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

Question

three-digit 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

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chetan2u · Accepted Answer

So the 3-digit number xyz=9n. 
Thus xyz is a multiple of 9, and as per the property of multiples of 9, x+y+z is a multiple of 9. x+y+z=9x. 
It could be 9,18,27 etc

(1) x + y + z < 15
So x+y+z can be 0 or 9. But if it is 0, the number becomes 000 or 0.
Hence x+y+z=9

(2) x + y + z > 8
It could be 9, 18..

A

Bunuel · Answer

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

Since three-digit number XYZ is the product of positive integer n and 9, then it's divisible by 9. A number is a divisible by 9 if the sum of its digit is divisible by 9. Thus a three-digit integer to be divisible by 9 the sum of its digits must be 9 (for example 126), 18 (for example, 189) or 27 (999).

From above z + y + z is 9, 18 or 27.

(1) x + y + z < 15 --> x + y + z = 9. Sufficient.
(2) x + y + z > 8 --> x + y + z = 9, 18 or 27. Not sufficient.

Answer: A.

Hope it's clear.

Kuanl · Answer

XYZ is a three digit no divisible by 9
so X+Y+Z has be a multiple of 9

From 1 we get the sum is less than 15 so only 9 is the no. which is divisible by 9 which is sufficient 
from 2 we get the sum is greater than 8 so we can have multiple values of the sum such as 9,18,27 etc which is insufficient

TarunKumar1234 · Answer

three-digit number XYZ is the product of positive integer n and 9. Is x + y + z = 9?

Given, xyz = 9*n. The divisibility of 9 means, x+y+z should be divisible by 9.

Stat 1: x + y + z < 15, we have only one option, x+y+z = 9. Sufficient

Stat 2: x + y + z > 8, we can have x+y+z = 9, 18...Not sufficient

So, I think A.

EgmatQuantExpert · Answer

Solution

Given  
  Three-digit number xyz = 9n

To find  
We need to determine
 • whether x + y + z = 9

Approach and Working out

• 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.

Thus, option A is the correct answer.
  Correct Answer: Option A

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

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GMAT Data Sufficiency (DS) Questions

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

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