What is the value of w^-2?

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sushantsahaji: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Mon Oct 05, 2015 10:32 am

by sushantsahaji » Sat Apr 16, 2016 10:05 pm

What is the value of w^-2?

1. w^-1 = 1/2
2. w^8 = 8

This is a misprinted question, But interesting! Wanted to check whether my ans correct.

My ans is A

Thanks,

Sushant

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Source: Beat The GMAT — Data Sufficiency | Sat Apr 16, 2016 10:05 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sat Apr 16, 2016 11:39 pm

Statement 1: wâ�»Â¹ = 1/2

wâ�»Â² = 1/4

Sufficient.

Statement 2: wâ�¸ = 8 (This does not agree with Statement 1. The statements of Official DS questions agree.)

wÂ² = âˆœ8

w could be negative or positive. So Statement 2 does not provide information sufficient for determining the value of w.

However, we don't need to know the sign of w to determine the following.

wâ�»Â² = 1/âˆœ8

Sufficient.

The correct answer is D.

Marty Murray
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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 » Sun Apr 17, 2016 7:10 am

sushantsahaji wrote:What is the value of wâ�»Â²?

1) wâ�»Â¹ = 1/2
2) wâ�¸ = 8

Target question: What is the value of wâ�»Â²?

Statement 1: wâ�»Â¹ = 1/2
In other words, 1/w = 1/2, which tells us that w MUST equal 2, which mean wâ�»Â² = 1/4

ALTERNATE APPROACH:
Given: wâ�»Â¹ = 1/2
Square both sides: (wâ�»Â¹)Â² = (1/2)Â²
We get: wâ�»Â² = 1/4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: wâ�¸ = 8
In this case w can EITHER positive OR negative.
That is, w can equal the positive 8th root of 8 or the negative 8th root of 8

HOWEVER, this does not mean statement 2 is not sufficient, because when we want to find the value of wâ�»Â²
Since wâ�»Â² = 1/(wÂ²), we can see that wÂ² will be positive (regardless of whether w is positive or negative), which means 1/(wÂ²) will be positive.

So....
Given: wâ�¸ = 8
Raise both sides to the power of -1/4 to get: (wâ�¸)^(â�»1/4) = (8)^(â�»1/4)
Apply power of a power law to get: wâ�»Â² = (8)^(â�»1/4)
Or we can rewrite this as: wâ�»Â² = 1/(8)^(1/4)
Or we can write: wâ�»Â² = 1/âˆœ8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Related Resources
The following free videos cover the concepts/strategies that are useful for answering this question:
- Laws of exponents - part I: https://www.gmatprepnow.com/module/gmat ... video/1025
- Negative exponents: https://www.gmatprepnow.com/module/gmat ... video/1028
- Laws of exponents - part II: https://www.gmatprepnow.com/module/gmat ... video/1029
- Other roots: https://www.gmatprepnow.com/module/gmat ... video/1035
- Fractional exponents: https://www.gmatprepnow.com/module/gmat ... video/1041
- Solving equations with exponents: https://www.gmatprepnow.com/module/gmat ... video/1043

IMPORTANT: Statement 1 essentially told us that wâ�»Â² = 1/4 and Statement 2 told us that wâ�»Â² = 1/âˆœ8 . On the GMAT, the two statements will never contradict each other.
For more on this, see this free video: https://www.gmatprepnow.com/module/gmat ... video/1104

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » Mon Apr 18, 2016 7:24 pm

sushantsahaji wrote:What is the value of w^-2?

1. w^-1 = 1/2
2. w^8 = 8

Required: w^-2

Statement 1: w^-1 = 1/2
Or 1/w = 1/2
Hence w = 2 and we can find w^-2 easily. No need to solve further
Sufficient

Statement 2: w^8 = 8
Hence (w^2) = 8^(1/4) = âˆœ8
Therefore w^(-2) = 1/âˆœ8
Sufficient

Correct Option: D
Sushant, can you tell what problems were you facing with statement 2?

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sushantsahaji: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Mon Oct 05, 2015 10:32 am

by sushantsahaji » Tue Apr 19, 2016 1:34 pm

OptimusPrep wrote:
sushantsahaji wrote:What is the value of w^-2?

1. w^-1 = 1/2
2. w^8 = 8

Required: w^-2

Statement 1: w^-1 = 1/2
Or 1/w = 1/2
Hence w = 2 and we can find w^-2 easily. No need to solve further
Sufficient

Statement 2: w^8 = 8
Hence (w^2) = 8^(1/4) = âˆœ8
Therefore w^(-2) = 1/âˆœ8
Sufficient

Correct Option: D
Sushant, can you tell what problems were you facing with statement 2?

Hi,

I missed the w^2 and considered st. 2 insufficient.

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OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » Wed Apr 20, 2016 8:34 pm

sushantsahaji wrote: Hi,

I missed the w^2 and considered st. 2 insufficient.

Ahhh ... that explains

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Thu Apr 21, 2016 6:44 am

Marty is right - both statements of DS questions must agree, because they must both be presumed to be true. You will never find an official GMAT question with contradictory statements. If the source of this question didn't know that, one must question what else this source is getting wrong...

What is the source of this question?

Posters, please ALWAYS post the source of your questions for exactly this reason! It's important for students to be able to determine which sources are high-quality, and which are not.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Thu Apr 21, 2016 8:34 am

I'll third Marty's and Ceilidh's point about contradictory statements. For those interested in an official question that touches on roots/exponents, see here: https://www.beatthegmat.com/nth-root-of- ... 79252.html

Veritas Prep | GMAT Instructor

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jsche229: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Fri Oct 08, 2010 7:15 pm

by jsche229 » Sat Oct 22, 2016 10:13 am

So this question is found in the OG 2016, DS # 20. What keeps throwing me off about this one is that if you try and solve for just W, it is very contradictory. For statement 1, W=2. For statement 2, you could have 2 values as the exponent of W is even. W could be either positive or negative.

Thoughts?

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Sat Oct 22, 2016 10:39 am

This question was new to OG2016, so even though the book had been out for a few months by April, I hadn't seen it yet.

If you look at the answer explanation in OG2016, you'll see that they print a correct, logical version of the question there:

What is the value of w^(-2)?

1. w^(-1) = 1/2
2. w^3 = 8

To your question:

jsche229 wrote:So this question is found in the OG 2016, DS # 20. What keeps throwing me off about this one is that if you try and solve for just W, it is very contradictory. For statement 1, W=2. For statement 2, you could have 2 values as the exponent of W is even. W could be either positive or negative.

We only think about positive & negative results when the exponent is EVEN. Since the correct version of the question (found in the answer explanation) has an ODD exponent, we don't have to worry about this.

In the misprinted version, you're partially right - we would get both a positive and a negative solution for w if we're given a value for w^8.

Keep in mind, though, that the question is asking for w^(-2), not w. So we'd get a positive and a negative result, but then we'd raise it to the power of (-2). Taking any base to an EVEN integer exponent (regardless of whether that exponent is positive or negative) will result in a positive value. So we'd still get just one value for w^(-2).

Does that help?

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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