Last visit was: 16 Jun 2024, 23:38 It is currently 16 Jun 2024, 23:38
Close
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 93698
Own Kudos [?]: 632361 [13]
Given Kudos: 82304
Send PM
avatar
Manager
Manager
Joined: 06 Jun 2016
Posts: 233
Own Kudos [?]: 111 [0]
Given Kudos: 212
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [0]
Given Kudos: 799
Location: Canada
Send PM
Director
Director
Joined: 12 Nov 2016
Posts: 569
Own Kudos [?]: 118 [0]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Send PM
Re: If |4 – x| = 8, what is the value of x? [#permalink]
Bunuel wrote:
If |4 – x| = 8, what is the value of x?

(1) x^2 is an even number.
(2) |x| is the square of a prime number.



Two ways to approach abs. value

4-x =8
x =-4

-l4-xl =8
-4 +x =8
x =12

Stmnt 1

Insuff because both are even

Stmtn 2

Suff because the only x value that could be a square of a prime number is 2
Intern
Intern
Joined: 18 Aug 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 68
Send PM
Re: If |4 – x| = 8, what is the value of x? [#permalink]
can anyone solve this using critical point method ?
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5233
Own Kudos [?]: 4068 [0]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: If |4 – x| = 8, what is the value of x? [#permalink]
Bunuel wrote:
If |4 – x| = 8, what is the value of x?

(1) x^2 is an even number.
(2) |x| is the square of a prime number.


|4-x|=8
=> x = 4+/-8 = -4 or 12

S1:
\(x^2\) is an even number
\((-4)^2 = 16\) is an even number
\(12^2 = 144\) is also an even number
INSUFFICIENT

S2:
|x| is the square of a prime number.
|-4| = 4 is the square of a prime number 2.
|12| = 12 is NOT a square of a prime number
x=-4
SUFFICIENT

IMO B
Intern
Intern
Joined: 06 Oct 2017
Posts: 4
Own Kudos [?]: 2 [0]
Given Kudos: 23
Send PM
Re: If |4 – x| = 8, what is the value of x? [#permalink]
GMATPrepNow wrote:
Bunuel wrote:
If |4 – x| = 8, what is the value of x?

(1) x² is an even number.
(2) |x| is the square of a prime number.


When solving equations involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Target question: What is the value of x?

Given: |4 – x| = 8
So, 4 - x = 8 or 4 - x = -8
If 4 - x = 8, then x = -4
If 4 - x = -8, then x = 12
So, x = -4 or x = 12

Statement 1: x² is an even number
We already know that x = -4 or x = 12, so there are two cases to consider:
case a: If x = -4, then x² = (-4)² = 16, which is an even number. So, x could equal -4
case b: If x = 12, then x² = (12)² = 144, which is an even number. So, x could equal 12
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x| is the square of a prime number
We already know that x = -4 or x = 12, so there are two cases to consider:
case a: If x = -4, then |-4| = 4, and 4 IS the square of a prime number (2). So, x could equal -4
case b: If x = 12, then |12| = 12, BUT 12 is NOT the square of a prime number. So, x cannot equal 12
So, x MUST equal -4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

RELATED VIDEO

——————————————————————————————-
x = 12 —> is clearly an extraneous root of give Equation, as per how you’ve taught. Thus, let’s focus only on x = -4 .

x = -4 —(Eq. 1)

I’ve solved Statement 2 below. Pls let me know if my steps of solution for Statement 2 are correct.

Statement 2: |x| is the square of a prime number

Statement 2: |x| = (prime number)^2 —(Eq. 2)
Note: P is a variable for [P = Prime Number]

=> |x| = (prime number)^2 —(Eq. 2)
=> |-4| = (Prime Number)^2 — (Eq.1) Putting x’s value
=> 4 = (Prime Number)^2 —Bringing ‘|-4|‘ out as ‘+4’
=> \sqrt{ (4) } = prime number
=> +2 or -2 = Prime Number
=> Since, we know (-ive)Intergers are NOT Prime numbers. Therefore, +2 is that only possible Prime number.

Finally, we’ve just ONE answer i.e. +2. Therefore, Statement 2 is Sufficent & Answer is ‘B’.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33613
Own Kudos [?]: 838 [0]
Given Kudos: 0
Send PM
Re: If |4 x| = 8, what is the value of x? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: If |4 x| = 8, what is the value of x? [#permalink]
Moderator:
Math Expert
93698 posts