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The positive integers r, s, and t are such that r is

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The positive integers r, s, and t are such that r is [#permalink]

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The positive integers r, s, and t are such that r is divisible by s and s is divisible by t. Is r even?

(1) st is odd.
(2) rt is even.
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Re: pretty hard one [#permalink]

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mehdiov wrote:
The positive integers r, s, and t are such that r is divisible by s
and s is divisible by t. Is r even?
(1) st is odd.
(2) rt is even.


(1) \(st=odd\), clearly not sufficient as no info about \(r\), for example if \(r=6\), \(s=1\) and \(t=1\) then answer is YES but if \(r=3\), \(s=1\) and \(t=1\) then the answer is NO.

(2) \(rt=even\). For product of 2 integers to be even either one or both must be even. Can \(r\) not to be even? The only chance would be if \(t\) is even and \(r\) is odd. Let's check if this scenario is possible: if \(t\) is even, so must be \(s\), as \(s\) is divisible by \(t\) (if an integer is divisible by even it's even too). Now, if \(s\) is even so must be \(r\) by the very same reasoning. So scenario when \(r\) is not even is not possible --> \(r=even\). Sufficient.

Answer: B.
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Re: pretty hard one [#permalink]

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New post 28 Jul 2010, 02:37
Bunuel wrote:
mehdiov wrote:
The positive integers r, s, and t are such that r is divisible by s
and s is divisible by t. Is r even?
(1) st is odd.
(2) rt is even.


(1) \(st=odd\), clearly not sufficient as no info about \(r\), for example if \(r=6\), \(s=1\) and \(t=1\) then answer is YES but if \(r=3\), \(s=1\) and \(t=1\) then the answer is NO.

(2) \(rt=even\). For product of 2 integers to be even either one or both must be even. Can \(r\) not to be even? The only chance would be if \(t\) is even and \(r\) is odd. Let's check if this scenario is possible: if \(t\) is even, so must be \(s\), as \(s\) is divisible by \(t\) (if an integer is divisible by even it's even too). Now, if \(s\) is even so must be \(r\) by the very same reasoning. So scenario when \(r\) is not even is not possible --> \(r=even\). Sufficient.

Answer: B.

many thanks looks easy after the explanation :)

Do you have an idea about the level of this question ?
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Re: pretty hard one [#permalink]

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New post 28 Jul 2010, 02:44
mehdiov wrote:
Bunuel wrote:
mehdiov wrote:
The positive integers r, s, and t are such that r is divisible by s
and s is divisible by t. Is r even?
(1) st is odd.
(2) rt is even.


(1) \(st=odd\), clearly not sufficient as no info about \(r\), for example if \(r=6\), \(s=1\) and \(t=1\) then answer is YES but if \(r=3\), \(s=1\) and \(t=1\) then the answer is NO.

(2) \(rt=even\). For product of 2 integers to be even either one or both must be even. Can \(r\) not to be even? The only chance would be if \(t\) is even and \(r\) is odd. Let's check if this scenario is possible: if \(t\) is even, so must be \(s\), as \(s\) is divisible by \(t\) (if an integer is divisible by even it's even too). Now, if \(s\) is even so must be \(r\) by the very same reasoning. So scenario when \(r\) is not even is not possible --> \(r=even\). Sufficient.

Answer: B.

many thanks looks easy after the explanation :)

Do you have an idea about the level of this question ?


Not very hard (600+) but tricky, as it's C-trap question: the question which is obviously sufficient if we take statements together. When we see such questions we should become very suspicious.
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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

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Re: pretty hard one [#permalink]

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New post 07 Aug 2010, 03:44
Not very hard (600+) but tricky, as it's C-trap question: the question which is obviously sufficient if we take statements together. When we see such questions we should become very suspicious.[/quote]



what is C-trap?
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Re: pretty hard one [#permalink]

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New post 07 Aug 2010, 05:47
Bunuel wrote:

(1) \(st=odd\), clearly not sufficient as no info about \(r\), for example if \(r=6\), \(s=1\) and \(t=1\) then answer is YES but if \(r=3\), \(s=1\) and \(t=1\) then the answer is NO.
Answer: B.

thanks...i was able to get to B but may be in 3 minutes.....
i complicated the question thinking like 2 4 8 and not thinking infact one can be one number or 2 numbers can be same 8 2 2 and so on...
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Re: pretty hard one [#permalink]

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New post 27 Apr 2014, 03:01
Bunuel wrote:
mehdiov wrote:
The positive integers r, s, and t are such that r is divisible by s
and s is divisible by t. Is r even?
(1) st is odd.
(2) rt is even.


(1) \(st=odd\), clearly not sufficient as no info about \(r\), for example if \(r=6\), \(s=1\) and \(t=1\) then answer is YES but if \(r=3\), \(s=1\) and \(t=1\) then the answer is NO.

(2) \(rt=even\). For product of 2 integers to be even either one or both must be even. Can \(r\) not to be even? The only chance would be if \(t\) is even and \(r\) is odd. Let's check if this scenario is possible: if \(t\) is even, so must be \(s\), as \(s\) is divisible by \(t\) (if an integer is divisible by even it's even too). Now, if \(s\) is even so must be \(r\) by the very same reasoning. So scenario when \(r\) is not even is not possible --> \(r=even\). Sufficient.

Answer: B.


HI Bunnel,

I have a doubt on this.

Generally we treat both the statements as seprate statements. then why are you mixing them.

If I will go with st2 i can r can be even or odd because rt = even ( r and t both can be even or one of them is even) now if we refer even to r and t then st1 will contradict.

is this the reason you are not considering both r and t as even?

Please clarify

Thanks.
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Re: pretty hard one [#permalink]

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New post 28 Apr 2014, 02:27
PathFinder007 wrote:
Bunuel wrote:
mehdiov wrote:
The positive integers r, s, and t are such that r is divisible by s
and s is divisible by t. Is r even?
(1) st is odd.
(2) rt is even.


(1) \(st=odd\), clearly not sufficient as no info about \(r\), for example if \(r=6\), \(s=1\) and \(t=1\) then answer is YES but if \(r=3\), \(s=1\) and \(t=1\) then the answer is NO.

(2) \(rt=even\). For product of 2 integers to be even either one or both must be even. Can \(r\) not to be even? The only chance would be if \(t\) is even and \(r\) is odd. Let's check if this scenario is possible: if \(t\) is even, so must be \(s\), as \(s\) is divisible by \(t\) (if an integer is divisible by even it's even too). Now, if \(s\) is even so must be \(r\) by the very same reasoning. So scenario when \(r\) is not even is not possible --> \(r=even\). Sufficient.

Answer: B.


HI Bunnel,

I have a doubt on this.

Generally we treat both the statements as seprate statements. then why are you mixing them.

If I will go with st2 i can r can be even or odd because rt = even ( r and t both can be even or one of them is even) now if we refer even to r and t then st1 will contradict.

is this the reason you are not considering both r and t as even?

Please clarify

Thanks.


The statements do not contradict: st is odd and rt is even is possible when r is even and both s and t are odd.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
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Re: The positive integers r, s, and t are such that r is [#permalink]

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Re: The positive integers r, s, and t are such that r is   [#permalink] 02 Jun 2016, 12:25
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