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What is the value of z?

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What is the value of z? [#permalink] New post 16 May 2013, 02:41
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What is the value of z?

(1) z^2= 25
(2) z = -|z|

Source Grockit but I think the answer they give is false. I will post my personal answer (I will wait for some responses) and tell me if I am wright or wrong... :lol:
[Reveal] Spoiler: OA
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Re: What is the value of z? [#permalink] New post 16 May 2013, 02:49
Answer should be C.

1) Z = 5 or - 5

2) Z is negative or 0.

Combined Z = - 5
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Re: What is the value of z? [#permalink] New post 16 May 2013, 03:45
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What is the value of z?

(1) z^2= 25. This implies that z=5 or z=-5. Not sufficient.
(2) z = -|z|. This implies that z\leq{0}. Not sufficient.

(1)+(2) Since from (2) z\leq{0}, then from (1) z=-5. Sufficient.

Answer: C.

P.S. Please indicate OA when posting.
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Re: What is the value of z? [#permalink] New post 16 May 2013, 05:51
Thanks MacFauz and Bunuel. I understand your explanation and yes, OA is C.

However, can you tell me where I am wrong :
- Statement 1 is clearly not sufficient because z could be 5 or -5.
- Statement 2 is z = -|z|, you can rewrite the expression such as -z = IzI (wright?) if we multiply both side by -1. In that case the only possible value for z is 0 because the only possible solution is - 0 = I0I. So it is sufficient, no??

help me please.
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Re: What is the value of z? [#permalink] New post 16 May 2013, 05:59
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tissime wrote:
Thanks MacFauz and Bunuel. I understand your explanation and yes, OA is C.

However, can you tell me where I am wrong :
- Statement 1 is clearly not sufficient because z could be 5 or -5.
- Statement 2 is z = -|z|, you can rewrite the expression such as -z = IzI (wright?) if we multiply both side by -1. In that case the only possible value for z is 0 because the only possible solution is - 0 = I0I. So it is sufficient, no??

help me please.
Thanks


Yes, z = -|z| is the same as |z|=-z. But in this case z could be 0 or any negative number. For example, z=-2 --> |z|=|-2|=2 and -z=-(-2)=2 --> |z|=-z.

Absolute value properties:
When x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|\leq{-(some \ expression)}. For example: |-5|=5=-(-5);

When x\geq{0} then |x|=x, or more generally when some \ expression\geq{0} then |some \ expression|\leq{some \ expression}. For example: |5|=5.

For more check Absolute Value chapter of Math Book: math-absolute-value-modulus-86462.html

DS questions on absolute value to practice: search.php?search_id=tag&tag_id=37
PS questions on absolute value to practice: search.php?search_id=tag&tag_id=58

Tough absolute value and inequity questions with detailed solutions: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.
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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: What is the value of z? [#permalink] New post 16 May 2013, 06:24
Thank you so much Bunuel. Your help is precious!
Re: What is the value of z?   [#permalink] 16 May 2013, 06:24
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