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M20-15

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M20-15 [#permalink]

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New post 16 Sep 2014, 01:08
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Operation \(@\) is defined as \(@x = x + 1\) if \(x\) is negative and \(@x = x - 1\) if \(x\) is positive or 0. If \(@(@(@a)) = 5\), what is the value of \(a\) ?

A. -7
B. -5
C. 2
D. 8
E. 10
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 01:08
Official Solution:

Operation \(@\) is defined as \(@x = x + 1\) if \(x\) is negative and \(@x = x - 1\) if \(x\) is positive or 0. If \(@(@(@a)) = 5\), what is the value of \(a\) ?

A. -7
B. -5
C. 2
D. 8
E. 10

Backsolve: \(@(@(@8)) = 8 - 1 - 1 - 1 = 5\).

Answer: D
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Re: M20-15 [#permalink]

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New post 30 Jun 2016, 08:52
Bunuel wrote:
Official Solution:

Operation \(@\) is defined as \(@x = x + 1\) if \(x\) is negative and \(@x = x - 1\) if \(x\) is positive or 0. If \(@(@(@a)) = 5\), what is the value of \(a\) ?

A. -7
B. -5
C. 2
D. 8
E. 10

Backsolve: \(@(@(@8)) = 8 - 1 - 1 - 1 = 5\).

Answer: D


Hi Bunuel,

@x given and given that if \(@x = x + 1\) if \(x\) is negative and \(@x = x - 1\) if \(x\) is positive or 0.

and given @a , but here how we can consider a as positive.

Since there is no negative sign then you considerd a as +ve ? Please let me know.

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Re: M20-15 [#permalink]

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New post 30 Jun 2016, 08:58
msk0657 wrote:
Bunuel wrote:
Official Solution:

Operation \(@\) is defined as \(@x = x + 1\) if \(x\) is negative and \(@x = x - 1\) if \(x\) is positive or 0. If \(@(@(@a)) = 5\), what is the value of \(a\) ?

A. -7
B. -5
C. 2
D. 8
E. 10

Backsolve: \(@(@(@8)) = 8 - 1 - 1 - 1 = 5\).

Answer: D


Hi Bunuel,

@x given and given that if \(@x = x + 1\) if \(x\) is negative and \(@x = x - 1\) if \(x\) is positive or 0.

and given @a , but here how we can consider a as positive.

Since there is no negative sign then you considerd a as +ve ? Please let me know.


The question is solved by backsolving, by substituting the options.
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Re: M20-15 [#permalink]

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New post 23 Jul 2016, 18:53
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The symbol represents one step in the number line, whether the numbe is negative or positive. Therefore, since the symbol appears three times, the \(a\) must be either \(a+3\) or \(a-3\). Furthermore, since both hypothetical results are positive (5+3, 5-3), only the former -- 8-- works since all positive numbers are deducted one.

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Re: M20-15 [#permalink]

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New post 26 Jan 2017, 08:22
hello,

i understood Bunuel's solution. However, i'd a question: how does one decide if one should use back substitution or equations to solve? in this case, i tried solving with equations. since we don't know sign of a, i solved for both and got 2 and 8 as answers then back substituted to check ( since both 2 and 8 are in answer choices) and then found only 9 works. any advise?

thanks.

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Re: M20-15 [#permalink]

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New post 06 Feb 2017, 22:04
sanjay1810 wrote:
hello,

i understood Bunuel's solution. However, i'd a question: how does one decide if one should use back substitution or equations to solve? in this case, i tried solving with equations. since we don't know sign of a, i solved for both and got 2 and 8 as answers then back substituted to check ( since both 2 and 8 are in answer choices) and then found only 9 works. any advise?

thanks.


If you take a step back and look at the operation it's pretty simple. If x > 0, subtract 1. If x < 0, add one. The initial number then definitely can't be negative or lower than 5 since you'd then have no way to get up to 5. Hence, if you want to get to 5 you have to start higher, since eventually you'll just keep getting alternating values of 0, -1, 0, -1, 0, -1.

If the operation isn't that simple it's a game time decision I'd think. I typically just backsolve. The only time I'd consider not backsolving is if the answer options are nasty or if the operation is "normal" and just a function - f(k) or f(x) or whatever.

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Re: M20-15 [#permalink]

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New post 10 Feb 2017, 09:34
Without backsolving :

@(@(@a))=5

Consider full underline part as 1 unit say X
then above equation becomes: @(X)=5
Now X is positive so we can substitute @X=X−1
X−1 = 5 ==> X is 6

Now again following above step :
@(@a)=6 ==> X-1 = 6 ==> 7
Now last iteration :
@a= 7 ==> X-1 = 7 ==> X=8 .

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Re: M20-15 [#permalink]

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New post 03 Oct 2017, 05:58
+1 for D.
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Re: M20-15 [#permalink]

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New post 12 Oct 2017, 23:09
Bunuel wrote:
Operation \(@\) is defined as \(@x = x + 1\) if \(x\) is negative and \(@x = x - 1\) if \(x\) is positive or 0. If \(@(@(@a)) = 5\), what is the value of \(a\) ?

A. -7
B. -5
C. 2
D. 8
E. 10


I got the answer right but still link to similar question type please. Thanks.

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Re: M20-15 [#permalink]

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New post 12 Oct 2017, 23:12
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aashishagarwal2 wrote:
Bunuel wrote:
Operation \(@\) is defined as \(@x = x + 1\) if \(x\) is negative and \(@x = x - 1\) if \(x\) is positive or 0. If \(@(@(@a)) = 5\), what is the value of \(a\) ?

A. -7
B. -5
C. 2
D. 8
E. 10


I got the answer right but still link to similar question type please. Thanks.


Check the topics below. There you can find all the articles and questions we have.
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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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Re: M20-15   [#permalink] 12 Oct 2017, 23:12
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