GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 May 2019, 02:12 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # What is the value of x? (1) |x| = 4. (2) x^2 = 16.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Current Student G
Joined: 19 Aug 2016
Posts: 149
Location: India
GMAT 1: 640 Q47 V31 GPA: 3.82
What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

1
1 00:00

Difficulty:   5% (low)

Question Stats: 88% (00:24) correct 12% (00:26) wrong based on 274 sessions

### HideShow timer Statistics

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?

_________________
Consider giving me Kudos if you find my posts useful, challenging and helpful!
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

1
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 $$\sqrt{x}$$, 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.
_________________
##### General Discussion
Current Student G
Joined: 19 Aug 2016
Posts: 149
Location: India
GMAT 1: 640 Q47 V31 GPA: 3.82
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

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 $$\sqrt{x}$$, 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.
_________________
Consider giving me Kudos if you find my posts useful, challenging and helpful!
Verbal Forum Moderator V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2290
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

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 $$\sqrt{x}$$, 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
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful
Manager  G
Joined: 16 May 2016
Posts: 202
Location: India
Concentration: Marketing, Healthcare
GPA: 3.5
WE: Analyst (Consulting)
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

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
_________________
Not Giving UP! Kudos if you like the question SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1671
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

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)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Intern  B
Joined: 02 Dec 2017
Posts: 17
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

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 $$\sqrt{x}$$, 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...
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

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 $$\sqrt{x}$$, 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.
_________________
Intern  B
Joined: 02 Dec 2017
Posts: 17
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

my question is because Root x^2 ->|x|-> |x| = 4
whats wrong with this assumption.
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.  [#permalink]

### Show Tags

1
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.
_________________ Re: What is the value of x? (1) |x| = 4. (2) x^2 = 16.   [#permalink] 05 Apr 2018, 05:35
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  