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# M02-31

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Math Expert
Joined: 02 Sep 2009
Posts: 51214

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15 Sep 2014, 23:18
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:18) correct 32% (01:39) wrong based on 184 sessions

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If $$x$$ and $$y$$ represent digits of a positive two-digit number divisible by 3, is the two-digit number less than 50?

(1) Sum of the digits is a multiple of 18

(2) Product of the digits is a multiple of 9

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:18
1
Official Solution:

Statement (1) by itself is sufficient. The only two digit number with the sum of its digits representing a multiple of 18 is 99. $$9 + 9 = 18$$.

Statement (2) by itself is insufficient. There are several possibilities. For example, 36: $$3 * 6 = 18$$, is a multiple of 9, and 99: $$9 * 9 = 81$$, is a multiple of 9 as well.

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Joined: 11 Sep 2013
Posts: 150
Concentration: Finance, Finance

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03 Dec 2014, 20:25
Hi, Bunuel

In exam how will I quickly get to the number 99 in statement 1? Please show me the process
Math Expert
Joined: 02 Sep 2009
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04 Dec 2014, 03:50
Raihanuddin wrote:
Hi, Bunuel

In exam how will I quickly get to the number 99 in statement 1? Please show me the process

Let me ask a question: what other multiple of 18 can you get by adding two single-digit numbers (out of which one is non-zero)?
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Joined: 11 Sep 2013
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04 Dec 2014, 08:37
Ok got it thanks
Intern
Joined: 21 Dec 2015
Posts: 1

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13 Jan 2016, 13:30
i am not sure i understand the question properly. does it mean the # will be greater than 50 or not or sum of two digits will be greater than 50 or not. If it is by # it self, 99 is greater than 50, but I think 42 works as well. 4+2=6 is multiple of 18 and 42 less than 50.
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Joined: 02 Sep 2009
Posts: 51214

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13 Jan 2016, 23:32
rtommy wrote:
i am not sure i understand the question properly. does it mean the # will be greater than 50 or not or sum of two digits will be greater than 50 or not. If it is by # it self, 99 is greater than 50, but I think 42 works as well. 4+2=6 is multiple of 18 and 42 less than 50.

6 is NOT a multiple of 18, it's a factor of 18.
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Joined: 16 Jan 2018
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15 Aug 2018, 09:39
Bunuel wrote:
rtommy wrote:
i am not sure i understand the question properly. does it mean the # will be greater than 50 or not or sum of two digits will be greater than 50 or not. If it is by # it self, 99 is greater than 50, but I think 42 works as well. 4+2=6 is multiple of 18 and 42 less than 50.

6 is NOT a multiple of 18, it's a factor of 18.

Hi Bunuel

MY question is the following:

Assuming that 1 is a multiple of all integers, couldn't statement 1 also be interpreted as:
x+Y=1 X=1 Y=0 ->number is 10 (which is a 2 digit positive number and respects the premises)
Since there is no restriction of XorY being non zero, other than together must for a two digit integer, this option should be contemplated and therefore statement becomes invalid (an actually correct answer would be E)

What do you think?

Thank you very much,
Math Expert
Joined: 02 Sep 2009
Posts: 51214

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15 Aug 2018, 12:48
bpegenaute wrote:
Bunuel wrote:
rtommy wrote:
i am not sure i understand the question properly. does it mean the # will be greater than 50 or not or sum of two digits will be greater than 50 or not. If it is by # it self, 99 is greater than 50, but I think 42 works as well. 4+2=6 is multiple of 18 and 42 less than 50.

6 is NOT a multiple of 18, it's a factor of 18.

Hi Bunuel

MY question is the following:

Assuming that 1 is a multiple of all integers, couldn't statement 1 also be interpreted as:
x+Y=1 X=1 Y=0 ->number is 10 (which is a 2 digit positive number and respects the premises)
Since there is no restriction of XorY being non zero, other than together must for a two digit integer, this option should be contemplated and therefore statement becomes invalid (an actually correct answer would be E)

What do you think?

Thank you very much,

1 is not a multiple of every integer, it's a FACTOR (a divisor) of every integer.
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Re: M02-31 &nbs [#permalink] 15 Aug 2018, 12:48
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# M02-31

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