Number XYZ is the product of positive integer n and 9. Is x + y + z =

Solution

 Three-digit number xyz = 9n

• whether x + y + z = 9

• Question Statement Analysis
o Three-digit number xyz = 9n

 xyz is divisible by 9

• x + y + z is divisible by 9. (By the divisibility test of 9)
• x + y + z = 0, 9, 18, 27, 36, 45,…. (multiples of 9)
o Since x, y, z are single digits from 0 through 9, x + y + z lies between 0 and 27, inclusive.
o x + y + z = 0, 9, 18, 27

 Now, xyz is a three digit number, so x cannot be 0.

• Hence, x + y + z cannot be 0.
• x + y + z = 9, 18, 27 --------(1)


• Statement 1

o x + y + z < 15

 From (1), x + y + z = 9, 18, 27

• The only sum less than 15 is 9.
o Hence, x + y + z = 9.
o Statement 1 is sufficient alone.

• Statement 2

o x + y + z > 8

 From (1), x + y + z = 9, 18, 27

• Each of these is greater than 8.
o Statement 2 is insufficient alone.