Can we find better ways to handle this problem.
[spoiler]OA  E; Source: Grockit[/spoiler]
DS  interesting problem
This topic has expert replies

 Legendary Member
 Posts: 784
 Joined: 03 Apr 2011
 Thanked: 114 times
 Followed by:12 members
My answer is B.IfÂ x Î¦ y = (2x  y)/(2y  x),Â where x â‰ 2y, then isÂ (a Î¦ b) > (b Î¦ a)?
(1)Â a < b
(2)Â 2a < b
St1 is insufficient (inequality will change sign based on different numbers chosen, for example (a, b) = (1, 3) and (a, b) = (2, 3)).
St2 is sufficient. Both (aÎ¦b) and (bÎ¦a) will be negative, and LHS > RHS.

 Legendary Member
 Posts: 784
 Joined: 03 Apr 2011
 Thanked: 114 times
 Followed by:12 members
sT2 is also not sufficient check with (5, 1)edge wrote:My answer is B.IfÂ x Î¦ y = (2x  y)/(2y  x),Â where x â‰ 2y, then isÂ (a Î¦ b) > (b Î¦ a)?
(1)Â a < b
(2)Â 2a < b
St1 is insufficient (inequality will change sign based on different numbers chosen, for example (a, b) = (1, 3) and (a, b) = (2, 3)).
St2 is sufficient. Both (aÎ¦b) and (bÎ¦a) will be negative, and LHS > RHS.
 GMATGuruNY
 GMAT Instructor
 Posts: 15532
 Joined: 25 May 2010
 Location: New York, NY
 Thanked: 13060 times
 Followed by:1897 members
 GMAT Score:790
Question: Is (2ab)/(2ba) > (2ba)/(2ab)?IfÂ x Î¦ y = (2x  y)/(2y  x),Â where x â‰ 2y, then isÂ (a Î¦ b) > (b Î¦ a)?
(1)Â a < b
(2)Â 2a < b
Look for values that satisfy both statements.
Statements 1 and 2: a < b and 2a < b.
Let a=1 and b=3.
2ab = 2*1  3 = 1.
2ba = 2*3  1 = 5.
Is (2ab)/(2ba) > (2ba)/(2ab)?
1/5 > 5/1
1/5 > 5.
Yes.
Let a = 3 and b = 1.
2ab = 2(3)  (1) = 5.
2ba = 2(1)  (3) = 1.
Is (2ab)/(2ba) > (2ba)/(2ab)?
5/1 > 1/5
5 > 1/5.
No.
Since in the first case the answer is Yes and in the second case the answer is No, both statements combined are insufficient.
The correct answer is E.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
hi all. it seems that it is kind of problems in which plugging and obtaining yes and no answer works better than any other ways, i honestly tried to simplify but looks like it does not work here
at first we need to determine
does ((2ab)/(2ba))>((2ba)/2ab))
after simplify i got
does (a^2b^2)/((2ba)(2ab)) not great relieve....
(1)b=3, a=1. provided that b>a (3>1)
(23)/(61)=1/5
(61)/23)=5 as a result 1/5>5 and the answer is yes
but b=1, a=3 (b>a)
(61)/(2+3)=7/5
and the right part of the inequality=5/7, here the answer is no as 7/5<5/7 so 1 st insuff
(2) the same values for a and b works here as for st1
b=3, a=1.3>2*1, and the answer is yes
b=1, a=3, 1>2(3) the answer is no
both: the same values work for combined st
3a<2b
a=1,b=3 3*1<2*3 the answer is yes
a=3 b=1, 3*(3)<2*1 the answer is no
so E looks valid answer
at first we need to determine
does ((2ab)/(2ba))>((2ba)/2ab))
after simplify i got
does (a^2b^2)/((2ba)(2ab)) not great relieve....
(1)b=3, a=1. provided that b>a (3>1)
(23)/(61)=1/5
(61)/23)=5 as a result 1/5>5 and the answer is yes
but b=1, a=3 (b>a)
(61)/(2+3)=7/5
and the right part of the inequality=5/7, here the answer is no as 7/5<5/7 so 1 st insuff
(2) the same values for a and b works here as for st1
b=3, a=1.3>2*1, and the answer is yes
b=1, a=3, 1>2(3) the answer is no
both: the same values work for combined st
3a<2b
a=1,b=3 3*1<2*3 the answer is yes
a=3 b=1, 3*(3)<2*1 the answer is no
so E looks valid answer

 Legendary Member
 Posts: 784
 Joined: 03 Apr 2011
 Thanked: 114 times
 Followed by:12 members
Thanks Mitch. I always enjoy the simplicity of all your posts. Thanks.
Could you suggest how shall we pick nos to solve DS problems, esp when the problem involves 2 variables. Do you recommend some standard approach for the same.
thanks.
Patanjali
 sl750
 Master  Next Rank: 500 Posts
 Posts: 496
 Joined: 07 Jun 2011
 Thanked: 38 times
 Followed by:1 members
The question asks whether 3(ab)(a+b)/(2ba)(2ab) > 0 ?
For statement 1 a<b,
a=1,b=3 (For b=2, we get a divide by zero)
3(2)(4)/(5)(1) > 0
a=3,b=1
3(2)(4)/(1)(5) < 0. eliminate A and D
For statement 2 2a<b,
a=1,b=3, we get a yes,
a=3,b=1, we get a no. eliminate B
Combining both, we don't get any new information. So answer is E
For statement 1 a<b,
a=1,b=3 (For b=2, we get a divide by zero)
3(2)(4)/(5)(1) > 0
a=3,b=1
3(2)(4)/(1)(5) < 0. eliminate A and D
For statement 2 2a<b,
a=1,b=3, we get a yes,
a=3,b=1, we get a no. eliminate B
Combining both, we don't get any new information. So answer is E
 GMATGuruNY
 GMAT Instructor
 Posts: 15532
 Joined: 25 May 2010
 Location: New York, NY
 Thanked: 13060 times
 Followed by:1897 members
 GMAT Score:790
Try to determine what's being tested.patanjali.purpose wrote:
Thanks Mitch. I always enjoy the simplicity of all your posts. Thanks.
Could you suggest how shall we pick nos to solve DS problems, esp when the problem involves 2 variables. Do you recommend some standard approach for the same.
thanks.
Patanjali
The DS question above is about inequalities: whether one value is greater than another.
Both a and b are being subtracted.
Subtracting a positive number yields a decrease; subtracting a negative number yields an increase.
Hence the approach that I used above: trying both positive and negative values for a and b that satisfy the two statements.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
IF a(b)=(2ab)/(2ba) THEN b(a)=(2a (2ab)/(2ba)) / (2*(2ab)/(2ba)  a)
Simplifying, b(a)=b/(2ba) / (2ab)/(ba) = b(ba) / (2ba)(2ab)
We compare a(b) and b(a) OR (2ab)/(2ba) and b(ba) / (2ba)(2ab)
We may cancel out (2ba) in the denominators to get (2ab) and b(ba)/(2ab)
Further we may notice that (2ab) is repeated in the numerator and denominator, so we handle it as (2ab)^2 and b(ba)
The main question is whether (2ab)^2 > b(ba), we can immediately check that if b(ba)<0 then the answer is Yes, because the LHS will be squared and positive.
St(1) a<b implies that a is less than b merely, and we don't know either the value nor the sign of b. Hence Insuff
St(2) 2a<b the same as statement 1
Combining both we get no additional info, hence answer is E
Simplifying, b(a)=b/(2ba) / (2ab)/(ba) = b(ba) / (2ba)(2ab)
We compare a(b) and b(a) OR (2ab)/(2ba) and b(ba) / (2ba)(2ab)
We may cancel out (2ba) in the denominators to get (2ab) and b(ba)/(2ab)
Further we may notice that (2ab) is repeated in the numerator and denominator, so we handle it as (2ab)^2 and b(ba)
The main question is whether (2ab)^2 > b(ba), we can immediately check that if b(ba)<0 then the answer is Yes, because the LHS will be squared and positive.
St(1) a<b implies that a is less than b merely, and we don't know either the value nor the sign of b. Hence Insuff
St(2) 2a<b the same as statement 1
Combining both we get no additional info, hence answer is E
 Attachments

 Function.doc
 (32 KiB) Downloaded 31 times
Success doesn't come overnight!