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# If ab ≠ 0, is |a-b| > |a+b|?

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Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

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07 Jan 2017, 09:07
Top Contributor
|a-b|>|a+b| will be true only when a and b have different signs, as when we are doing
-> |a-b| we are actually adding the values of a and b and
-> |a+b| we are actually subtracting the values of a and b.

STAT1
ab < 0 => a and b have different signs
SUFFICIENT

STAT2
a > b
a and b can have the same sign or can have different signs too
example:
1. a = 7 b = 2 => a> b
but |a-b|<|a+b| (|5| < |9|)
2. a = 7 b = -2 => a> b
|a-b|>|a+b| (|9| > |5|)
So, INSUFFICIENT

Hope it helps!
nayanparikh wrote:
If ab ≠ 0, is |a-b|>|a+b|?

1) ab < 0
2) a > b

Can any one please provide explanation on how to solve these type of questions ?
@Bunnel ?

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Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

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13 Mar 2017, 10:21
nayanparikh wrote:
If ab ≠ 0, is |a-b|>|a+b|?

1) ab < 0
2) a > b

Can any one please provide explanation on how to solve these type of questions ?
@Bunnel ?

Bunnel has already explained that squaring both the sides of this inequality is the easiest.

What I did was that for the following to be true:
|a-b|>|a+b|

Quick substitution of values tells us that the above inequality will be true only when a and b are of opposite signs. We can try a=1, b=-2 OR a=-2, b=1

So, the question basically is if a and b are of opposite signs.

(1) says ab < 0. This clearly means that b are of opposite signs. So sufficient.

(2) says a > b. This does not tell us that b are of opposite signs. So not sufficient.
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If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

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15 Apr 2017, 11:12
Bunuel wrote:
If $$ab ≠ 0$$, is $$|a-b| > |a+b|$$?

Square $$|a-b| > |a+b|$$ (we can safely do this since both sides are nonnegative): is $$a^2 - 2ab + b^2 > a^2 +2ab + b^2$$ --> is $$ab < 0$$?

(1) $$ab < 0$$. Directly answers the question. Sufficient.

(2) $$a > b$$. Not sufficient to say whether ab < 0.

Hi Bunuel, to confirm, the sign of the sides matters because if we multiply by a -ve, then the inequality sign would need to flip, correct?
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Posts: 47077
Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

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15 Apr 2017, 11:17
2
Cez005 wrote:
Bunuel wrote:
If $$ab ≠ 0$$, is $$|a-b| > |a+b|$$?

Square $$|a-b| > |a+b|$$ (we can safely do this since both sides are nonnegative): is $$a^2 - 2ab + b^2 > a^2 +2ab + b^2$$ --> is $$ab < 0$$?

(1) $$ab < 0$$. Directly answers the question. Sufficient.

(2) $$a > b$$. Not sufficient to say whether ab < 0.

Hi Bunuel, to confirm, the sign of the sides matters because if we multiply by a -ve, then the inequality sign would need to flip, correct?

We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).
For example:
$$2<4$$ --> we can square both sides and write: $$2^2<4^2$$;
$$0\leq{x}<{y}$$ --> we can square both sides and write: $$x^2<y^2$$;

But if either of side is negative then raising to even power doesn't always work.
For example: $$1>-2$$ if we square we'll get $$1>4$$ which is not right. So if given that $$x>y$$ then we cannot square both sides and write $$x^2>y^2$$ if we are not certain that both $$x$$ and $$y$$ are non-negative.

Check the link below for more:
Inequality tips
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Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

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17 Apr 2017, 23:54
Bunuel wrote:
If $$ab ≠ 0$$, is $$|a-b| > |a+b|$$?

Square $$|a-b| > |a+b|$$ (we can safely do this since both sides are nonnegative): is $$a^2 - 2ab + b^2 > a^2 +2ab + b^2$$ --> is $$ab < 0$$?

(1) $$ab < 0$$. Directly answers the question. Sufficient.

(2) $$a > b$$. Not sufficient to say whether ab < 0.

Hai,
I am new here. I have a doubt. Where are the options mentioned, I don't see any A,B,C,D and E beneath the questions.
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Posts: 47077
Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

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18 Apr 2017, 02:11
subhash29 wrote:
Bunuel wrote:
If $$ab ≠ 0$$, is $$|a-b| > |a+b|$$?

Square $$|a-b| > |a+b|$$ (we can safely do this since both sides are nonnegative): is $$a^2 - 2ab + b^2 > a^2 +2ab + b^2$$ --> is $$ab < 0$$?

(1) $$ab < 0$$. Directly answers the question. Sufficient.

(2) $$a > b$$. Not sufficient to say whether ab < 0.

Hai,
I am new here. I have a doubt. Where are the options mentioned, I don't see any A,B,C,D and E beneath the questions.

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.
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Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

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18 Apr 2017, 09:15
Bunuel wrote:
subhash29 wrote:
Bunuel wrote:
If $$ab ≠ 0$$, is $$|a-b| > |a+b|$$?

Square $$|a-b| > |a+b|$$ (we can safely do this since both sides are nonnegative): is $$a^2 - 2ab + b^2 > a^2 +2ab + b^2$$ --> is $$ab < 0$$?

(1) $$ab < 0$$. Directly answers the question. Sufficient.

(2) $$a > b$$. Not sufficient to say whether ab < 0.

Hai,
I am new here. I have a doubt. Where are the options mentioned, I don't see any A,B,C,D and E beneath the questions.

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.

Thnx bunuel...

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Re: If ab ≠ 0, is |a-b| > |a+b|? [#permalink]

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03 Aug 2017, 11:29
Re: If ab ≠ 0, is |a-b| > |a+b|?   [#permalink] 03 Aug 2017, 11:29

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