If x y z are the 3 consecutive multiples ofa, what is the value of uy

1.	If x y z are the 3 consecutive multiples ofa, what is the value of uy az?
Answer» ANSWER: Here are some examples of consecutive multiples of 3: 6, 9, 12 24, 27, 30 51, 54, 57 Notice that each value is 3 greater than the value before it So, if x, y, and z are three consecutive multiples of 3, then we can write: x = x y = x + 3 z = x + 6 Quantity A: The remainder when the sum of x + 1, y — 2, and z + 3 is divided by 9 We want the remainder when [(x + 1) + (y - 2) + (z + 3)] is divided by 9 Replace y and z with their equivalent VALUES above to get: [(x + 1) + (x + 3 - 2) + (x + 6 + 3)] Simplify to get: 3x + 11 IMPORTANT: Since x is a multiple of 3, we know that x = 3k, for some INTEGER k So, we can take our sum of 3x + 11 and rewrite it as: 3(3k) + 11 Simplify to get: 9k + 11 We can rewrite this as: 9k + 9 + 2 And then factor to get: 9(k + 1) + 2 When we write it this way, we can see that are sum is TWO GREATER then some multiple of 9. So when we divide the sum by 9, the remainder must be 2 Quantity B: 2 So, the two quantities are equal. Answer: C

If x y z are the 3 consecutive multiples ofa, what is the value of uy az?

Answer»

Here are some examples of consecutive multiples of 3:

6, 9, 12

24, 27, 30

51, 54, 57

Notice that each value is 3 greater than the value before it

So, if x, y, and z are three consecutive multiples of 3, then we can write:

x = x

y = x + 3

z = x + 6

Quantity A: The remainder when the sum of x + 1, y — 2, and z + 3 is divided by 9

We want the remainder when [(x + 1) + (y - 2) + (z + 3)] is divided by 9

Replace y and z with their equivalent VALUES above to get:

[(x + 1) + (x + 3 - 2) + (x + 6 + 3)]

Simplify to get: 3x + 11

IMPORTANT: Since x is a multiple of 3, we know that x = 3k, for some INTEGER k

So, we can take our sum of 3x + 11 and rewrite it as: 3(3k) + 11

Simplify to get: 9k + 11

We can rewrite this as: 9k + 9 + 2

And then factor to get: 9(k + 1) + 2

When we write it this way, we can see that are sum is TWO GREATER then some multiple of 9.

So when we divide the sum by 9, the remainder must be 2

Quantity B: 2

So, the two quantities are equal.

Answer: C