If a, b are integers and |a-b|=8, which of the following is the smalle

Question

If a, b are integers and |a-b|=8, which of the following is the smallest possible value of ab? 
A. -16 
 B. 0 
 C. 16 
 D. 7 
 E. 40

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ShreyasCM · Accepted Answer

The value will be lowest when a= -4 and b= 4--> | -4 - 4| = 8
(an)min = 4*-4 = -16
Hence A.

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MathRevolution · Answer

a=4, b=-4. Hence, the answer is A.

yk510 · Answer

Why is the answer not 0? If a=8 and b=0?

amanvermagmat · Answer

Hi

The question asks, "What is the  smallest possible value  of a*b?"

Like you, when I read the question, I also noticed that getting '0' is easy: take a=8 and b=0. But then I saw that there is another option given which is less than 0 (which is -16). So we have to check whether -16 is also possible or not, since the question asks for lowest value possible.

So with some trial/error, I saw that indeed -16 is possible when I take a=-4 and b=4. because |-4-4| = |-8| = 8, and -4*4 = 16.

pushpitkc · Answer

In min-max expression questions, 
we have to take the maximum value of one integer 
and a minimum value of another integer which satisfy the equation
Since the expression is |a-b| = 8
the range of this expression must be -8 <= a - b <= 8

This is possible when a=-4 and b=4 or a=4,b=-4
In either case, ab = -16(Option A)

vnitnagpur · Answer

When you convert this expression to liner equation it is a+(-b) = 8 when a>b or a + (-b) = -8 when a<b.

So, now if you see the values of a and b for which the product wil be minimum when corresponding values are 4 and -4 and hence the product = -16. Hope this makes sense

rishab0507 · Answer

Min / Max value of a sum of a integer is when both the digits are same. So max product or min product will occur when x.y = Same digit, 
|x-y|= 8, so x, y should be 4 , 
x= 4, y=-4 or x= -4, y= 4 :As we are looking for min value so one of x,y has to be negative to get min value.

4*-4 = -16
Answer : A

surjin · Answer

Also, check for the negative values as one of the options is a negative integer.

Shrey08 · Answer

The smallest possible value of  ab   will be the largest possible value with a  −ve  sign.

ab  will be negative if either  a  or  b  is negative.

Since either  a  or  b  is negative  |a−b|=8  represents the sum of  a & b 
Now for a given sum of 2 numbers the product is maximum when the numbers are same.

Therefore,  a=b;a+a=8;2a=8;a=4 
The product is  16 
Again, the smallest possible value of  ab  will be the largest possible value with a  −ve  sign.

−16 , option A

chacinluis · Answer

Notice that |a-b|=8 is literally saying two numbers who's distance is 8 from each other.
This can happen anywhere in the number line.

If both a and b are positive then ab>0
If both a and b are negative then ab>0
But if one is negative and the other positive the product ab<0

So we are shooting for a and b of opposite signs.
a=-7, b=1, ab=-7
a=-6, b=2, ab=-12
a=-5, b=3, ab=-15
a=-4, b=4, ab=-16
a=-3, b=5, ab=-15
.
.
we can see when we choose 4 and -4 the product is minimized to -16
Answer: A

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If a, b are integers and |a-b|=8, which of the following is the smalle

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If a, b are integers and |a-b|=8, which of the following is the smalle

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