MGMAT absolute values

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iamseer: Master | Next Rank: 500 Posts; Posts: 170; Joined: Wed Jun 10, 2009 5:59 am; Thanked: 13 times

by iamseer » Tue May 04, 2010 8:30 am

If a and b are integers, and |a| > |b|, is a Â· |b| < (a - b)?

(1) a < 0

(2) ab >= 0

Source: MGMAT CAT
OA : E

What is the best way to tackle such questions? Is there some technique to handle these kind of absolute value questions better?

Thanks.

"Choose to chance the rapids and dance the tides"

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Source: Beat The GMAT — Data Sufficiency | Tue May 04, 2010 8:30 am

akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Tue May 04, 2010 8:54 am

iamseer wrote:If a and b are integers, and |a| > |b|, is a Â· |b| < (a - b)?

(1) a < 0

(2) ab >= 0

a Â· |b| =>>>> is it product?

Confirm?

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iamseer: Master | Next Rank: 500 Posts; Posts: 170; Joined: Wed Jun 10, 2009 5:59 am; Thanked: 13 times

by iamseer » Tue May 04, 2010 9:11 am

Yes.

Once again the question is:

If a and b are integers, and |a| > |b|, is a*|b| < (a - b)?

(1) a < 0

(2) a*b >= 0

"Choose to chance the rapids and dance the tides"

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Tue May 04, 2010 9:33 am

Statement 1:
|a| > |b| and a < 0
Assume a = -5, b = +4 or -4

a*|b| < (a - b)
-5 * 4 < -5 - (-4 or +4)
-20 < -1 or -9 TRUE

Assume a = -1/2, b = +1/3 or -1/3
a*|b| < (a - b)
-1/2 * 1/3 < -1/2 - (-1/3 or +1/3)
-0.166 < -0.834 or -0.166 NOT TRUE

Not Sufficient

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rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Tue May 04, 2010 9:42 am

akhp77 wrote:Statement 1:
|a| > |b| and a < 0
Assume a = -5, b = +4 or -4

a*|b| < (a - b)
-5 * 4 < -5 - (-4 or +4)
-20 < -1 or -9 TRUE

Assume a = -1/2, b = +1/3 or -1/3
a*|b| < (a - b)
-1/2 * 1/3 < -1/2 - (-1/3 or +1/3)
-0.166 < -0.834 or -0.166 NOT TRUE

Not Sufficient

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Why are we assuming A and B as fractions ? The question requires them to be integers right ? OR am I missing some thing important here ?

"Know thyself" and "Nothing in excess"

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rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Tue May 04, 2010 11:00 am

iamseer wrote:If a and b are integers, and |a| > |b|, is a Â· |b| < (a - b)?

(1) a < 0

(2) ab >= 0

Source: MGMAT CAT
OA : E

What is the best way to tackle such questions? Is there some technique to handle these kind of absolute value questions better?

Thanks.

The best way to solve these kind of question is squaring both sides .

Lets look at the question .

We have |a| > |b| --- squaring both sides

a^2 > b ^2 ----> a^2 - b^2 > 0 .

Now we need to know is a Â· |b| < (a - b)?

Thats a yes / no question . Again square both sides

a^2 b^2 < a^2 - 2ab - b^2

a^2 b^2+ 2ab < a^2 - b^2

so the question becomes is ab(ab+2) < a^2 - b^2 ?

(1) a < 0

Nothing is said about ' b' so insufficient .

(2) ab >= 0

Now if ab = 0 we get

a^2 - b^2 > 0 that is same as what is given in question so nothing new .

But if we do consider ab > 0 . We will get an answer .

So again we can not say for sure .

Insufficient .

Lets combine 1 and 2 .

we know a = negative so b is also negative as ab >0 from 2 .

But it dose not matter if a and b are positive or negative it will lead to the same situation as in statement 2 . Where ab could be equal to zero .

hence this too is not sufficient .

Ans E.

"Know thyself" and "Nothing in excess"

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Tue May 04, 2010 6:31 pm

rockeyb - Yes you are right. a and b are integer

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sat Sep 04, 2010 1:06 am

Got this problem wrong. But found an easy approach after the test. Wanted to share with all.

Need to check whether a*|b|<a-b
-> a*|b| -a +b<0
a*(|b|-1)+b <0

stmt1 says a<0.
B can be 0 or <0 or >0
Assume B to be 0,1,-1

Substitute and check if it works in the eqtn a*(|b|-1)+b <0

when b=0,
a<0, hence -a>0
-a+0 >0
-a>0... NO

when b=-1
-1<0..YES

No need to check b=1. one YES and one NO.
hence INSUFF

(2) ab >= 0
a and b can both be negative or a is negative and b=0
These 2 cases We have already covered in stmt1.
hence INSUFF

Combining:
We still have the same failing case.
hence INSUFF

pick E.

"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

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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 » Sat Sep 04, 2010 3:18 am

iamseer wrote:If a and b are integers, and |a| > |b|, is a Â· |b| < (a - b)?

(1) a < 0

(2) ab >= 0

Source: MGMAT CAT
OA : E

What is the best way to tackle such questions? Is there some technique to handle these kind of absolute value questions better?

Thanks.

Plugging in values works well if you choose wisely. To be efficient, search for values that satisfy both statements, recognizing how the problem is restricted -- and how it isn't. Here's what would go through my head as I read through the problem:

a and b are integers. Ok, no decimals.
|a| > |b|. Ok, a has to be farther from 0 than b.
Looking at statement 1: a<0. Ok, only negative values for a.
Looking ahead to statement 2: ab>=0. Ok, to satisfy both statements, b must be negative or 0.

So let's try a = -2, b = -1, and b=0. These values satisfy all the conditions.

If a = -2 and b = -1:
Is a Â· |b| < (a - b)?
-2 * |-1| < (-2 - (-1))
-2 < -1 Yes.

If a = -2 and b=0:
Is a Â· |b| < (a - b)?
-2 Â· |0| < (-2 - 0)
0 < -2 No.

Since the answer can be both yes and no, and since we've chosen values that satisfy both statements, the correct answer is E.

By recognizing how the problem is restricted -- and how it isn't -- and by choosing values that satisfy both statements, we make the process much more efficient.

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