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Is |a – 2| = b^2 – c^3 ?

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Is |a – 2| = b^2 – c^3 ? [#permalink] New post 02 Sep 2012, 20:36
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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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Re: Is |a – 2| = b2 – c3 [#permalink] New post 02 Sep 2012, 22:27
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] New post 03 Sep 2012, 02:59
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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.

Answer: C.

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] New post 20 Sep 2013, 00:03
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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Re: Is |a – 2| = b^2 – c^3 ? [#permalink] New post 20 Sep 2013, 00:21
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This post received
KUDOS
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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is |a – 2| = b^2 – c^3 ? [#permalink] New post 20 Sep 2013, 00:54
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 ?
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Re: Is |a – 2| = b^2 – c^3 ? [#permalink] New post 20 Sep 2013, 00:57
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Is |a – 2| = b^2 – c^3 ?   [#permalink] 20 Sep 2013, 00:57
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