BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

What is the value of \(x?\)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Mon Nov 25, 2019 12:19 am
M7MBA wrote:What is the value of \(x?\)

(1) \(x^2+x+10=16\)

(2) \(x=4y^4+2y^2+3\)

[spoiler]OA=C[/spoiler]

Source: Veritas Prep
Let's take each statement one by one.

(1) \(x^2+x+10=16\)

=> x^2 + x - 6 = 0 => x = -3 or 2. No unique value of x. Insufficient

(2) \(x=4y^4+2y^2+3\)

Since we do not have the unique value y, we can't get the unique value of x. Insufficient.

(1) and (2) together

From (2) \(x=4y^4+2y^2+3\), note that \(4y^4+2y^2+3\) is a positive value, irrespective of the value of y. Thus, from (1), one of the values of x = - 3 is ruled out. Thus x = 2. Sufficient.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GRE Classes Manhattan | GRE Prep Course Frankfurt | GRE Prep Bellevue | SAT Prep Course Orlando | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Nov 25, 2019 6:56 am
M7MBA wrote:What is the value of \(x?\)

(1) \(x^2+x+10=16\)

(2) \(x=4y^4+2y^2+3\)

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Target question: What is the value of x?

Statement 1: x² + x + 10 = 16
Subtract 16 from both sides to get: x² + x - 6 = 0
Factor: (x + 3)(x - 2) = 0
This means EITHER x = -3 OR x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 4y� + 2y² +3
x can have infinitely many values, depending on the value of y.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that EITHER x = -3 OR x = 2

Statement 2 tells us that x must be a POSITIVE number. We know this because 4y� and 2y² are always greater than or equal to 0.
So, when we add 3 to 4y� + 2y², it is guaranteed that 4y� + 2y² + 3 is POSITIVE, which means x is positive

So when we combine both statements we can be certain that x = 2

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1