give only 1 solution. I don't get it, it confuses me even more, what is the answer to this equation? The official answer says it has only 1 solution, Now how is that? What would this give?
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Math Expert
Joined: 02 Sep 2009
Posts: 53771
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Re: Square Root = Always Positive?
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14 Jan 2019, 05:51
Akshit03 wrote: Bunuel wrote: MartinSC wrote: I was counting on that, but what about this one:
If (x-1)^2=400, which of the following could be the value of ?
(A) 15
(B) 14
(C) –24
(D) –25
(E) –26
I thought "16" applying the "always positive" mantra, but the explanation goes as follows:
"Work the problem by taking the square root of both sides and solving for x.
Thus,
(x-1)^2=400
x-1= +/-20 (wait, I was not expecting to see the negative root!!)
So x= -19 or x=21 and
x-5=-24 or x-5=16" (which is not even an option).
Seeing that 16 was not among the choices, I could have picked (C)-24, which would have been correct, but it goes against the theory of the positive root...so I was left scratching my head.
Anyone has an idea?
Thks! When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is: \(\sqrt{9} = 3\), NOT +3 or -3; \(\sqrt[4]{16} = 2\), NOT +2 or -2; Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).\(p^2 = (q+1)^2\) Now according to you, this should give 2 solutions. But If I square root this, then it should give only 1 solution. I don't get it, it confuses me even more, what is the answer to this equation? The official answer says it has only 1 solution, Now how is that? What would this give? I think you messed up something there... If it's \(p^2 = (q+1)^2\), then this equation with TWO unknowns p and q will have infinitely many solutions. If it'st \(p^2=(p+1)^2\), then: \(p^2= p^2+2p+1\); \(p=-\frac{1}{2}\).
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
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Re: Square Root = Always Positive?
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14 Jan 2019, 10:03
BunuelI'm sorry for not mentioning that I'm not looking for absolute value. This was a DS question I was stuck on due to this concept that I still cannot understand. I only need to know whether p would be (q+1) OR 2 values{(q+1),-(q+1)} Now taking this into consideration and what I said previously, Can you correct my logic/approach/concept? I have spent 1 hour on this only.
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Math Expert
Joined: 02 Sep 2009
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Re: Square Root = Always Positive?
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14 Jan 2019, 10:20
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Re: Square Root = Always Positive?
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14 Jan 2019, 10:42
Bunuel wrote: Akshit03 wrote: BunuelI'm sorry for not mentioning that I'm not looking for absolute value. This was a DS question I was stuck on due to this concept that I still cannot understand. I only need to know whether p would be (q+1) OR 2 values{(q+1),-(q+1)} Now taking this into consideration and what I said previously, Can you correct my logic/approach/concept? I have spent 1 hour on this only. \(x^2 = positive \ number\) ALWAYS has TWO solutions: \(x = \sqrt{positive \ number}\) and \(x = -\sqrt{positive \ number}\). For example, x^2 = 9 --> \(x = \sqrt{9}=3\) or \(x = -\sqrt{9}=-3\). \(p^2=(q+1)^2\) means that \(|p|=|q+1|\), so p=q+1 or p=-(q+1) P.S. What DS question are you talking about? Q: If p and q are positive integers, is the greatest common factor of p and q greater than 1? 1: \(p^2 = pq + p\) 2: \(p^2 = q^2 + 2q + 1\) So you mean to say, if GMAT gives you square root, we take only positive. But when it gives square like \(x^2 = 9\) , we take both values?
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Re: Square Root = Always Positive?
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14 Jan 2019, 11:10
Akshit03 wrote: Bunuel wrote: Akshit03 wrote: BunuelI'm sorry for not mentioning that I'm not looking for absolute value. This was a DS question I was stuck on due to this concept that I still cannot understand. I only need to know whether p would be (q+1) OR 2 values{(q+1),-(q+1)} Now taking this into consideration and what I said previously, Can you correct my logic/approach/concept? I have spent 1 hour on this only. \(x^2 = positive \ number\) ALWAYS has TWO solutions: \(x = \sqrt{positive \ number}\) and \(x = -\sqrt{positive \ number}\). For example, x^2 = 9 --> \(x = \sqrt{9}=3\) or \(x = -\sqrt{9}=-3\). \(p^2=(q+1)^2\) means that \(|p|=|q+1|\), so p=q+1 or p=-(q+1) P.S. What DS question are you talking about? Q: If p and q are positive integers, is the greatest common factor of p and q greater than 1? 1: \(p^2 = pq + p\) 2: \(p^2 = q^2 + 2q + 1\) So you mean to say, if GMAT gives you square root, we take only positive. But when it gives square like \(x^2 = 9\) , we take both values? Notice that in the question we are told that p and q are POSITIVE. So, here from \(p^2=(q+1)^2\) it follows that \(p=q+1\) only. Finally, to answer your question, check the discussion on page 1. For example, this one: https://gmatclub.com/forum/square-root- ... l#p1437877When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is: \(\sqrt{9} = 3\), NOT +3 or -3; \(\sqrt[4]{16} = 2\), NOT +2 or -2; Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).
_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
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Re: Square Root = Always Positive?
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14 Jan 2019, 11:10
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