Doubt in a solution from the OG(13 Ed). Question No 157

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cruzerkk: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Tue Jan 20, 2015 9:32 pm

Doubt in a solution from the OG(13 Ed). Question No 157

by cruzerkk » Mon May 25, 2015 10:04 pm

This is with reference to DS Question # 157 from the 13th edition of the OG .

If n is a positive integer and k=5.1*(10^n), what is the value of k ?
1) 6000<k<500,000
2)k^2=2.601*(10^9)

The answer at the back is D.

I understood how statement 1 is sufficient.

But how is statement 2 sufficient ?

Solving statement 2 :
k = SqRt(2.601*(10^9)) = SqRt(2601*(10^6)) - Removing decimals by using 10s

ie, = SqRt(2601) * SqRt(10^6) ---- Now this will have 2 solutions , won't it ?
= -51 * 10^3 OR 51 * 10^3
= -51,000 OR 51,000 -- So should'nt this be INSUFFICIENT and the answer A ?

Can someone please explain this solution , why the negative Square root was ignored ?

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Source: Beat The GMAT — Data Sufficiency | Mon May 25, 2015 10:04 pm

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pm; Thanked: 115 times; Followed by:3 members

by theCEO » Tue May 26, 2015 1:24 am

cruzerkk wrote:This is with reference to DS Question # 157 from the 13th edition of the OG .

If n is a positive integer and k=5.1*(10^n), what is the value of k ?
1) 6000<k<500,000
2)k^2=2.601*(10^9)

The answer at the back is D.

I understood how statement 1 is sufficient.

But how is statement 2 sufficient ?

Solving statement 2 :
k = SqRt(2.601*(10^9)) = SqRt(2601*(10^6)) - Removing decimals by using 10s

ie, = SqRt(2601) * SqRt(10^6) ---- Now this will have 2 solutions , won't it ?
= -51 * 10^3 OR 51 * 10^3
= -51,000 OR 51,000 -- So should'nt this be INSUFFICIENT and the answer A ?

Can someone please explain this solution , why the negative Square root was ignored ?

The negative value is ignored because the question states that K is a positive number (k=5.1*(10^n))

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Tue May 26, 2015 4:00 am

negative value of k is ignored because -51000 not equal to 5.1 * 10n Even if n >0 or n <0.

so n >0 or n <0 doesn't matter.

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GMAT/MBA Expert

Brent@GMATPrepNow: 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 » Tue May 26, 2015 6:34 am

If n is a positive integer and k = (5.1)x(10^n), what is the value of k?

1) 6,000 < k < 500,000
2) kÂ² = 2.601 x 10^9

Target question: What is the value of k?

Given: n is a positive integer, and k = (5.1)x(10^n)
IMPORTANT: This since n can be ANY positive integer, there are several possible values of k.
They are: 51, 510, 5100, 51000, 510000, etc

Statement 1: 6,000 < k < 500,000
If we examine the possible values of k (51, 510, 5100, 51000, 510000, etc ), we can see that only ONE value (51,000) lies within the range defined by the inequality.
So, k must equal 51,000
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: kÂ² = 2.601 x 10^9
If kÂ²= 2.601 x 10^9, then EITHER k = âˆš(2.601 x 10^9) OR k = -âˆš(2.601 x 10^9). So, it appears that we cannot answer the target question.
HOWEVER, the question also tells us that k = 5.1 x 10^n, and since 5.1 x 10^n will always have a POSITIVE value, we know that k must be POSITIVE.
If k is POSITIVE, then k â‰ -âˆš(2.601 x 10^9)
This means that k must equal âˆš(2.601 x 10^9)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com