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If n is an integer, the greatest possible value of the
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05 Jan 2011, 07:44
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If n is an integer, the greatest possible value of the expression: 12  32  7n is A. 20 B. 1 C. 8 D. 9 E. 12 I know to answer this correctly I can just plug in numbers. I was wondering is there any tricks to solving it faster. Thanks.
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Re: Are there any tricks to solving this question
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Re: If n is an integer, the greatest possible value of the
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Re: If n is an integer, the greatest possible value of the
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04 Jul 2013, 01:35
Let the greatest possible value be x. 1. For n>4, i.e., when the value within the modulus is negative, the modulus becomes, (327n) 12 ( (327n))=x 12+327n=x x=447n so when n>4, x is greatest for n=5 and the value of x is 9. 2. For n<=4 , the modulus is 327n 12(327n)=x So when n<=4, the greatest value of x is 8 So , of the two, x=9 is the greater value.
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Re: If n is an integer, the greatest possible value of the
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03 Feb 2016, 17:54
PASSINGGMAT wrote: If n is an integer, the greatest possible value of the expression: 12  32  7n is
A. 20 B. 1 C. 8 D. 9 E. 12
I know to answer this correctly I can just plug in numbers. I was wondering is there any tricks to solving it faster. Thanks. good one...so...we need to get the greatest possible value..we have an absolute value..thus, it will always be positive. since n must be an integer, 7n can't be 32. it can be either 28, or 35. in case it's 35, then we have 3. in case it is 28, then 4. since we have a minus sign, we would rather have 3, since 123=9, but 124=8. thus, the max value is 9.



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Re: If n is an integer, the greatest possible value of the
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06 Jan 2017, 09:56
SravnaTestPrep wrote: Let the greatest possible value be x.
1. For n>4, i.e., when the value within the modulus is negative, the modulus becomes, (327n) 12 ( (327n))=x 12+327n=x x=447n so when n>4, x is greatest for n=5 and the value of x is 9.
2. For n<=4 , the modulus is 327n 12(327n)=x So when n<=4, the greatest value of x is 8
So , of the two, x=9 is the greater value. x is greatest for n = 5; x is 9 , when n = 6; x is 2 so greatest x =9
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Re: If n is an integer, the greatest possible value of the
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14 Jun 2017, 00:20
My approach, no difficult algebra needed, but please correct me if i'm wrong. I'm still learning!:
First look at 32  7n.
On the number line you would be at number 32 with 7n to the left en 7n to the right. The question asks for the greatest possible value of 12  X. X stands for 32  7n. So you know X must be small in order for the formula to turn out big.
You know n is an integer, and you know X needs to be small, so: 327*4=4 (Let's try one more) 327*5=3 (Bingo)
3 it is. (Absolute value, so 3)
123=9. There you go.



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Re: If n is an integer, the greatest possible value of the
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14 Jun 2017, 01:07
maximum value for the expression 12mod(x) to maximise the value of the expression x must be minimum mod(x)=357x x=4 mod x =4 x=5 mod x =3 x=6 mod x =7 Hence max value of the expression =9
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Re: If n is an integer, the greatest possible value of the
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30 Aug 2018, 03:28
Let's think of it like this 
n is an integer so 7n must also be an integer. Correct?
Now the question asks for the greatest value, for this the part in the modulus needs to be be the smallest value. (The smaller the number is from 12 the better)
Inside the modulus we have 2 numbers 327n
So, the value of 7n should be as close to the number 32 as possible to get a small value.
What multiples of 7 is the closest to 32? >>> You guessed it right it is 35. That means n=5, (since 7x5=35)
So now let's get to the simple math 
3235=3, Since there is modulus, it will only be 3
Next > 123=9. Which is the greatest value of the expression
Answer D




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