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a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil

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a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   15 Apr 2016, 07:09
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a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above
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C
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   15 Apr 2016, 07:31
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anceer wrote:
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above



Hi,
since we are looking for the maximum possible value, we will take two smallest negative integer, -10 and -9, and the largest possible positive integer thereafter..

few points--


1) we are taking two -ive and one +, so that the PRODUCT can be +..
2) we are taking biggest NUMERIC value in -, as a+b+c will become largest possible - integer, which will become + after being multiplied by another - sign

so \([abc – (a+b+c)] = (-10)(-9)(8) - (-10-9+8) = 720-(-11) = 731\)
C
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   15 Apr 2016, 07:27
Is the answer bank correct? Shouldn't option C be 713?

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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   06 Aug 2018, 22:26
chetan2u wrote:
anceer wrote:
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above



Hi,
since we are looking for the maximum possible value, we will take two smallest negative integer, -10 and -9, and the largest possible positive integer thereafter..

few points--


1) we are taking two -ive and one +, so that the PRODUCT can be +..
2) we are taking biggest NUMERIC value in -, as a+b+c will become largest possible - integer, which will become + after being multiplied by another - sign

so \([abc – (a+b+c)] = (-10)(-9)(8) - (-10-9+8) = 720-(-11) = 731\)
C



Hi chetan2u,

This might be a really stupid question but why could you please help understand why we didn't we take the value of abc as 987 which would make \([abc – (a+b+c)]\) = \(987 - (9+8+7)\) = 963 ?
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   06 Aug 2018, 22:36
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Shruti0805 wrote:
chetan2u wrote:
anceer wrote:
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above



Hi,
since we are looking for the maximum possible value, we will take two smallest negative integer, -10 and -9, and the largest possible positive integer thereafter..

few points--


1) we are taking two -ive and one +, so that the PRODUCT can be +..
2) we are taking biggest NUMERIC value in -, as a+b+c will become largest possible - integer, which will become + after being multiplied by another - sign

so \([abc – (a+b+c)] = (-10)(-9)(8) - (-10-9+8) = 720-(-11) = 731\)
C



Hi chetan2u,

This might be a really stupid question but why could you please help understand why we didn't we take the value of abc as 987 which would make \([abc – (a+b+c)]\) = \(987 - (9+8+7)\) = 963 ?


Shruti,
Reason is abc is a*b*c so 9*8*7=504
But you are taking it as 987 a 3-digit number.
If a and B are negative, ABC cannot be a integer.
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   04 Sep 2018, 05:52
chetan2u wrote:
anceer wrote:
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above



Hi,
since we are looking for the maximum possible value, we will take two smallest negative integer, -10 and -9, and the largest possible positive integer thereafter..

few points--


1) we are taking two -ive and one +, so that the PRODUCT can be +..
2) we are taking biggest NUMERIC value in -, as a+b+c will become largest possible - integer, which will become + after being multiplied by another - sign

so \([abc – (a+b+c)] = (-10)(-9)(8) - (-10-9+8) = 720-(-11) = 731\)
C


to get the maximum value,
we should have the maximum value of abc = (-10)(10)(-9) = 900
plus the maximum value of (a+b+c) = - (-10 - 9 - 8) = -(-27) = +27
so, the maxmium value should be 900+27 = 927

please kindly help advise if there's any problem with my concept here? Thanks
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   04 Sep 2018, 05:57
Monnie wrote:
chetan2u wrote:
anceer wrote:
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above



Hi,
since we are looking for the maximum possible value, we will take two smallest negative integer, -10 and -9, and the largest possible positive integer thereafter..

few points--


1) we are taking two -ive and one +, so that the PRODUCT can be +..
2) we are taking biggest NUMERIC value in -, as a+b+c will become largest possible - integer, which will become + after being multiplied by another - sign

so \([abc – (a+b+c)] = (-10)(-9)(8) - (-10-9+8) = 720-(-11) = 731\)
C


to get the maximum value,
we should have the maximum value of abc = (-10)(10)(-9) = 900
plus the maximum value of (a+b+c) = - (-10 - 9 - 8) = -(-27) = +27
so, the maxmium value should be 900+27 = 927

please kindly help advise if there's any problem with my concept here? Thanks


Ok, I got my problem!
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   04 Sep 2018, 05:58
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Monnie wrote:
[to get the maximum value,
we should have the maximum value of abc = (-10)(10)(-9) = 900
plus the maximum value of (a+b+c) = - (-10 - 9 - 8) = -(-27) = +27
so, the maxmium value should be 900+27 = 927

please kindly help advise if there's any problem with my concept here? Thanks


The prompt indicates that |a| ≠ |b| ≠ |c|, so a=-10 and b=10 is not a viable case.
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   04 Sep 2018, 05:59
Expert Reply
Monnie wrote:
chetan2u wrote:
anceer wrote:
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above



Hi,
since we are looking for the maximum possible value, we will take two smallest negative integer, -10 and -9, and the largest possible positive integer thereafter..

few points--


1) we are taking two -ive and one +, so that the PRODUCT can be +..
2) we are taking biggest NUMERIC value in -, as a+b+c will become largest possible - integer, which will become + after being multiplied by another - sign

so \([abc – (a+b+c)] = (-10)(-9)(8) - (-10-9+8) = 720-(-11) = 731\)
C


to get the maximum value,
we should have the maximum value of abc = (-10)(10)(-9) = 900
plus the maximum value of (a+b+c) = - (-10 - 9 - 8) = -(-27) = +27
so, the maxmium value should be 900+27 = 927

please kindly help advise if there's any problem with my concept here? Thanks



abc and a+b+c are part of same equation so you have take same value of a,B and c in both abc and a+b+c.. but here you have taken -10,10,-9 and -10,-9,-8
Secondly when you have taken abc you have taken a as -10 and b as 10 but it is given |a| is not equal to |b| but you have taken both |-10|=|10| hence wrong
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   11 Sep 2018, 22:29
anceer wrote:
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above




Can't we take the value of 'a' greater than 10?
e.g., a=20, 100,..
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   11 Sep 2018, 22:37
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castiel wrote:
anceer wrote:
a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a+b+c)]?


A. 524
B. 693
C. 731
D. 970
E. None of the above




Can't we take the value of 'a' greater than 10?
e.g., a=20, 100,..


no because it is given that -10 ≤ a, b, c ≤ 10, so a has to be within -10 and 10, that is any of -10,-9,-8,-7,-6,-5.....0,1,2,3....8,9,10
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Re: a, b, c are integers. |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What wil [#permalink] New post   11 Sep 2018, 22:43
We can take 10,9 and 8 to make the quantity max.
Also abc>0 and (a+b+c)<0
a=-10,b=-9 and c=8
C) will be the answer.
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Re: a, b, c are integers. |a| |b| |c| and -10 a, b, c 10. What wil [#permalink] New post   19 May 2023, 11:58
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Re: a, b, c are integers. |a| |b| |c| and -10 a, b, c 10. What wil [#permalink]
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