Question

If the product of two integers x and y is less than 82 with y being a multiple of
three. What is the highest value that x may have

Answer 1

Answer:

A2A.

First of all, y is a multiple of 3 if and only if it is in the form 3⋅k where k is any integer (including k=1 : so 3 is indeed a multiple of 3 , as well as any integer number is a multiple of itself).

Secondly, I think you forgot to say that x and y must be positive integers, otherwise you could set y equal to 0 or any negative multiple of 3, and then you could take x as big as you want.

That said, if x and y are both positive and their product is upper-bounded, for x to be as big as possible, then y has to be as small as possible.

The smallest possible positive multiple of 3 is 3 itself, which gives us

3x<82

and then

x<823

and finally

x=27

since 27 is the greatest integer value less than 823 .

Hope this helps.

Answer 2

Answer:

The highest possible value of x = 27

Step-by-step explanation:

Given,

The product of two integers x and y is less than 82

y is a multiple of 3

To find,

The highest possible value of 'x'

Solution:

Since y is a multiple of 3, we can take y as 3z,

then the product of the numbers = xy = x×3z = 3xz is also a multiple of 3

Highest possible multiple of 3 less than 82 = 81

Since 81 is a multiple of x and y, the value of 'x' is maximum when the value of 'y' is minimum

Since 'y' is a multiple of y, the minimum value of 'y' =  the least multiple of '3' = 3

Then we have,

x×3 = 81

x = 27

The highest possible value of x = 27

#SPJ2