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Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =
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05 Sep 2015, 03:22

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2

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.

Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =
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23 Jun 2017, 04:14

My gut was telling me A, however isn't that not necessarily correct?

Unless there is a rule on the GMAT that contradicts my reasoning, there is nothing that says XYZ can't the same integer (000).

If n is 0 then 9n = 0 and X + Y +Z can be equal to 0. Maybe its a stretch, but the stem could benefit from clarity by saying 3 digit number XYZ instead of just number XYZ

Number XYZ is the product of positive integer n and 9. Is x + y + z =
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23 Jun 2017, 06:37

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laxpro2001 wrote:

My gut was telling me A, however isn't that not necessarily correct?

Unless there is a rule on the GMAT that contradicts my reasoning, there is nothing that says XYZ can't the same integer (000).

If n is 0 then 9n = 0 and X + Y +Z can be equal to 0. Maybe its a stretch, but the stem could benefit from clarity by saying 3 digit number XYZ instead of just number XYZ

It's a great idea to consider the possibility that XYZ = 000, however there's one piece of given information that you forgot: XYZ is the product of positive integer n and 9 If n is a positive integer, then the product (n)(9) will be positive (which means XYZ can't equal zero)

Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =
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23 Jun 2017, 06:52

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allenh wrote:

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

To avoid any confusion/ambiguity, we might add some additional information that states x, y, and z are DIGITS. Some students might think that XYZ is the product of 3 numbers. That said, I love this question!

Target question:Is x + y + z = 9?

Given: XYZ is the product of positive integer n and 9 This is a HUGE piece of information, because it tells us that XYZ is a multiple of 9 A great feature of all positive multiples of 9 is that the sum of their digits will always be a multiple of 9. For example, 873 is a multiple of 9, and the sum of its digits = 8 + 7 + 3 = 18, and 18 is a multiple of 9 Likewise, 113,004 is a multiple of 9, and the sum of its digits = 1 + 1 + 3 + 0 + 0 + 4 = 9, and 9 is a multiple of 9 So, we can conclude that the sum, x + y + z must equal 9 or 18 or 27 ASIDE: the greatest possible sum is 27, since there are three digits and the greatest value of each digit is 9

Statement 1: x + y + z < 15 We already know that x + y + z must equal 9 or 18 or 27 So, if x + y + z < 15, then we can be certain that x + y + z = 9 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x + y + z > 8 We already know that x + y + z must equal 9 or 18 or 27 So, if x + y + z > 8, then it COULD be the case that x + y + z = 9 OR it COULD be the case that x + y + z = 18 OR it COULD be the case that x + y + z = 27 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =
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01 Sep 2018, 10:18

allenh wrote:

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

OA:A Number XYZ is the product of positive integer n and 9. As Number XYZ is multiple of 9, Sum of its digits should be divisible by 9. X+Y+Z = 9 m , where m is a positive integer Value of X+Y+Z can be 9,18,27,36,.................

Question : Is X + Y + Z = 9?

(1) X + Y + Z < 15 As per question stem,Value of X+Y+Z can be 9,18,27,36,................. Statement 1 i.e X + Y + Z < 15 leads to only one value of X+Y+Z i.e 9. Is X + Y + Z = 9? : Yes Statement 1 alone is sufficient

2) X + Y + Z > 8 As per question stem,Value of X+Y+Z can be 9,18,27,36,................. Statement 2 i.e X + Y + Z > 8 leads to multiple value of X+Y+Z .It can be 9,18,27 and so on. Is X + Y + Z = 9? : Answer can be yes or no Statement 2 alone is insufficient