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# Is |a – 2| = b^2 – c^3 ?

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Is |a – 2| = b^2 – c^3 ? [#permalink]

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02 Sep 2012, 21:36
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Is |a – 2| = b^2 – c^3 ?

(1) a < 2
(2) a + b^2 = c^3 + 2

I'm struggling to solve this problem.

Any good material on absolute values/modules available?
[Reveal] Spoiler: OA
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Joined: 28 Aug 2012
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Re: Is |a – 2| = b2 – c3 [#permalink]

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02 Sep 2012, 23:27
Statement (1) is clearly insufficient.

Statement (2):
a + b^2 = c^3 + 2
b^2 - c^3 = 2 - a

Substituting b^2 - c^3 in the original equation:
Is |a - 2| = 2 - a

If a is higher than 2, the equation will not hold true.
If a is equal or lower than 2, the equation will be ok.
--> not sufficient

(1) + (2) together:
Because of statement (1) we know that "a" must be lower than 2.
Statement (2) told us, that if "a" is lower than 2, the equation is true.
--> sufficient
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Re: Is |a – 2| = b^2 – c^3 ? [#permalink]

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03 Sep 2012, 03:59
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Is |a – 2| = b^2 – c^3 ?

(1) a < 2. Not sufficient, since no info about b and c.

(2) a + b^2 = c^3 + 2 --> re-arrange: $$b^2-c^3=2-a$$. So, the question becomes: is $$|a-2|=2-a$$? Now, if $$a>{2}$$, then $$|a-2|=a-2$$ and the answer is NO but if $$a\leq{2}$$, then $$|a-2|=-(a-2)=2-a$$ and the answer is YES. Not sufficient.

(1)+(2) Since from (1) $$a < 2$$, then $$|a-2|=-(a-2)=2-a$$, so the answer is YES. Sufficient.

Theory on absolute values: math-absolute-value-modulus-86462.html

PS questions on Absolute Values: search.php?search_id=tag&tag_id=58
DS questions on Absolute Values: search.php?search_id=tag&tag_id=37

Tough inequality and absolute value questions: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.
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Re: Is |a – 2| = b^2 – c^3 ? [#permalink]

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20 Sep 2013, 01:03
qweert wrote:
Is |a – 2| = b^2 – c^3 ?

(1) a < 2
(2) a + b^2 = c^3 + 2

I'm struggling to solve this problem.

Any good material on absolute values/modules available?

Why is this method not working?

from the stem |a-2| can be positive or negative

if |a-2| is negative then removing the mod we get -a+2 = b^2 - c^3 , so question becomes is -a+2= b^2-c^3 ?
or is a-2= c^3- b^2 ?

which is exactly what is given in statement 2 after rearranging statement (2)

so I thought (2) was sufficient. what is wrong with this method?
Thank you.
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- Stne

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Re: Is |a – 2| = b^2 – c^3 ? [#permalink]

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20 Sep 2013, 01:21
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Expert's post
stne wrote:
qweert wrote:
Is |a – 2| = b^2 – c^3 ?

(1) a < 2
(2) a + b^2 = c^3 + 2

I'm struggling to solve this problem.

Any good material on absolute values/modules available?

Why is this method not working?

from the stem |a-2| can be positive or negative

if |a-2| is negative then removing the mod we get -a+2 = b^2 - c^3 , so question becomes is -a+2= b^2-c^3 ?
or is a-2= c^3- b^2 ?

which is exactly what is given in statement 2 after rearranging statement (2)

so I thought (2) was sufficient. what is wrong with this method?
Thank you.

IF a-2 is negative (so IF a<2), the question is whether -(a – 2) = b^2 – c^3 ?
IF a-2 is non-negative (so IF a>=2), the question is whether a – 2 = b^2 – c^3 ?

From (1) the question becomes: is -(a – 2) = b^2 – c^3 ?
(2) says that -(a – 2) = b^2 – c^3. But we don't know whether a-2 is negative.

Combined we have all info needed.

Does this make sense?
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Re: Is |a – 2| = b^2 – c^3 ? [#permalink]

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20 Sep 2013, 01:54
Bunuel wrote:
stne wrote:
qweert wrote:
Is |a – 2| = b^2 – c^3 ?

(1) a < 2
(2) a + b^2 = c^3 + 2

I'm struggling to solve this problem.

Any good material on absolute values/modules available?

Why is this method not working?

from the stem |a-2| can be positive or negative

if |a-2| is negative then removing the mod we get -a+2 = b^2 - c^3 , so question becomes is -a+2= b^2-c^3 ?
or is a-2= c^3- b^2 ?

which is exactly what is given in statement 2 after rearranging statement (2)

so I thought (2) was sufficient. what is wrong with this method?
Thank you.

IF a-2 is negative (so IF a<2), the question is whether -(a – 2) = b^2 – c^3 ?
IF a-2 is non-negative (so IF a>=2), the question is whether a – 2 = b^2 – c^3 ?

From (1) the question becomes: is -(a – 2) = b^2 – c^3 ?
(2) says that -(a – 2) = b^2 – c^3. But we don't know whether a-2 is negative.

Combined we have all info needed.

Does this make sense?

Thank you , think I got it
Let me retry

Is |a – 2| = b^2 – c^3 ?

meaning
if a- 2 is positive then Is a-2 = b^2 – c^3? or if a-2 is negative then Is -a+2 = b^2-c^3?

Statement 2 says -a+2 = b^2- c^3 , but it doesn't tell us that a-2 is negative, if it had told us that a-2 is negative and
-a+2 = b^2- c^3 then it would have been sufficient

1+2

we know that a<2 so a- 2 is negative from 1
and -a+2 = b^2- c^3 from 2 hence we have all the info. tricky one

Have I got it ?
_________________

- Stne

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Re: Is |a – 2| = b^2 – c^3 ? [#permalink]

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20 Sep 2013, 01:57
stne wrote:
Bunuel wrote:
stne wrote:

Why is this method not working?

from the stem |a-2| can be positive or negative

if |a-2| is negative then removing the mod we get -a+2 = b^2 - c^3 , so question becomes is -a+2= b^2-c^3 ?
or is a-2= c^3- b^2 ?

which is exactly what is given in statement 2 after rearranging statement (2)

so I thought (2) was sufficient. what is wrong with this method?
Thank you.

IF a-2 is negative (so IF a<2), the question is whether -(a – 2) = b^2 – c^3 ?
IF a-2 is non-negative (so IF a>=2), the question is whether a – 2 = b^2 – c^3 ?

From (1) the question becomes: is -(a – 2) = b^2 – c^3 ?
(2) says that -(a – 2) = b^2 – c^3. But we don't know whether a-2 is negative.

Combined we have all info needed.

Does this make sense?

Thank you , think I got it
Let me retry

Is |a – 2| = b^2 – c^3 ?

meaning
if a- 2 is positive then Is a-2 = b^2 – c^3? or if a-2 is negative then Is -a+2 = b^2-c^3?

Statement 2 says -a+2 = b^2- c^3 , but it doesn't tell us that a-2 is negative, if it had told us that a-2 is negative and
-a+2 = b^2- c^3 then it would have been sufficient

1+2

we know that a<2 so a- 2 is negative from 1
and -a+2 = b^2- c^3 from 2 hence we have all the info. tricky one

Have I got it ?

Yes, thats' correct.
_________________
Re: Is |a – 2| = b^2 – c^3 ?   [#permalink] 20 Sep 2013, 01:57
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