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

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ashikaverma13
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What is the value of x? (1) |x| = 4. (2) x^2 = 16. [#permalink] New post   11 May 2017, 11:56
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What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.


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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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E
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Bunuel
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16. [#permalink] New post   11 May 2017, 12:10
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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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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16. [#permalink] 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] 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] 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] 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] 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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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16. [#permalink] New post   05 Apr 2018, 03:49
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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.
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16. [#permalink] 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] New post   05 Apr 2018, 05:35
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gmatmo wrote:
my question is because Root x^2 ->|x|-> |x| = 4
whats wrong with this assumption.


Nothing wrong. The next step would be |x| = 4 --> x = 4 or x = -4. The same as we have in the solution above.
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16. [#permalink] New post   17 Jan 2024, 07:21
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Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16. [#permalink]
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