Is \(x = 4?\)
\((1)\quad |x + 2| < 10\)
\((2) \quad |x + 5| > 10\)
[spoiler]OA=B[/spoiler]
Source: Veritas Prep
Is \(x = 4?\)
This topic has expert replies
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Let's take each statement one by one.Vincen wrote:Is \(x = 4?\)
\((1)\quad |x + 2| < 10\)
\((2) \quad |x + 5| > 10\)
[spoiler]OA=B[/spoiler]
Source: Veritas Prep
\((1)\quad |x + 2| < 10\)
=> x + 2 < 10 => x < 8; taking plus sign
=> x + 2 > - 10 => x > -12; taking minus sign
Thus, -12 < x < 8. x can have any value between -12 and 8, including 4. So, x is not necessarily equal to 4. Insufficient.
\((2) \quad |x + 5| > 10\)
=> x + 5 > 10 => x > 5; taking plus sign
=> x + 5 < -10 => x < -15; taking minus sign
So, x is either less than - 15 or is greater than 5. In either case x ≠4. The answer is no. Sufficient.
Another way of checking it by plugging in the value of x in the inequality; we see that x = 4 does not satisfy the inequality \( \quad |x + 5| > 10\).
The correct answer: B
Hope this helps!
-Jay
_________________
Manhattan Review GRE Prep
Locations: GRE Classes Miami | GRE Prep Course Munich | GRE Prep Denver | LSAT Prep Course Orlando | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
-
- Senior | Next Rank: 100 Posts
- Posts: 46
- Joined: Sun Dec 27, 2015 7:03 am
- Thanked: 8 times
- Followed by:1 members
TWO ways..Vincen wrote:Is \(x = 4?\)
\((1)\quad |x + 2| < 10\)
\((2) \quad |x + 5| > 10\)
[spoiler]OA=B[/spoiler]
Source: Veritas Prep
(I) Just substitute x=4 and see what happens..
\((1)\quad |x + 2| < 10\)
|4+2|<10...6<10..Yes
But x as -4, 0, 1 and so on also fit in
Insuff
\((2) \quad |x + 5| > 10\)
|4+5|>10...9>10..NO
SO we get an answer for sure, and the answer is NO. We are not bothered what is the range or value of x, till we know that it does not include 4.
Suff
(II) Solve for x
\((1)\quad |x + 2| < 10\)
Think of a number line where distance of x from 2 is less than 10, so x lies between 2-10 and 2+10...-8<x<12
It can be 4 or may not be 4.
Insuff
\((2) \quad |x + 5| > 10\)
This says that x is not within 10 units from 5, so x<5-10, that is x<-5 or x>5+10, that is x>15.
So we can see that 4 cannot be a value..
B
NOTE - You can solve the Modulus by CRITICAL point or even by SQUARING two sides as both sides are positive