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Math Expert V
Joined: 02 Sep 2009
Posts: 59712
For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  [#permalink]

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1 00:00

Difficulty:   5% (low)

Question Stats: 93% (00:55) correct 7% (01:32) wrong based on 109 sessions

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For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which of the following could be a value of x?

A. -4
B. -3
C. 2
D. 3
E. 6

Kudos for correct solution.

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Verbal Forum Moderator V
Status: Greatness begins beyond your comfort zone
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Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
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Re: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  [#permalink]

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1
5%x = 9
=>(5+x)(5-x) = 9
=> 25 - x^2 = 9
=> x^2 = 16
=> x = 4 or -4

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Manager  B
Joined: 07 May 2015
Posts: 174
Location: India
GMAT 1: 660 Q48 V31 GPA: 3
Re: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  [#permalink]

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5%x = (5+x)(5-x)
25-x^2 = 9
x^2 = 16
x=-4,4

Ans: A
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Re: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  [#permalink]

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One vote for A.

According to formula we have: 5 %x = (5-x)( 5+x) = 5^2 - x^2 = 25- x^2 = 9
=> x^2 = 16=> x = 4 or x = -4.
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Senior Manager  Joined: 20 Aug 2015
Posts: 384
Location: India
GMAT 1: 760 Q50 V44 For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  [#permalink]

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Bunuel wrote:
For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which of the following could be a value of x?

A. -4
B. -3
C. 2
D. 3
E. 6

Kudos for correct solution.

Given: a%b = (a + b)(a - b)
And 5%x = 9

5%x = (5+x)*(5-x) = 25 - $$x^2$$
Therefore 25 -$$x^2$$ = 9

$$x^2$$ = 16
x = -4 or 4
Option A
Manager  Joined: 26 Feb 2016
Posts: 71
GMAT 1: 760 Q49 V44 For all integers a and b, a%b = (a + b)(a - b).  [#permalink]

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For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which of the following could be a value of x?

A -4
B -3
C 2
D 3
E 6

This question came up on Veritas. I guessed it right but I had no idea what the % symbol stood for. Could anyone help explain? Unfortunately googling or searching for the % symbol is voided CEO  S
Joined: 20 Mar 2014
Posts: 2560
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  [#permalink]

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ddb1990 wrote:
For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which of the following could be a value of x?

A -4
B -3
C 2
D 3
E 6

This question came up on Veritas. I guessed it right but I had no idea what the % symbol stood for. Could anyone help explain? Unfortunately googling or searching for the % symbol is voided Follow posting guidelines (link in my signatures) and make sure to search for a question before starting a new thread. Refer above for the solution. Topics merged.

For this question, do not get intimidated by the % sign. It could mean many different operations and 1 of them is already mentioned in the question,a%b = (a + b)(a - b)

Thus, 5%x = 9 ---> (5+x)/(5-x)=9 ---> x=4.

How did you guess the correct answer when you did not understand the question?

Hope this helps.
Manager  Joined: 26 Feb 2016
Posts: 71
GMAT 1: 760 Q49 V44 Re: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  [#permalink]

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Thanks Engr - and apologies for posting this twice, I searched for the topic name but nothing came up so figured it wasn't covered yet.

So should I be aware of what the % sign means outside of percentage? As I've never seen it used in this context before and curious if this would come up in GMAT?

I literally just guessed, Engr, no estimated guess took place as I had no idea what the % sign stood for, was kind of dumbfounded by it popping up in this context!
Veritas Prep GMAT Instructor G
Joined: 01 Jul 2017
Posts: 81
Location: United States
Re: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  [#permalink]

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While this problem isn't necessarily a difficult question, it highlights a great trick that the GMAT sometimes employs to deliberately confuse some students. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full "GMAT Jujitsu" for this question:

First, how the GMAT uses the "%" symbol here is an example of a common problem structure: temporarily-defined, abstract functions. Such functions often borrow symbols that would normally be seen in entirely different contexts. This is a deliberate, psychological attempt on the part of the GMAT to trap novice test takers. You expect the symbol to do one thing, but the GMAT defines it as something different. Now, we are actually accustomed to using abstract symbols to represent mathematical functions with a defined order of operations (after all, we know that "a÷b" means "take the value in the 'a' spot and divide it by the value in the 'b' spot.") Temporarily defining other characters to perform other mathematical operators is just the next level of this same idea. Any symbol can be temporarily defined as something else. For example, I have seen %, ^, &, #, @, §, , @, and various characters of the alphabet used.

In the context of this question, the symbol "%" doesn't mean "percent." The question defines "%" as a mathematical operator that takes two inputs: $$a$$ and $$b$$. For this question, for any given $$a$$ and $$b$$, $$a$$%$$b$$ is defined as $$(a + b)(a - b)$$. Once we understand the basic rules of the function, then the mathematics of the question become very obvious.

There are two main ways you can do this question. First, just Do the Math, plugging in the values the problem gives you and then solving for $$x$$:
$$a$$%$$b=(a + b)(a - b) = a^2 -b^2$$ (This is called the "difference of squares.")
$$9 = 5^2 - x^2$$
$$x^2 = 25-9 = 16$$
$$x = +4$$ or $$-4$$ (Don't forget the negative solution for $$x^2$$)

The second way to solve this problem is to Back Solve, looking for the answer choice that would work for the equation $$(5 + x)(5 - x) = 9$$. Since the answer choices are all integers, this means that as soon as we can tell that either $$(5+x)$$ or $$(5-x)$$ ISN'T a multiple of $$9$$, we know that such an answer CAN'T be right.

A) $$(5-4)(5+4) = 1(9) = 9$$ (This works, and so we don't even need to go further! The answer must be A.)
B) $$(5-3)(5+3) = 2(8) \neq 9$$
C) $$(5+2)(5-2) = 7(3) \neq 9$$
D) $$(5+3)(5-3) = 8(2) \neq 9$$
E) $$(5+6)(5-6) = 11(-1) \neq 9$$

And that is how you think like the GMAT.
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Aaron Pond
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Hit "+1 Kudos" if this post helped you understand the GMAT better.
Visit me at https://www.veritasprep.com/gmat/aaron-pond/ if you would like to learn even more "GMAT Jujitsu"! Re: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which   [#permalink] 26 Jan 2019, 15:30
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# For all integers a and b, a%b = (a + b)(a - b). If 5%x = 9, then which  