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

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

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Updated on: 05 Sep 2015, 03:13
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85% (hard)

Question Stats:

49% (02:00) correct 51% (02:15) wrong based on 195 sessions

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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

Originally posted by allenh on 05 Sep 2015, 02:06.
Last edited by Bunuel on 05 Sep 2015, 03:13, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

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05 Sep 2015, 03:22
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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.

Hope it's clear.
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Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

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

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23 Jun 2017, 06:37
Top Contributor
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)

Cheers,
Brent
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Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

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23 Jun 2017, 06:52
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Top Contributor
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

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Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

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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
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Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

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01 Sep 2018, 20:34
Product XYZ must be divisible by 9.

(A number is a divisible by 9 if the sum of its digit is divisible by 9.)

Value of XYZ could be: 9, 18, 27.....

(1) X+Y+Z<15. So X+Y+Z must be 9. [Suff]

(2) X+Y+Z>8. So X+Y+Z can be 9 or 18. [Insuff]

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Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =  [#permalink]

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24 Oct 2019, 05:48
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Re: Number XYZ is the product of positive integer n and 9. Is x + y + z =   [#permalink] 24 Oct 2019, 05:48
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