December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST. December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 07 Aug 2012
Posts: 20

If S and T are nonzero numbers and
[#permalink]
Show Tags
Updated on: 04 Nov 2012, 14:06
Question Stats:
35% (02:00) correct 65% (01:24) wrong based on 229 sessions
HideShow timer Statistics
If S and T are nonzero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true? A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above M1819 Explanation provided:
1/S + 1/T = S+T;
T+S/ST = S+T→;
Crossmultiply: S+T=(S+T)∗ST;
(S+T)(ST−1)=0. Either S+T=0 or ST=1. Now, notice that if S+T=0 is true then none of the options must be true.
The correct answer is E
Question: I understand the way of the equation, however, what I would have done is interfere at the following step: S+T = (S+T)*ST > (S+T)/(S+T)=ST > ST = 1
Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ??
Thanks in advance, best regards
P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Exhaust your body, proceed your mind, cultivate your soul.
Originally posted by SirGMAT on 04 Nov 2012, 07:20.
Last edited by Bunuel on 04 Nov 2012, 14:06, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 51100

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
04 Nov 2012, 14:08




Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 595
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: GMATClub M1819  Arithmetic: Equations
[#permalink]
Show Tags
04 Nov 2012, 07:46
SirGMAT wrote: If S and T are nonzero numbers and 1S+1T=S+T, which of the following must be true? A. ST=1 B. S+T=1 C. 1/S=T D. S/T=1 E. none of the above Explanation provided: 1/S + 1/T = S+T; T+S/ST = S+T→; Crossmultiply: S+T=(S+T)∗ST; (S+T)(ST−1)=0. Either S+T=0 or ST=1. Now, notice that if S+T=0 is true then none of the options must be true. The correct answer is E Question: I understand the way of the equation, however, what I would have done is interfere at the following step: S+T = (S+T)*ST > (S+T)/(S+T)=ST > ST = 1 Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ?? Thanks in advance, best regards P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere. Yes, this is not correct way of cancelling. I'll show you one example. 5* 0 = 3*0 if we cancel 0 on both side, we get 5=3. is it correct? No. The crux (and the rule) is, we can cancel out a term only when we know its not 0. So the way it is done in explanation is absolutely correct and the right method. Hope it helps
_________________
Lets Kudos!!! Black Friday Debrief



VP
Joined: 02 Jul 2012
Posts: 1178
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: GMATClub M1819  Arithmetic: Equations
[#permalink]
Show Tags
04 Nov 2012, 08:43
SirGMAT wrote: If S and T are nonzero numbers and 1S+1T=S+T, which of the following must be true?
A. ST=1 B. S+T=1 C. 1/S=T D. S/T=1 E. none of the above
Explanation provided:
1/S + 1/T = S+T;
T+S/ST = S+T→;
Crossmultiply: S+T=(S+T)∗ST;
(S+T)(ST−1)=0. Either S+T=0 or ST=1. Now, notice that if S+T=0 is true then none of the options must be true.
The correct answer is E
Question: I understand the way of the equation, however, what I would have done is interfere at the following step: S+T = (S+T)*ST > (S+T)/(S+T)=ST > ST = 1
Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ??
Thanks in advance, best regards
P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere. There was this fun derivation that my math teacher showed us in school. Just to demonstrate how cancelling of 0 could yield wrong results. He claimed that he could prove that 1=2 and hence all numbers are equal. It goes as below: Let, \(a=b\) Multiplying both sides by a, We get \(a^2 = ab\) Subtracting \(b^2\) from both sides \(a^2  b^2 = ab  b^2\) \((a+b)(ab) = b(ab)\) Cancelling \((ab)\) on both sides, \(a+b = b\) Since \(a=b\) \(a+a = a\) \(2a = a\) \(2=1\)
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Intern
Joined: 07 Aug 2012
Posts: 20

Re: GMATClub M1819  Arithmetic: Equations
[#permalink]
Show Tags
04 Nov 2012, 14:06
Vips0000 wrote: Yes, this is not correct way of cancelling. I'll show you one example. 5* 0 = 3*0 if we cancel 0 on both side, we get 5=3. is it correct? No. The crux (and the rule) is, we can cancel out a term only when we know its not 0. So the way it is done in explanation is absolutely correct and the right method. Hope it helps Thanks  lol I am an idiot  ...! I even thought of the zero number things, but mistakenly memorized the prompt as telling me that the respective equation could not be "0", though it only said that each number alone is nonzero.... Thanks guys!
_________________
Exhaust your body, proceed your mind, cultivate your soul.



Manager
Joined: 27 Dec 2011
Posts: 60

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
07 Nov 2012, 00:12
Hi bunuel,
In this step: s+t = (s+t)st can't we just cancel (s+t) and get > st =1?
thanks, K



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1134
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
07 Nov 2012, 00:19
Bunuel wrote: If S and T are nonzero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true?
A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above
OE:
\(\frac{1}{S} + \frac{1}{T} = S + T\) > \(\frac{T+S}{ST}=S+T\) > crossmultiply: \(S+T=(S+T)*ST\) > \((S+T)(ST1)=0\) > either \(S+T=0\) or \(ST=1\). So, if \(S+T=0\) is true then none of the options must be true.
Answer: E.
Bunuel, in your solution I need to ask one thing. Inequalities, there is a rule that if you dont know the sign of denominator, then dont cross multiply. In your solution, how can you be so sure of the sign of ST. Please let me know if i am missing something
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Math Expert
Joined: 02 Sep 2009
Posts: 51100

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
07 Nov 2012, 01:30
kartik222 wrote: Hi bunuel,
In this step: s+t = (s+t)st can't we just cancel (s+t) and get > st =1?
thanks, K Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.So, if you divide (reduce) s+t = (s+t)st by (s+t), you assume, with no ground for it, that (s+t) does not equal to zero thus exclude a possible solution (notice that both st=1 AND (s+t)=0 satisfy the equation). Hope it's clear.
_________________
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



Math Expert
Joined: 02 Sep 2009
Posts: 51100

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
07 Nov 2012, 01:43
Marcab wrote: Bunuel wrote: If S and T are nonzero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true?
A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above
OE:
\(\frac{1}{S} + \frac{1}{T} = S + T\) > \(\frac{T+S}{ST}=S+T\) > crossmultiply: \(S+T=(S+T)*ST\) > \((S+T)(ST1)=0\) > either \(S+T=0\) or \(ST=1\). So, if \(S+T=0\) is true then none of the options must be true.
Answer: E.
Bunuel, in your solution I need to ask one thing. Inequalities, there is a rule that if you dont know the sign of denominator, then dont cross multiply. In your solution, how can you be so sure of the sign of ST. Please let me know if i am missing something We are concerned with the sign when we crossmultiply an inequality because this operation might affect (flip) its sign (> to <, for example) but it's always safe to crossmultiply an equation.
_________________
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



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1134
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
07 Nov 2012, 02:05



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 449
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
10 Feb 2013, 05:03
Bunuel wrote: If S and T are nonzero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true?A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above OE:\(\frac{1}{S} + \frac{1}{T} = S + T\) > \(\frac{T+S}{ST}=S+T\) > crossmultiply: \(S+T=(S+T)*ST\) > \((S+T)(ST1)=0\) > either \(S+T=0\) or \(ST=1\). So, if \(S+T=0\) is true then none of the options must be true. Answer: E. P.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Please pay attention to the rule #3. Thank you. Bunuel, Since S+T=0 OR ST=1 and the question asks what must be true, the answer is E ? Another way to answer the question. . Is my reasoning right?
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Math Expert
Joined: 02 Sep 2009
Posts: 51100

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
10 Feb 2013, 05:09
Sachin9 wrote: Bunuel wrote: If S and T are nonzero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true?A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above OE:\(\frac{1}{S} + \frac{1}{T} = S + T\) > \(\frac{T+S}{ST}=S+T\) > crossmultiply: \(S+T=(S+T)*ST\) > \((S+T)(ST1)=0\) > either \(S+T=0\) or \(ST=1\). So, if \(S+T=0\) is true then none of the options must be true. Answer: E. P.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Please pay attention to the rule #3. Thank you. Bunuel, Since S+T=0 OR ST=1 and the question asks what must be true, the answer is E ? Another way to answer the question. . Is my reasoning right? Yes, if for example s=1 and t=1 (s+t=11=0), then none of the options is true (none of the options MUST be true).
_________________
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



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 449
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
10 Feb 2013, 06:04
I understand what you are trying to say bunuel.. my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true.. So based on this reasoning, can we say the answer is E..? For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2.. Hope you are getting what I am trying to ask..
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 595
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
10 Feb 2013, 13:55
Sachin9 wrote: I understand what you are trying to say bunuel.. my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true..
So based on this reasoning, can we say the answer is E..?
For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2..
Hope you are getting what I am trying to ask.. I would say that don't generalize this point. You know that because there are two solutions, any of the given options need not be a MUST. But if u really have an option that says (s+t)(st1)=0 then that MUST be true.
_________________
Lets Kudos!!! Black Friday Debrief



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 449
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
10 Feb 2013, 18:17
Vips0000 wrote: Sachin9 wrote: I understand what you are trying to say bunuel.. my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true..
So based on this reasoning, can we say the answer is E..?
For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2..
Hope you are getting what I am trying to ask.. I would say that don't generalize this point. You know that because there are two solutions, any of the given options need not be a MUST. But if u really have an option that says (s+t)(st1)=0 then that MUST be true. But if u really have an option that says (s+t)(st1)=0 then that MUST be true. Ididn;t understand this.. if (s+t)(st1)=0 then either s+t=0 or st1=0.. we still have a OR here
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 595
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
11 Feb 2013, 00:59
Sachin9 wrote: Vips0000 wrote: Sachin9 wrote: I understand what you are trying to say bunuel.. my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true..
So based on this reasoning, can we say the answer is E..?
For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2..
Hope you are getting what I am trying to ask.. I would say that don't generalize this point. You know that because there are two solutions, any of the given options need not be a MUST. But if u really have an option that says (s+t)(st1)=0 then that MUST be true. But if u really have an option that says (s+t)(st1)=0 then that MUST be true. Ididn;t understand this.. if (s+t)(st1)=0 then either s+t=0 or st1=0.. we still have a OR here If the question were to be this: If S and T are nonzero numbers and \(\frac{1}{S} + \frac{1}{T} = S + T\), which of the following must be true? A. \(ST = 1\) B. \(S + T = 1\) C. \(\frac{1}{S} = T\) D. \(\frac{S}{T} = 1\) E. None of the above F. (s+t)(st1)=0 Then your generalization will go wrong as you have an ans choice F that must hold true.
_________________
Lets Kudos!!! Black Friday Debrief



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 449
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
11 Feb 2013, 01:55
I get it Vippss. But in all other cases, the generalization will hold good right?
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 595
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
11 Feb 2013, 07:44
Sachin9 wrote: I get it Vippss. But in all other cases, the generalization will hold good right? Rules are good, generalizations are not Enjoy and practice kudos :p
_________________
Lets Kudos!!! Black Friday Debrief



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 449
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
11 Feb 2013, 07:51
Vips0000 wrote: Sachin9 wrote: I get it Vippss. But in all other cases, the generalization will hold good right? Rules are good, generalizations are not Enjoy and practice kudos :p why on earth do u need kudos u already done with ur gmat. .
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 595
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: If S and T are nonzero numbers and
[#permalink]
Show Tags
11 Feb 2013, 07:59
Sachin9 wrote: Vips0000 wrote: Sachin9 wrote: I get it Vippss. But in all other cases, the generalization will hold good right? Rules are good, generalizations are not Enjoy and practice kudos :p why on earth do u need kudos u already done with ur gmat. . Retake bro.. Coming soon
_________________
Lets Kudos!!! Black Friday Debrief




Re: If S and T are nonzero numbers and &nbs
[#permalink]
11 Feb 2013, 07:59



Go to page
1 2
Next
[ 28 posts ]



