If a, b, c are integers such that – 50

Question

If a, b, c are integers such that – 50 < a, b, c < 50 and a + b + c = 30, what is the maximum possible value of abc?

A. 1000
B. 4410
C. 4560
D. 5000
E. 8000

chetan2u · Answer

Now we know a, b and c are between -50 and 50...
Way to maximize is to ensure that the product is positive and for that we can have two scenarios
 1) All three positive.. 
Here all three should be closest, so 10=10+10=30 and abc = 10*10*10=100
 2) two are negative and one is positive.. 
Here a+b+c=30 tells us that the positive has to be 30 more than the absolute value of sum of the negative ones. That is, if a is positive a=30+|b+c|
So |b+c| will be maximum when a is maximum or 49. Thus  |c+b|=49-30=19 .
But b and c are negative, so b+c=-19.  Now for bc to be maximum, b and c should be closest possible to each other. Hence b and c are -10 and -9. 
abc=49*-10*-9=4410

B

GMATinsight · Answer

Product of the values is maximum when their absolute values must be as big as possible and sign must be +ve i.e. either one of them or all of them must be +ve

a + b + c = 30
Maximizing a i.e. at a = 49, 
b = -10 and c= -19

abc = 49*(-10)*(-9) = 4410

Answer: Option B

vishalgan · Answer

chetan2u   GMATinsight

Thank you for your explanations!

Shouldn't the answer be -49 x 40 x 39? Since the question asks, "what is the  maximum possible value  of abc?"

Thanks again!

GMATinsight · Answer

vishalgan

The Product of -49, 40 and 39 is NOT Negative and Hence it is NOT maximum

chetan2u · Answer

You will get the maximum absolute value but with a NEGATIVE sign. 
So in the end what you have is the least possible value.

Haardy7007 · Answer

Let a=-10, b=-10 and c=50 then sun would be 30 and product would be 5000.

Can someone help me in figuring out what I am missing here?

AikyaSP · Answer

The values of a, b, and C are to be greater than -50 and less than 50
You misread it as greater than equal to and Less than Equal to.

bumpbot · Answer

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If a, b, c are integers such that – 50 < a, b, c < 50 and a + b + c =

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