allenh wrote:DS:
Number XYZ is the product of positive integer n and 9. Is X+Y+Z=9?
(1) x+y+z<15
(2) x+y+z>8
This question could be worded better.
I believe that XYZ is supposed to represent some 3-digit number, where X is the hundreds digit, Y represents the tens digit and Z represents the units digit.
If this is the case, then the solution is based on the fact that,
if a number is divisible by 9, the SUM of its digits will be divisible by 9
For example, we know that 13005 is divisible by 9, because 1+3+0+0+5 = 9, and 9 is divisible by 9.
Likewise, 88551 is divisible by 9, because 8+8+5+5+1 = 27, and 27 is divisible by 9.
The question tells us that XYZ = 9n, which means XYZ is divisible by 9.
So, the sum of its digits is divisible by 9. Also, the GREATEST sum of the 3 digits is 27
So, x + y + x, must equal 9 or 18 or 27
Now onto the question.............
Target question: Is x + y + z = 9?
Statement 1: x + y + z < 15
We already concluded that x + y + z must equal 9, 18 or 27
If x + y + z < 15, then
x + y + z must equal 9
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x + y + z > 8
We already concluded that x + y + z must equal 9, 18 or 27
If x + y + z > 8, then
x + y + z COULD equal 9 or 18 or 27
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
