Author 
Message 
TAGS:

Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 542
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
Updated on: 19 Jun 2017, 04:59
Question Stats:
56% (01:15) correct 44% (01:21) wrong based on 1199 sessions
HideShow timer Statistics
If q, s, and t are all different numbers, is q < s < t ? (1) t  q = t  s + s  q (2) t > q
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges
Originally posted by AbdurRakib on 19 Jun 2017, 04:44.
Last edited by Bunuel on 19 Jun 2017, 04:59, edited 1 time in total.
Renamed the topic and edited the question.




Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 596

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
19 Jun 2017, 13:27
AbdurRakib wrote: If q, s, and t are all different numbers, is q < s < t ?
(1) t  q = t  s + s  q
(2) t > q With less math: Start with statement 2. This is insufficient, since s could be greater than t, or s could be between q and t. Eliminate answers B and D.Statement 1: When you see x  y, think 'distance between x and y on the number line'. That's all that means. So, this statement says that t  q is equal to the distance between t and s, plus the distance between s and q. In other words, s has to be between t and q. Jot down some diagrams on your paper to convince yourself of that: in order for the distances to make sense, s has to be in the middle. Also, tq has to be positive, since it's the sum of two absolute values. So, t is greater than q. If t is greater than q and s is in the middle, you know that q < s < t. Sufficient.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 49268

If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
19 Jun 2017, 05:28
If q, s, and t are all different numbers, is q < s < t ?(1) t  q = t  s + s  q Notice that the right hand side is positive (it's the sum of two absolute values, so two nonnegative values, in fact, in our case two positive values, since we know that the variables are distinct). Thus the left hand side must also be positive, which means that t > q. So, we can have 3 cases for s: a. sqtIn this case \(s < q < t\): \(t  s > 0\) and \(s  q < 0\), which would mean that \(t  s = t s\) and \(s  q = (s  q)\) (recall that x = x when x > 0 and x = x when x <= 0). So, \(t  s + s  q = (t s)  (s  q) = t  2s + q\). So, in his case we'd have \(t  q = t  2s + q\) or \(q=s\). But we are told that q, s, and t are all different numbers, so this case is out. b. qstIn this case \(q < s < t\): \(t  s > 0\) and \(s  q > 0\), which would mean that \(t  s = t s\) and \(s  q = s  q\). So, \(t  s + s  q = (t s) + (s  q) = t  q\). This matches the info given in the statement. c. qtsIn this case \(q < t < s\): \(t  s < 0\) and \(s  q > 0\), which would mean that \(t  s = (t s)\) and \(s  q = s  q\). So, \(t  s + s  q = (t s) + (s  q) = t + 2s  q\). So, in his case we'd have \(t  q = t + 2s  q\) or \(t=s\). But we are told that q, s, and t are all different numbers, so this case is out. Only q < s < t case is possible. Sufficient. (2) t > q. Not sufficient. Answer: A.
_________________
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: 14 Jul 2017
Posts: 9

If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
22 Aug 2017, 06:38
Could someone please explain the little struggle I'm having with Option B)?
If we want to prove that q < s < t, that means that also q < t (regardless of the placement of s).
Now B tells us, that q > t, hence q < t can't be true at the same time? Can't I conclude that q < s < t doesn't hold when q > t and clearly answer the question with a no?
What mistake am I making here?



Math Expert
Joined: 02 Sep 2009
Posts: 49268

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
22 Aug 2017, 07:08



Intern
Joined: 14 Jul 2017
Posts: 9

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
22 Aug 2017, 07:10
Bunuel wrote: Vezax27 wrote: Could someone please explain the little struggle I'm having with Option B)?
If we want to prove that q < s < t, that means that also q < t (regardless of the placement of s).
Now B tells us, that q > t, hence q < t can't be true at the same time? Can't I conclude that q < s < t doesn't hold when q > t and clearly answer the question with a no?
What mistake am I making here? We want to answer whether q < s < t and (2) says that t > q, NOT q > t. Oh gosh, how stupid of me... Guess I need a break for the day



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3517
Location: United States (CA)

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
17 Nov 2017, 12:48
AbdurRakib wrote: If q, s, and t are all different numbers, is q < s < t ?
(1) t  q = t  s + s  q
(2) t > q We need to determine whether q < s < t, given that q, s, and t are all different numbers. Statement One Alone: t  q = t  s + s  q Since q, s, and t are different numbers, both t  s and s  q are positive quantities, and their sum t  s + s  q will also be positive. This also makes the lefthand side t  q positive. Since t  q > 0, we have t > q. We know t > q, but we still have to determine whether s is between them. That is, is q < s < t? We have three scenarios to consider. (1) If q < s < t, then t > s and s > q, and then: t  q = t  s + s  q t  q = t  q We see that this equation holds true: t  q = t  s + s  q, and furthermore q < s < t. (2) If s < q < t, then t > s and q > s, and thus t s is positive while s  q is negative, and we have: t  s + s  q t  s + [(s  q)] t  s  s + q t  2s + q ≠ t  q Since t  2s + q ≠ t  q, the equation does not hold and we can’t have s < q < t. (3) If q < t < s, then s > t and s > q, and thus t  s is negative while s  q is positive, and we have: t  s + s  q (t  s) + s  q t + s + s  q t + 2s  q Since t + 2s  q ≠ t  q, we see that the equation does not hold, so we can’t have q < t < s. We see that only scenario 1 is true if t  q = t  s + s  q, and we do have q < s < t. Statement one alone is sufficient. Statement Two Alone: t > q We know t > q, but we still have to determine whether s is between them. It’s possible that q < s < t, but it is also possible that s < q < t or q < t < s. Since we don’t know anything about s, we can’t determine which case is valid. Statement two alone is not sufficient. Answer: A
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Senior Manager
Joined: 29 Jun 2017
Posts: 427

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
15 Dec 2017, 10:11
the fastest way to solve this is to draw the number line qts look at 1 absolute value is the length of the line section if s is in between, the answer is yes s can not be outside qt because if s is so, we can not have condition 1. remember /sq/= the line of sq. length sq can not be length of sq+length of ts.
that is all.



Manager
Joined: 15 Aug 2015
Posts: 62
Location: India
GPA: 3.21

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
23 Dec 2017, 14:26
Bunuel wrote: If q, s, and t are all different numbers, is q < s < t ?
(1) t  q = t  s + s  q
Notice that the right hand side is positive (it's the sum of two absolute values, so two nonnegative values, in fact, in our case two positive values, since we know that the variables are distinct). Thus the left hand side must also be positive, which means that t > q. So, we can have 3 cases for s:
a. sqt In this case \(s < q < t\): \(t  s > 0\) and \(s  q < 0\), which would mean that \(t  s = t s\) and \(s  q = (s  q)\) (recall that x = x when x > 0 and x = x when x <= 0). So, \(t  s + s  q = (t s)  (s  q) = t  2s + q\).
So, in his case we'd have \(t  q = t  2s + q\) or \(q=s\). But we are told that q, s, and t are all different numbers, so this case is out.
b. qst In this case \(q < s < t\): \(t  s > 0\) and \(s  q > 0\), which would mean that \(t  s = t s\) and \(s  q = s  q\). So, \(t  s + s  q = (t s) + (s  q) = t  q\).
This matches the info given in the statement.
c. qts In this case \(q < t < s\): \(t  s < 0\) and \(s  q > 0\), which would mean that \(t  s = (t s)\) and \(s  q = s  q\). So, \(t  s + s  q = (t s) + (s  q) = t + 2s  q\).
So, in his case we'd have \(t  q = t + 2s  q\) or \(t=s\). But we are told that q, s, and t are all different numbers, so this case is out.
Only q < s < t case is possible. Sufficient.
(2) t > q. Not sufficient.
Answer: A. Bunnuel I tried it in this way . Is it right or wrong given If q, s, and t are all different numbers, is q < s < t ? or is 0<sq<tq? Since i am doing the same operation on all the parts on inequality it doesn't violates any rule i suppose ST 1 t  q = t  s + s  q Here tq is positive ( sum of two mod's) and also greater than sq as something is been added to s  q Now this equation can be solved in two ways only either same sign or opposite sign of mods same sign leads tq= ts +sq lhs=rhs therefore 0<sq<tq different signs lead to tq= ts s+q ,,,,,, not possible or tq = t+s+sq ,,,,,, again lhs is not equal to rhs . this means that the case sq<0<tq doesnt holds Hence st 1 is sufficient st 2 clearly not suficient hence a



Intern
Joined: 07 Mar 2018
Posts: 2

If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
23 Mar 2018, 01:07
AbdurRakib wrote: If q, s, and t are all different numbers, is q < s < t ?
(1) t  q = t  s + s  q
(2) t > q This seems pretty easy and faster with picking numbers, try numbers in the given order 1,2,3 assigned for q,s,t respectively then try with a different order 1,3,2. In first case the equation in the first option will satisfy i.e LHS=RHS, while in the second case it will fail. Hence the the numbers should be in ascending order to satisfy the first option, so 1st option is suff. In second case no detail about s, so insuff. So answer is A.



Manager
Joined: 29 Jan 2015
Posts: 87
Location: India
Concentration: Marketing, Entrepreneurship
GPA: 3.7
WE: Information Technology (Internet and New Media)

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
28 Jun 2018, 06:12
Would anyone please explain this question by plugging in value ?
Thanks in advance.



Intern
Joined: 03 Jan 2016
Posts: 4

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
18 Jul 2018, 09:57
Hi,
I have a quick question: Why is (i) is sufficient? Considering we have a total of four mutually exclusive cases with (i) and only one of them follows or is true and rest are not. This fact alone makes (i) insufficient? Please help. Thanks



Director
Joined: 09 Mar 2016
Posts: 863

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
26 Aug 2018, 05:09
Bunuel wrote: If q, s, and t are all different numbers, is q < s < t ?
(1) t  q = t  s + s  q
Notice that the right hand side is positive (it's the sum of two absolute values, so two nonnegative values, in fact, in our case two positive values, since we know that the variables are distinct). Thus the left hand side must also be positive, which means that t > q. So, we can have 3 cases for s:
a. sqt In this case \(s < q < t\): \(t  s > 0\) and \(s  q < 0\), which would mean that \(t  s = t s\) and \(s  q = (s  q)\) (recall that x = x when x > 0 and x = x when x <= 0). So, \(t  s + s  q = (t s)  (s  q) = t  2s + q\).
So, in his case we'd have \(t  q = t  2s + q\) or \(q=s\). But we are told that q, s, and t are all different numbers, so this case is out.
b. qst In this case \(q < s < t\): \(t  s > 0\) and \(s  q > 0\), which would mean that \(t  s = t s\) and \(s  q = s  q\). So, \(t  s + s  q = (t s) + (s  q) = t  q\).
This matches the info given in the statement.
c. qts In this case \(q < t < s\): \(t  s < 0\) and \(s  q > 0\), which would mean that \(t  s = (t s)\) and \(s  q = s  q\). So, \(t  s + s  q = (t s) + (s  q) = t + 2s  q\).
So, in his case we'd have \(t  q = t + 2s  q\) or \(t=s\). But we are told that q, s, and t are all different numbers, so this case is out.
Only q < s < t case is possible. Sufficient.
(2) t > q. Not sufficient.
Answer: A. Bunuel can you pls explain how from this \(t  q = t  2s + q\) you deduce that \(q=s\)
_________________
In English I speak with a dictionary, and with people I am shy.



Math Expert
Joined: 02 Sep 2009
Posts: 49268

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
26 Aug 2018, 05:16
dave13 wrote: Bunuel wrote: If q, s, and t are all different numbers, is q < s < t ?
(1) t  q = t  s + s  q
Notice that the right hand side is positive (it's the sum of two absolute values, so two nonnegative values, in fact, in our case two positive values, since we know that the variables are distinct). Thus the left hand side must also be positive, which means that t > q. So, we can have 3 cases for s:
a. sqt In this case \(s < q < t\): \(t  s > 0\) and \(s  q < 0\), which would mean that \(t  s = t s\) and \(s  q = (s  q)\) (recall that x = x when x > 0 and x = x when x <= 0). So, \(t  s + s  q = (t s)  (s  q) = t  2s + q\).
So, in his case we'd have \(t  q = t  2s + q\) or \(q=s\). But we are told that q, s, and t are all different numbers, so this case is out.
b. qst In this case \(q < s < t\): \(t  s > 0\) and \(s  q > 0\), which would mean that \(t  s = t s\) and \(s  q = s  q\). So, \(t  s + s  q = (t s) + (s  q) = t  q\).
This matches the info given in the statement.
c. qts In this case \(q < t < s\): \(t  s < 0\) and \(s  q > 0\), which would mean that \(t  s = (t s)\) and \(s  q = s  q\). So, \(t  s + s  q = (t s) + (s  q) = t + 2s  q\).
So, in his case we'd have \(t  q = t + 2s  q\) or \(t=s\). But we are told that q, s, and t are all different numbers, so this case is out.
Only q < s < t case is possible. Sufficient.
(2) t > q. Not sufficient.
Answer: A. Bunuel can you pls explain how from this \(t  q = t  2s + q\) you deduce that \(q=s\) \(t  q = t  2s + q\); Cancel t: \( q =  2s + q\); Rearrange: \(2s= q + q\); \(2s=2q\); \(q=s\).
_________________
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: 11 Jan 2018
Posts: 79
Location: United States
GPA: 3.32
WE: Operations (Retail)

If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
Updated on: 15 Sep 2018, 14:09
msram45 wrote: AbdurRakib wrote: If q, s, and t are all different numbers, is q < s < t ?
(1) t  q = t  s + s  q
(2) t > q This seems pretty easy and faster with picking numbers, try numbers in the given order 1,2,3 assigned for q,s,t respectively then try with a different order 1,3,2. In first case the equation in the first option will satisfy i.e LHS=RHS, while in the second case it will fail. Hence the the numbers should be in ascending order to satisfy the first option, so 1st option is suff. In second case no detail about s, so insuff. So answer is A. You got the answer right, but your approach wouldn't qualify statement 1. Am I wrong to think that way? 1. one way: q= 1, s= 2, and t= 3 tq = lt  sl + ls  ql 31 = l3  2l + l2  1l 2 = l1l + l1l sufficient second way: q= 1, s = 3, and t = 2 tq = lt  sl + ls  ql 21 = l23l + l31l 1 = l1l + l2l 1 does not equal 3, therefore choosing q=1, s=3, and t=2 cannot be right numbers to verify. I get it that t has to be great than s since second way doesn't yield the equation right. But how do we ensure that this will always hold true for any numbers we use?
Originally posted by hanamana on 15 Sep 2018, 14:01.
Last edited by hanamana on 15 Sep 2018, 14:09, edited 1 time in total.



Manager
Joined: 11 Jan 2018
Posts: 79
Location: United States
GPA: 3.32
WE: Operations (Retail)

Re: If q, s, and t are all different numbers, is q < s < t ?
[#permalink]
Show Tags
15 Sep 2018, 14:07
ccooley wrote: AbdurRakib wrote: If q, s, and t are all different numbers, is q < s < t ?
(1) t  q = t  s + s  q
(2) t > q With less math: Start with statement 2. This is insufficient, since s could be greater than t, or s could be between q and t. Eliminate answers B and D.Statement 1: When you see x  y, think 'distance between x and y on the number line'. That's all that means. So, this statement says that t  q is equal to the distance between t and s, plus the distance between s and q. In other words, s has to be between t and q. Jot down some diagrams on your paper to convince yourself of that: in order for the distances to make sense, s has to be in the middle. Also, tq has to be positive, since it's the sum of two absolute values. So, t is greater than q. If t is greater than q and s is in the middle, you know that q < s < t. Sufficient. This is awesome. Made it so much easier to understand. Thank you.




Re: If q, s, and t are all different numbers, is q < s < t ? &nbs
[#permalink]
15 Sep 2018, 14:07






