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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] New post 28 Jul 2010, 01:01
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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.
[Reveal] Spoiler: OA
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Re: pretty hard one [#permalink] New post 28 Jul 2010, 01:22
Expert's post
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] New post 28 Jul 2010, 01:37
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] New post 28 Jul 2010, 01:44
Expert's post
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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: pretty hard one [#permalink] New post 07 Aug 2010, 02:44
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] New post 07 Aug 2010, 04:47
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] New post 27 Apr 2014, 02:01
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] New post 28 Apr 2014, 01:27
Expert's post
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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: pretty hard one   [#permalink] 28 Apr 2014, 01:27
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