Is |a|=|b|?

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NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 amFollowed by: 2 members; Thanked: 3 times

by NandishSS » Sun Oct 02, 2016 2:01 am

Is |a|=|b|?
1) a+b=0
2) a-b=2

[spoiler]*MathRevolution::Answer: If we modify the original condition and the question, we get a=Â±b?. Since the condition 1) is a=-b, the answer is yes and the correct answer is A.[/spoiler]

My doubt-Option 2) says -No.Then Why ans is ABecause it is basically asking are a and b equidistant from 0 however Option 2 says No.Pls let me know if i'm missing something

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Source: Beat The GMAT — Data Sufficiency | Sun Oct 02, 2016 2:01 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Oct 02, 2016 2:43 am

NandishSS wrote:Is |a|=|b|?
1) a+b=0
2) a-b=2

Statement 1:
a = -b.
Since a = -b, |a|=|b|.
SUFFICIENT.

Statement 2:
a = b+2.
If b=0, then a=2.
In this case, |a|â‰ |b|.
If b=-1, then a=1.
In this case, |a|=|b|.
INSUFFICIENT.

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by [email protected] » Sun Oct 02, 2016 9:49 am

Hi NandishSS,

In many cases, DS question 'test' the thoroughness of your thinking. In real basic terms, do you see more than just the obvious answer (for example, in the realm of math there are more than just positive integers - are you considering any other options when solving a DS question besides the ones that first come to mind?).

Here, we're asked if |A| = |B|. This is a YES/NO question.

1) A+B = 0

This Fact tell us that A and B are opposites (meaning a positive and negative version of the same number; re: +2 and -2) OR that they're both 0. In all cases, the |A| does equal the |B|, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) A-B = 2

Based on this Fact, and the work that you did in Fact 1, your first though is probably "they can't both be 0 and they can't both be opposites...", but is that REALLY true?

IF...
A = 2, B = 0, then the answer to the question is NO.
A = 1, B = -1, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Notice how the 'math work' in this question was pretty simple - because your ability to do math was NOT what this question was really testing. It was testing the thoroughness of your thinking.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

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NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 amFollowed by: 2 members; Thanked: 3 times

by NandishSS » Mon Oct 03, 2016 8:42 pm

[email protected] wrote:Hi NandishSS,

In many cases, DS question 'test' the thoroughness of your thinking. In real basic terms, do you see more than just the obvious answer (for example, in the realm of math there are more than just positive integers - are you considering any other options when solving a DS question besides the ones that first come to mind?).

Here, we're asked if |A| = |B|. This is a YES/NO question.

1) A+B = 0

This Fact tell us that A and B are opposites (meaning a positive and negative version of the same number; re: +2 and -2) OR that they're both 0. In all cases, the |A| does equal the |B|, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) A-B = 2

Based on this Fact, and the work that you did in Fact 1, your first though is probably "they can't both be 0 and they can't both be opposites...", but is that REALLY true?

IF...
A = 2, B = 0, then the answer to the question is NO.
A = 1, B = -1, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Notice how the 'math work' in this question was pretty simple - because your ability to do math was NOT what this question was really testing. It was testing the thoroughness of your thinking.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Thanks Alot Rich. You and Guru are just awesome every time I read your explanations I take away some thing.Happy Prepping

Thanks
Nandish

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crackverbal: Master | Next Rank: 500 Posts; Posts: 157; Joined: Mon Aug 16, 2010 7:30 pmFollowed by: 3 members; Location: India; Thanked: 65 times

by crackverbal » Wed Oct 05, 2016 12:26 am

Hi Nandish,

One approach to solve such problems is by plugging in values to get a YES and a NO. This approach is the safest but not necessarily the fastest as it requires you to be flexible with the types of numbers you choose. One strategy you can think of employing while dealing with DS questions based on Algebra and Word Problems is to 'Deconstruct and rephrase the question'.

While dealing with questions where you have a modulus on both sides of an equality/inequality for eg. |x| = |y| or |x| < |y|, the blanket rule that you can follow to deconstruct the question is to square both sides and remove the modulus. Now the reason we do this is because of an important relationship that |x| = root(x^2).

Now the question here is 'Is |a| = |b|'. We can deconstruct the question by squaring both sides and removing the modulus.

The question now becomes 'Is a^2 = b^2' which can be rephrased as 'Is (a+b)(a-b) = 0'.

Now for this to be true either one among a-b and a+b must be 0.

Statement 1 : Directly gives us a-b as 0. So sufficient.

Statement 2 : Gives us a-b as 2 but does not give us any information about a+b. If a+b = 0 then we get (a-b)(a+b) = 0 which answers a YES to the above question and if a+b = 1 then we get a NO to the above question.

OA : A

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