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M02-31

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M02-31  [#permalink]

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New post 15 Sep 2014, 23:18
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A
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E

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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Re M02-31  [#permalink]

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New post 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.


Answer: A
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Re: M02-31  [#permalink]

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New post 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
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Re: M02-31  [#permalink]

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New post 04 Dec 2014, 03:50
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Re: M02-31  [#permalink]

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New post 04 Dec 2014, 08:37
Ok got it thanks
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Re: M02-31  [#permalink]

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New post 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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Re: M02-31  [#permalink]

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New post 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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Re: M02-31  [#permalink]

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New post 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

As always super helpful on your explanations

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,
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Re: M02-31  [#permalink]

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New post 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

As always super helpful on your explanations

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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New to the Math Forum?
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M02-31 &nbs [#permalink] 15 Aug 2018, 12:48
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