Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44628

New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 07:56
32
This post received KUDOS
Expert's post
162
This post was BOOKMARKED
The next set of medium/hard PS algebra questions. I'll post OA's with detailed explanations after some discussion. Please, post your solutions along with the answers.1. If \(x=\sqrt[4]{x^3+6x^2}\), then the sum of all possible solutions for x is:A. 2 B. 0 C. 1 D. 3 E. 5 Solution: https://gmatclub.com/forum/newalgebra ... l#p12009482. The equation x^2 + ax  b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0 is 3. What is the value of b?A. 64 B. 16 C. 15 D. 1/16 E. 1/64 Solution: https://gmatclub.com/forum/newalgebra ... l#p12009503. If a and b are positive numbers, such that a^2 + b^2 = m and a^2  b^2 = n, then ab in terms of m and n equals to:A. \(\frac{\sqrt{mn}}{2}\) B. \(\frac{\sqrt{mn}}{2}\) C. \(\frac{\sqrt{m^2n^2}}{2}\) D. \(\frac{\sqrt{n^2m^2}}{2}\) E. \(\frac{\sqrt{m^2+n^2}}{2}\) Solution: https://gmatclub.com/forum/newalgebra ... l#p12009564. What is the maximum value of 3x^2 + 12x 2y^2  12y  39 ?A. 39 B. 9 C. 0 D. 9 E. 39 Solution: https://gmatclub.com/forum/newalgebra ... l#p12009625. If x^2 + 2x 15 = m, where x is an integer from 10 and 10, inclusive, what is the probability that m is greater than zero?A. 2/7 B. 1/3 C. 7/20 D. 2/5 E. 3/7 Solution: https://gmatclub.com/forum/newalgebra ... l#p12009706. If mn does not equal to zero, and m^2n^2 + mn = 12, then m could be:I. 4/n II. 2/n III. 3/n A. I only B. II only C. III only D. I and II only E. I and III only Solution: https://gmatclub.com/forum/newalgebra ... l#p12009737. If x^4 = 29x^2  100, then which of the following is NOT a product of three possible values of x? I. 50 II. 25 III. 50 A. I only B. II only C. III only D. I and II only E. I and III only Solution: https://gmatclub.com/forum/newalgebra ... l#p12009758. If m is a negative integer and m^3 + 380 = 381m , then what is the value of m?A. 21 B. 20 C. 19 D. 1 E. None of the above Solution: https://gmatclub.com/forum/newalgebra ... l#p12009809. If \(x=(\sqrt{5}\sqrt{7})^2\), then the best approximation of x is:A. 0 B. 1 C. 2 D. 3 E. 4 Solution: https://gmatclub.com/forum/newalgebra ... l#p120098210. If f(x) = 2x  1 and g(x) = x^2, then what is the product of all values of n for which f(n^2)=g(n+12) ?A. 145 B. 24 C. 24 D. 145 E. None of the above Solution: https://gmatclub.com/forum/newalgebra ... l#p1200987Kudos points for each correct solution!!!
_________________
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: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1353
GRE 1: 1540 Q800 V740

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 11:55
2
This post received KUDOS
@Bunuel, for Q5, shouldn't the original question also say that we are only looking for solutions where x is an integer? For this to be satisfied, in x^2 + 2x 15 = m, 4  4(m15)>0 and 44(m15) must be a perfect square => 4 (16m) must be a perfect square and >0 => 16m must be a perfect square and >0 The only values that satisfy this for 10<=m<=10 are m=9,0,7 of which only 7 is positive => probability = 1/3
_________________
GyanOne  Top MBA Rankings and MBA Admissions Blog
Top MBA Admissions Consulting  Top MiM Admissions Consulting
Premium MBA Essay ReviewBest MBA Interview PreparationExclusive GMAT coaching
Get a FREE Detailed MBA Profile Evaluation  Call us now +91 98998 31738



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:00



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:05
2. The equation x^2 + ax  b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0 is 3. What is the value of b? A. 64 B. 16 C. 15 D. 1/16 E. 1/64 Let the roots of \(x^2 + ax +b = 0\) are h and h So sum of the roots i.e \(2h = a\) and product of the roots i.e \(h^2 = b\) Now one root of \(x^2 + ax + 15=0\) is 5 So the other root must be 5 as the product is 15. So \(a =  (5+3) = 8\) So, \(8 = 2h\) or, \(h=4\) So \(b = 4^2 = 16\) B it is
_________________
Have an MBA application Question? ASK ME ANYTHING!
My Stuff: Four Years to 760  MBA Trends for Indian Applicants
My GMAT Resources V30V40: How to do it!  GMATPrep SC  GMATPrep CR  GMATPrep RC  Critical Reasoning Megathread  CR: Numbers and Statistics  CR: Weaken  CR: Strengthen  CR: Assumption  SC: Modifier  SC: Meaning  SC: SV Agreement  RC: Primary Purpose  PS/DS: Numbers and Inequalities  PS/DS: Combinatorics and Coordinates
My MBA Resources Everything about the MBA Application  OverRepresented MBA woes  Fit Vs Rankings  Low GPA: What you can do  Letter of Recommendation: The Guide  Indian B Schools accepting GMAT score  Why MBA?
My Reviews Veritas Prep Live Online



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:11



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:17



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:33
5. If x^2 + 2x 15 = m, where m is an integer from 10 and 10, inclusive, what is the probability that m is greater than zero? A. 2/7 B. 1/3 C. 7/20 D. 2/5 E. 3/7 x^2 + 2x  15 =m or x^2 + 2x + (m15) = 0 or (x+5)(x3) = m Now since m is an integer so x must also be an integer. x=1 m= 12 NO x=2 m= 7 YES x=3 m= 0 YES x=4 m= 9 YES x=5 m= 20 NO No further values will satisfy! So m has 3 values so far! x= 0 m= 15 NO x= 1 m= 16 NO x= 2 m= 15 NO x= 3 m= 12 NO x= 4 m= 7 YES x= 5 m= 0 YES x= 6 m= 9 YES x= 7 m= 20 NO SO m can take 3 values 7, 0 and 9 and only ONE of them is greater than 0 SO the probability is 1/3 B
_________________
Have an MBA application Question? ASK ME ANYTHING!
My Stuff: Four Years to 760  MBA Trends for Indian Applicants
My GMAT Resources V30V40: How to do it!  GMATPrep SC  GMATPrep CR  GMATPrep RC  Critical Reasoning Megathread  CR: Numbers and Statistics  CR: Weaken  CR: Strengthen  CR: Assumption  SC: Modifier  SC: Meaning  SC: SV Agreement  RC: Primary Purpose  PS/DS: Numbers and Inequalities  PS/DS: Combinatorics and Coordinates
My MBA Resources Everything about the MBA Application  OverRepresented MBA woes  Fit Vs Rankings  Low GPA: What you can do  Letter of Recommendation: The Guide  Indian B Schools accepting GMAT score  Why MBA?
My Reviews Veritas Prep Live Online



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:42



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:47
8. If m is a negative integer and m^3 + 380 = 381m , then what is the value of m? A. 21 B. 20 C. 19 D. 1 E. None of the above Lets just start with the bottom and solve 1 clearly does not work lets see for m = 19 and I have a good feeling because 380 is divisible by 19 \(19*19*19 + 380\) \(= 19(19^220)\) \(=19(36120)\) Not working Lets try 20 \(20^3 + 380\) \(= 20(40019)\) \(=20(381)\) \(=381m\) BINGO B
_________________
Have an MBA application Question? ASK ME ANYTHING!
My Stuff: Four Years to 760  MBA Trends for Indian Applicants
My GMAT Resources V30V40: How to do it!  GMATPrep SC  GMATPrep CR  GMATPrep RC  Critical Reasoning Megathread  CR: Numbers and Statistics  CR: Weaken  CR: Strengthen  CR: Assumption  SC: Modifier  SC: Meaning  SC: SV Agreement  RC: Primary Purpose  PS/DS: Numbers and Inequalities  PS/DS: Combinatorics and Coordinates
My MBA Resources Everything about the MBA Application  OverRepresented MBA woes  Fit Vs Rankings  Low GPA: What you can do  Letter of Recommendation: The Guide  Indian B Schools accepting GMAT score  Why MBA?
My Reviews Veritas Prep Live Online



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:50



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 13:53



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
18 Mar 2013, 16:15



VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1036
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: New Algebra Set!!! [#permalink]
Show Tags
19 Mar 2013, 01:15
souvik101990 wrote: 4. What is the maximum value of 3x^2 + 12x 2y^2  12y  39 ?
A. 39 B. 9 C. 0 D. 9 E. 39
differentiating with respect to x and equating with 0
\(6x + 12 = 0, OR x=2\)
differentiating with respect to y and equating with 0
\(4y  12 =0, OR y=3\)
So max value of the expression \(3x^2 + 12x 2y^2  12y  39\) is at (2, 3) i.e 12+2418+3639 = 9 B Hi Souvik I liked ur approach cn u pls expand on it...i mean is there any hard and fast rule that u r following.....completely missed this question.... Archit



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 621

Re: New Algebra Set!!! [#permalink]
Show Tags
19 Mar 2013, 01:48
1
This post received KUDOS
4. 3x^2 + 12x 2y^2  12y  39 = 3x^2+12x122y^212y1839+18+12 = 3(x2)^22(y+3)^2 9. Now a negative sign is attached to both the squares. Thus the maximum value is at x=2 and y=3 and equals 9. B.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
19 Mar 2013, 01:57
Archit143 wrote: souvik101990 wrote: 4. What is the maximum value of 3x^2 + 12x 2y^2  12y  39 ?
A. 39 B. 9 C. 0 D. 9 E. 39
differentiating with respect to x and equating with 0
\(6x + 12 = 0, OR x=2\)
differentiating with respect to y and equating with 0
\(4y  12 =0, OR y=3\)
So max value of the expression \(3x^2 + 12x 2y^2  12y  39\) is at (2, 3) i.e 12+2418+3639 = 9 B Hi Souvik I liked ur approach cn u pls expand on it...i mean is there any hard and fast rule that u r following.....completely missed this question.... Archit I used calculus maxima minima. However you are free to use the "completing the square" method where you are left with 2 perfect squares and a 9 as the guy above me did.
_________________
Have an MBA application Question? ASK ME ANYTHING!
My Stuff: Four Years to 760  MBA Trends for Indian Applicants
My GMAT Resources V30V40: How to do it!  GMATPrep SC  GMATPrep CR  GMATPrep RC  Critical Reasoning Megathread  CR: Numbers and Statistics  CR: Weaken  CR: Strengthen  CR: Assumption  SC: Modifier  SC: Meaning  SC: SV Agreement  RC: Primary Purpose  PS/DS: Numbers and Inequalities  PS/DS: Combinatorics and Coordinates
My MBA Resources Everything about the MBA Application  OverRepresented MBA woes  Fit Vs Rankings  Low GPA: What you can do  Letter of Recommendation: The Guide  Indian B Schools accepting GMAT score  Why MBA?
My Reviews Veritas Prep Live Online



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 621

Re: New Algebra Set!!! [#permalink]
Show Tags
Updated on: 19 Mar 2013, 05:40
1
This post received KUDOS
8.\(m^3 + 380 = 381m\) or m^3m = 380(m1) or m(m1)(m+1) = 380(m1) AS m !=1, thus, m(m+1) = 380 = 19*20 Thus, as m<0, only m=20 satisfies. B.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions
Originally posted by mau5 on 19 Mar 2013, 02:17.
Last edited by mau5 on 19 Mar 2013, 05:40, edited 1 time in total.



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 621

Re: New Algebra Set!!! [#permalink]
Show Tags
19 Mar 2013, 02:25
1
This post received KUDOS
9. x = \((\sqrt{5}\sqrt{7})^2\) As from the given options we know that x>0. Thus, I can safely write that \(\sqrt{x} = \sqrt{7}\sqrt{5}\) or \(\sqrt{7} = \sqrt{x} +\sqrt{5}\) x can not be 1 or more than 1 as then \(\sqrt{7}\)>3 which is not true. Thus, on approximation, x=0. A.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 621

Re: New Algebra Set!!! [#permalink]
Show Tags
19 Mar 2013, 02:30
1
This post received KUDOS
7. \(x^4 = 29x^2  100\) or \(x^4  29x^2+100 = 0\) Let \(x^2 = t\), thus \(t^229+100 = 0\) or (t25)(t4) = 0 t = 25 > x = 5/5 or t = 4 > x = 2/2 Out of any three possible values of x, only 25 is not possible. B.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Director
Joined: 25 Apr 2012
Posts: 704
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: New Algebra Set!!! [#permalink]
Show Tags
Updated on: 19 Mar 2013, 17:10
1
This post received KUDOS
Hello Bunuel, Nice set of Questions Here goes my solutions 10. If f(x) = 2x  1 and g(x) = x^2, then what is the product of all values of n for which f(n^2)=g(n+12) ?[/b] Sol: From the given function we have f(n^2)=g(n+12) > 2n^21= (n+12)^2 Solving this eqn we get n^2  24n  145= 0> n^2 29n+ 5n  145 =0 Possible values of n are 29 and 5. Product will be 145 and hence ans is option A
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Originally posted by WoundedTiger on 19 Mar 2013, 07:05.
Last edited by WoundedTiger on 19 Mar 2013, 17:10, edited 1 time in total.



Intern
Joined: 29 Dec 2012
Posts: 3
Concentration: Finance, International Business
WE: Information Technology (Computer Software)

Re: New Algebra Set!!! [#permalink]
Show Tags
19 Mar 2013, 10:57
GyanOne wrote: 4. 3x^2 + 12x 2y^2  12y  39 = 3(x^2 + 4x  13) + 2(y^26y)
Now x^2 +4x  13 has its maximum value at x = 4/2 = 2 and y^2  6y has its maximum value at y=6/2 = 3 Therefore max value of the expression = 3(4 + 8 13) + 2 (9+18) = 27 + 18 = 9
Should be B Hi GyanOne, Can you please explain how you found x/y which gives max value for the 2 cases here? Is there a formula?



MBA Section Director
Joined: 19 Mar 2012
Posts: 4935
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: New Algebra Set!!! [#permalink]
Show Tags
19 Mar 2013, 11:18
NeverQuit wrote: GyanOne wrote: 4. 3x^2 + 12x 2y^2  12y  39 = 3(x^2 + 4x  13) + 2(y^26y)
Now x^2 +4x  13 has its maximum value at x = 4/2 = 2 and y^2  6y has its maximum value at y=6/2 = 3 Therefore max value of the expression = 3(4 + 8 13) + 2 (9+18) = 27 + 18 = 9
Should be B Hi GyanOne, Can you please explain how you found x/y which gives max value for the 2 cases here? Is there a formula? \(3x^2 + 12x 2y^2  12y  39\) \(=3(x^24x)2(y^2+6y) 39\) \(=3(x^24x+44)2(y^2+6y+99)39\) \(=3(x2)^2 +12 2(y+3)^2 +18 39\) NOW The above expression will be minimum IFF \((x2)^2=0\) and \((y+3)^2=0\) which leaves the maximum value to be \(12+1839=9\)
_________________
Have an MBA application Question? ASK ME ANYTHING!
My Stuff: Four Years to 760  MBA Trends for Indian Applicants
My GMAT Resources V30V40: How to do it!  GMATPrep SC  GMATPrep CR  GMATPrep RC  Critical Reasoning Megathread  CR: Numbers and Statistics  CR: Weaken  CR: Strengthen  CR: Assumption  SC: Modifier  SC: Meaning  SC: SV Agreement  RC: Primary Purpose  PS/DS: Numbers and Inequalities  PS/DS: Combinatorics and Coordinates
My MBA Resources Everything about the MBA Application  OverRepresented MBA woes  Fit Vs Rankings  Low GPA: What you can do  Letter of Recommendation: The Guide  Indian B Schools accepting GMAT score  Why MBA?
My Reviews Veritas Prep Live Online




Re: New Algebra Set!!!
[#permalink]
19 Mar 2013, 11:18



Go to page
Previous
1 2 3 4 5 6 7
Next
[ 139 posts ]



