Data Sufficiency - Roots - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Data Sufficiency - Roots

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shahfahad: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Fri Oct 30, 2015 9:01 am

by shahfahad » Tue Nov 10, 2015 12:43 pm

https://www.gmatprepnow.com/module/gmat- ... video/1034

Hi.I was going through this question and had a little bit of confusion.

The first statement of question says that âˆšx2 = 4. The problem is:

1) If I square both sides the result is x2 = 16. Then x could be either 4 or -4. Therefore, the statement is INSUFFICIENT.

2) However, the square on left side of equation could be cancelled with the square root as well. Then x MUST be 4. Therefore, the statement is SUFFICIENT.

The same problem is with the second statement. Could you please guide?

Thanks.

Regards,

Fahad

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Source: Beat The GMAT — Problem Solving | Tue Nov 10, 2015 12:43 pm

Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Fri Nov 13, 2015 1:32 pm

You can't just 'cancel' the square and the root. You have to treat the operations separately and handle them in order.

When you have x^2 = 16, there are 2 possible answers 4 and -4

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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 » Fri Nov 13, 2015 2:38 pm

Hi Fahad!

âˆšxÂ² actually works out to |x|, not x.

For instance, if x = -2, then âˆšxÂ² = âˆš(-2)Â² = âˆš4 = 2. So if x is negative, the âˆšxÂ² transforms a negative into a positive, and we're left with |x|, not x itself.

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shahfahad: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Fri Oct 30, 2015 9:01 am

by shahfahad » Sat Nov 14, 2015 3:48 am

Jim@StratusPrep and Matt@VeritasPrep: Ok but what rule is being applied here? PEDMAS? Because we have to solve the Parenthesis first? And the square root falls in the category of Exponents?

1) But if this is true then for the first statement where "âˆšx^2 = 4". The square root falls in the exponent category and ^2 is also an exponent. "On what rules" do we decide which to solve first.

2) In statement 2 we can say that PEDMAS applies as we are solving Parenthesis first and then squaring it. So x could not be negative.

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