factor26 wrote:The value of x is one quarter of z. The sum of x, y, and z is equal to 26. If the value of y is twice the value of z, what is the largest factor of the sum of y and z?
A- 2
B- 3
C- 8
D- 12
E- 24
ANSWER IS E CAN SOMEONE PLEASE EXPLAIN THE LOGIC BEING TESTED HERE?
Plug in a value for z in order to determine the ratio of x:y:z.
Let z= 4.
The value of x is one quarter of z:
Thus, x = (1/4)*4 = 1.
The value of y is twice the value of z:
Thus, y = 2*4 = 8.
Thus, x:y:z = 1:8:4.
The sum of x, y, and z is equal to 26:
x+y+z = 1+8+4 = 13.
All the values need to double.
Thus, x =2, y=16, and z=8, so that x+y+z = 2+16+8 = 26.
Thus, y+z = 16+8 = 24.
The largest factor of 24 is 24.
The correct answer is
E.
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