if x + y is divisible by 0, which of the following expressions must also be divisible by:
a. x/y + 9
b. (9x) + y
c. x + (9y)
d. xy + 9
e. 2x + 2y
SORRY I MEANT DIVISIBLE BY 9 NOT 0
look at e)
2x + 2y = 2(x+y)
but x+y is divisible by 9, so would be any multiple of x+y
what about the others.
All we need is one case where the statement would be false, and we can rule out that choice.
let x=2, y = 7, clearly x+y is divisible by 9
a) 2/7 + 9 divisible by 9? NO
b) 9(2) + 7 = 25 , NO
c) 2 + 9(7) = 65 , NO
d) (2)(7) + 9 = 23, NO
looks like e) is it.
btw, for a number to be divisible by 9, the sum of its digits will be divisible by 9
LIFE SAVER.
To determine which expression must also be divisible by x + y, we need to consider the properties of divisibility.
First of all, it is important to note that x + y cannot be divisible by 0. Divisibility is defined for two numbers, where the divisor cannot be 0.
However, if we assume that x + y is divisible by some non-zero number, we can analyze the options based on their properties and simplify them.
a. x/y + 9: This expression involves dividing x by y, which could result in a non-integer value. Therefore, we cannot guarantee divisibility.
b. (9x) + y: Since we are only performing addition here, we can be sure that if x + y is divisible by a number, this expression will also be divisible by the same number. Therefore, this expression must be divisible.
c. x + (9y): Similar to option b, this expression only involves addition, so if x + y is divisible, this expression will also be divisible.
d. xy + 9: This expression involves multiplying x and y, which means it may not be divisible by the same number as x + y. Therefore, we cannot guarantee divisibility.
e. 2x + 2y: Once again, this expression only involves addition, so if x + y is divisible, this expression will also be divisible.
In summary, options b, c, and e are the expressions that must be divisible by x + y.