Value of X

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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

by jain2016 » Mon Mar 14, 2016 8:42 am

What is the value of X ?

1) x^2 + x + 10 = 16

2) x= 4y^4 + 2y^2 + 2

OAC

Hi Experts ,

Please explain.

Many thanks in advance.

SJ

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Source: Beat The GMAT — Data Sufficiency | Mon Mar 14, 2016 8:42 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Mar 14, 2016 8:53 am

jain2016 wrote:What is the value of X ?

1) xÂ² + x + 10 = 16

2) x = 4yâ�´ + 2yÂ² + 2

Target question: What is the value of x?

Statement 1: xÂ² + x + 10 = 16
Rewrite as: xÂ² + x - 6 = 0
Factor: (x + 3)(x - 2) = 0
So, x = -3 or x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 4yâ�´ + 2yÂ² + 2
There are several values of x and y that satisfy statement 2. Here are two:
Case a: if y = 0, then x = 4(0â�´) + 2(0Â²) + 2 = 2
Case b: if y = 1, then x = 4(1â�´) + 2(1Â²) + 2 = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = -3 or 2
Statement 2 tells us that x = 4yâ�´ + 2yÂ² + 2
IMPORTANT: Since yâ�´ > 0 and since yÂ² > 0 for all values of y, we can see that 4yâ�´ + 2yÂ² + 2 MUST BE greater than or equal to 2.
This means that x CANNOT EQUAL -3, which means x MUST EQUAL 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

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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

by jain2016 » Tue Mar 15, 2016 7:05 am

IMPORTANT: Since yâ�´ > 0 and since yÂ² > 0 for all values of y, we can see that 4yâ�´ + 2yÂ² + 2 MUST BE greater than or equal to 2.
This means that x CANNOT EQUAL -3, which means x MUST EQUAL 2

Hi Brent ,

Many thanks for your reply.

Can you please explain the above part.

Thanks,

SJ

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Mar 15, 2016 7:19 am

jain2016 wrote:
IMPORTANT: Since yâ�´ > 0 and since yÂ² > 0 for all values of y, we can see that 4yâ�´ + 2yÂ² + 2 MUST BE greater than or equal to 2.
This means that x CANNOT EQUAL -3, which means x MUST EQUAL 2

Hi Brent ,

Many thanks for your reply.

Can you please explain the above part.

Thanks,

SJ

In statement 1, we concluded that x = -3 or x = 2
In statement 2, we concluded that x must be greater than or equal to 2. Here's how we made this conclusion:
yâ�´ > 0 and since yÂ² > 0 for all values of y
This means that 4yâ�´ > 0 and 2yÂ² > 0
We're told that x = 4yâ�´ + 2yÂ² + 2
In other words, x = (some number greater than or equal to zero) + (some number greater than or equal to zero) + 2
This means that x = some number greater than or equal to 2
This means that x CANNOT EQUAL -3, which means x MUST EQUAL 2

Does that help?

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

by jain2016 » Tue Mar 15, 2016 10:08 am

In statement 1, we concluded that x = -3 or x = 2
In statement 2, we concluded that x must be greater than or equal to 2. Here's how we made this conclusion:
yâ�´ > 0 and since yÂ² > 0 for all values of y
This means that 4yâ�´ > 0 and 2yÂ² > 0
We're told that x = 4yâ�´ + 2yÂ² + 2
In other words, x = (some number greater than or equal to zero) + (some number greater than or equal to zero) + 2
This means that x = some number greater than or equal to 2
This means that x CANNOT EQUAL -3, which means x MUST EQUAL 2

Does that help?

Cheers,
Brent

[/quote]

Hi Brent ,

Thank you so much sir for your explanation.

It helps and all clear.

Thanks,

SJ

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Mar 17, 2016 10:54 pm

jain2016 wrote: Can you please explain the above part.

Thanks,

SJ

Another key takeaway here is that anything^(an even power) will be 0 or greater than 0. We could see this with a little bit of number properties:

Positive * Positive = Positive
Negative * Negative = Positive
0 * 0 = 0

So anything times itself must be 0 or positive, and from there any number raised to an EVEN power must be 0 or positive.

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