Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 22 Jun 2010
Posts: 34

The positive integers r, s, and t are such that r is [#permalink]
Show Tags
28 Jul 2010, 02:01
1
This post received KUDOS
13
This post was BOOKMARKED
Question Stats:
47% (01:24) correct 53% (01:29) wrong based on 497 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 45429

The positive integers r, s, and t are such that r is [#permalink]
Show Tags
28 Jul 2010, 02:22
1
This post received KUDOS
Expert's post
9
This post was BOOKMARKED
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 22 Jun 2010
Posts: 34

Re: pretty hard one [#permalink]
Show Tags
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 ?



Math Expert
Joined: 02 Sep 2009
Posts: 45429

Re: pretty hard one [#permalink]
Show Tags
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 Ctrap question: the question which is obviously sufficient if we take statements together. When we see such questions we should become very suspicious.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 24 Apr 2010
Posts: 56

Re: pretty hard one [#permalink]
Show Tags
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...



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1902

Re: Even or Odd [#permalink]
Show Tags
07 Sep 2011, 02:40
jamifahad 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. r/s>Integer s/t>Integer (1) st is odd. Both s and t are odd. r=9; s=3; t=1 r=6; s=3; t=1 Not Sufficient. (2) rt is even. Either r or t or both are even. r=even. Fantastic. t=Even; s becomes even; t has to be even. See this: s/t=Integer; t=Even; s=Even*Integer=Even; r/s=Integer; s=Even; r=Even*Integer=Even; So, r is definitely even. Sufficient. Ans: "B"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1472
Location: United States (IN)
Concentration: Strategy, Technology

Re: Even or Odd [#permalink]
Show Tags
07 Sep 2011, 02:44
(1) st is odd means that s and t are odd, but r can be even or odd e.g r = 10, s = 5, t = 1 r = 15, s = 5, t = 1 Insufficient (2) If rt is even then at least one of t or r is even So r = k*s s = m*t => r = k*m*t (where k and m are positive integers) => rt = r * r/(km) = r^2/km is an even integer (as per question) => r^2 is even => r is even Sufficient Answer  B
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 10 Mar 2014
Posts: 214

Re: pretty hard one [#permalink]
Show Tags
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.



Math Expert
Joined: 02 Sep 2009
Posts: 45429

Re: pretty hard one [#permalink]
Show Tags
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: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 09 Apr 2017
Posts: 38
Location: United States
GMAT 1: 690 Q47 V38 GMAT 2: 720 Q48 V41
GPA: 3.5

Re: The positive integers r, s, and t are such that r is [#permalink]
Show Tags
23 Jun 2017, 07:04
This is how I solved it:
Is r even?
r is divisible by s, hence r = ns s is divisible by t, hence s = mt combining, r = nmt
1> st = odd. This implies, both s and t are odd. no impact on r. insuff. 2 > rt = even Hence, r = even or t = even or both = even If t = even, then r = nmt = even If r = odd, then r is even for rt = even Suff.



Manager
Joined: 05 Nov 2014
Posts: 115
Location: India
Concentration: Strategy, Operations
GPA: 3.75

Re: The positive integers r, s, and t are such that r is [#permalink]
Show Tags
24 Jun 2017, 06:41
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.
Solution:
The Tricky part in this question is to remember that r,s and t are integers.
Statement 1: No information about r is given. r can be either even or odd. Insufficient.
Statement 2: r has to be even as Odd number divided by odd will never yield a even number and Odd number divided by even will not yield a integer. Therefore r must be even.
Answer :Option B.



Manager
Joined: 23 Jul 2015
Posts: 163

Re: The positive integers r, s, and t are such that r is [#permalink]
Show Tags
08 Aug 2017, 09:02
r = sx s = ty
r = tyx
1. st is odd O = O*y ==> y = odd r = O*O*x.. we don't know x. Therefore, not sufficient
2. rt = even r = tyx O=E*y*x or E = O*y*x
evaluate whether both outcomes are possible. when r is odd t, y, and x must be odd which is not possible since t is even in this case.
thus, r is even
Ans. B



Director
Joined: 12 Nov 2016
Posts: 776
Location: United States
GRE 1: 315 Q157 V158
GPA: 2.66

Re: The positive integers r, s, and t are such that r is [#permalink]
Show Tags
27 Sep 2017, 00:44
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. The thing about these problems is that even though they appear to be very simple math they are designed to be very misleading Statement 1 you could have 12 3 1 or 9 3 1 insuff Statement 2 R cannot be odd because t has to be a multiple of 2  because t has to be a factor of r suff B



Manager
Joined: 19 Aug 2016
Posts: 77

Re: The positive integers r, s, and t are such that r is [#permalink]
Show Tags
18 Oct 2017, 08:39
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. What happens when t is odd?



Math Expert
Joined: 02 Sep 2009
Posts: 45429

Re: The positive integers r, s, and t are such that r is [#permalink]
Show Tags
18 Oct 2017, 08:43
zanaik89 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. What happens when t is odd? For (2) if t is odd then r must be even right away, because rt=even.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics




Re: The positive integers r, s, and t are such that r is
[#permalink]
18 Oct 2017, 08:43






