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What is the value of x? (1) |x| = 4. (2) x^2 = 16.

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What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 11 May 2017, 11:56
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What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?

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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 11 May 2017, 12:10
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4
ashikaverma13 wrote:
What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?


What is the value of x?

(1) |x| = 4 --> x = 4 or x = -4. Not sufficient.

(2) x^2 = 16 --> the same here: x = 4 or x = -4. Not sufficient.

(1)+(2) Same two values from both: x = 4 or x = -4. Not sufficient.

Answer: E.

As for your question: when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{16}=4\), NOT +4 or -4. Even roots have only a positive value on the GMAT.

In contrast, the equation \(x^2=16\) has TWO solutions, +4 and -4.

Hope it's clear.
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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

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What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 11 May 2017, 14:12
Bunuel wrote:
ashikaverma13 wrote:
What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?


What is the value of x?

(1) |x| = 4 --> x = 4 or x = -4. Not sufficient.

(2) x^2 = 16 --> the same here: x = 4 or x = -4. Not sufficient.

(1)+(2) Same two values from both: x = 4 or x = -4. Not sufficient.

Answer: E.

As for your question: when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{16}=4\), NOT +4 or -4. Even roots have only a positive value on the GMAT.

In contrast, the equation \(x^2=16\) has TWO solutions, +4 and -4.

Hope it's clear.


I think I understood but one more thing. So if, the statement B had said x = \(\sqrt{16}\) then it would have been sufficient?

but what is the difference if I, on my own am taking a square root of the statement B. That is my confusion. If I take square root of the entire statement B then won't it be:

\(\sqrt{x^2}\) = \(\sqrt{16}\) which, therefore, will lead to x =4?

unless I am doing something wrong by taking square root of the entire statement.
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 11 May 2017, 21:44
ashikaverma13 wrote:
Bunuel wrote:
ashikaverma13 wrote:
What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?


What is the value of x?

(1) |x| = 4 --> x = 4 or x = -4. Not sufficient.

(2) x^2 = 16 --> the same here: x = 4 or x = -4. Not sufficient.

(1)+(2) Same two values from both: x = 4 or x = -4. Not sufficient.

Answer: E.

As for your question: when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{16}=4\), NOT +4 or -4. Even roots have only a positive value on the GMAT.

In contrast, the equation \(x^2=16\) has TWO solutions, +4 and -4.

Hope it's clear.


I think I understood but one more thing. So if, the statement B had said x = \(\sqrt{16}\) then it would have been sufficient?

but what is the difference if I, on my own am taking a square root of the statement B. That is my confusion. If I take square root of the entire statement B then won't it be:

\(\sqrt{x^2}\) = \(\sqrt{16}\) which, therefore, will lead to x =4?

unless I am doing something wrong by taking square root of the entire statement.



1. \(\sqrt{16}\)=4
The square root of a negative number is not a real number and is not tested on the GMAT.

2. x^2 = 16
=> x = 4 or -4
In this case , we have an exponent . If we square the number 4 , we get 16 . If we square the number - 4 , we get 16 .
Therefore, both numbers are possible values for x, because both make the equation true.

3. \(\sqrt{x^2}\) = \(\sqrt{16}\)

Now squaring both sides, we get
x^2 = 16
the above is same as case 2 , thus x can have 2 values -> 4 and - 4
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 25 Dec 2017, 21:51
ashikaverma13 wrote:
What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?

1. Value of X can be +4 or -4
2. Value of X can be +4 or -4 as 4^2=16 and (-4)^2=16
Both are giving 2 different values and hence none is sufficient . Answer: E
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 30 Dec 2017, 09:43
ashikaverma13 wrote:
What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?


(1) |x| = 4.

(2) x^2 = 16.

st 1: |x| means x = - 4 or x = 4 as "|x|" shows the distance of "x" from "0" on the number line is "4". And distance is always >= 0

So st 1 is insufficient

st 2: x^2 = 16

Value of exponent over the number shows the number of roots so, here "x" can take 2 values -4 & +4

So insufficient.

combining 1 & 2 do not give us any single value so (E)
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 05 Apr 2018, 03:46
Bunuel wrote:
ashikaverma13 wrote:
What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?


What is the value of x?

(1) |x| = 4 --> x = 4 or x = -4. Not sufficient.

(2) x^2 = 16 --> the same here: x = 4 or x = -4. Not sufficient.

(1)+(2) Same two values from both: x = 4 or x = -4. Not sufficient.

Answer: E.

As for your question: when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{16}=4\), NOT +4 or -4. Even roots have only a positive value on the GMAT.

In contrast, the equation \(x^2=16\) has TWO solutions, +4 and -4.

Hope it's clear.



isn't the root of x^2 = the absolute value of x therefore i thought you need to combine the ac...
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Joined: 02 Sep 2009
Posts: 47920
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 05 Apr 2018, 03:49
gmatmo wrote:
Bunuel wrote:
ashikaverma13 wrote:
What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?


What is the value of x?

(1) |x| = 4 --> x = 4 or x = -4. Not sufficient.

(2) x^2 = 16 --> the same here: x = 4 or x = -4. Not sufficient.

(1)+(2) Same two values from both: x = 4 or x = -4. Not sufficient.

Answer: E.

As for your question: when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{16}=4\), NOT +4 or -4. Even roots have only a positive value on the GMAT.

In contrast, the equation \(x^2=16\) has TWO solutions, +4 and -4.

Hope it's clear.



isn't the root of x^2 = the absolute value of x therefore i thought you need to combine the ac...


Yes, \(\sqrt{x^2}=|x|\). Could not understand what you mean after that.
_________________

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: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 05 Apr 2018, 04:56
my question is because Root x^2 ->|x|-> |x| = 4
whats wrong with this assumption.
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

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New post 05 Apr 2018, 05:35
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16. &nbs [#permalink] 05 Apr 2018, 05:35
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