Find all School-related info fast with the new School-Specific MBA Forum

It is currently 14 Jul 2014, 07:45

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

NEW!!! Tough and tricky exponents and roots questions

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
38 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18532
Followers: 3197

Kudos [?]: 21480 [38] , given: 2547

NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 02:03
38
This post received
KUDOS
Expert's post
29
This post was
BOOKMARKED
Exponents and roots problems are very common on the GMAT. So, it's extremely important to know how to manipulate them, how to factor out, take roots, multiply, divide, etc. Below are 11 problems to test your skills. Please post your thought process/solutions along with the answers.

I'll post OA's with detailed solutions tomorrow. Good luck.


1. What is the value of \sqrt{25+10\sqrt{6}}+\sqrt{25-10\sqrt{6}}?
A. 2\sqrt{5}
B. \sqrt{55}
C. 2\sqrt{15}
D. 50
E. 60

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029216

2. What is the units digit of (17^3)^4-1973^{3^2}?
A. 0
B. 2
C. 4
D. 6
E. 8

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029219

3. If 5^{10x}=4,900 and 2^{\sqrt{y}}=25 what is the value of \frac{(5^{(x-1)})^5}{4^{-\sqrt{y}}?
A. 14/5
B. 5
C. 28/5
D. 13
E. 14

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029221

4. What is the value of 5+4*5+4*5^2+4*5^3+4*5^4+4*5^5?
A. 5^6
B. 5^7
C. 5^8
D. 5^9
E. 5^10

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029222

5. If x=23^2*25^4*27^6*29^8 and is a multiple of 26^n, where n is a non-negative integer, then what is the value of n^{26}-26^n?
A. -26
B. -25
C. -1
D. 0
E. 1

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029223

6. If x=\sqrt[5]{-37} then which of the following must be true?
A. \sqrt{-x}>2
B. x>-2
C. x^2<4
D. x^3<-8
E. x^4>32

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029224

7. If x=\sqrt{10}+\sqrt[3]{9}+\sqrt[4]{8}+\sqrt[5]{7}+\sqrt[6]{6}+\sqrt[7]{5}+\sqrt[8]{4}+\sqrt[9]{3}+\sqrt[10]{2}, then which of the following must be true:
A. x<6
B. 6<x<8
C. 8<x<10
D. 10<x<12
E. x>12

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029227

8. If x is a positive number and equals to \sqrt{6+{\sqrt{6+\sqrt{6+\sqrt{6+...}}}}}, where the given expression extends to an infinite number of roots, then what is the value of x?
A. \sqrt{6}
B. 3
C. 1+\sqrt{6}
D. 2\sqrt{3}
E. 6

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029228

9. If x is a positive integer then the value of \frac{22^{22x}-22^{2x}}{11^{11x}-11^x} is closest to which of the following?
A. 2^{11x}
B. 11^{11x}
C. 22^{11x}
D. 2^{22x}*11^{11x}
E. 2^{22x}*11^{22x}

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029229

10. Given that 5x=125-3y+z and \sqrt{5x}-5-\sqrt{z-3y}=0, then what is the value of \sqrt{\frac{45(z-3y)}{x}}?
A. 5
B. 10
C. 15
D. 20
E. Can not be determined

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029231

11. If x>0, x^2=2^{64} and x^x=2^y then what is the value of y?
A. 2
B. 2^(11)
C. 2^(32)
D. 2^(37)
E. 2^(64)

Solution: tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029232
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
1 KUDOS received
Intern
Intern
avatar
Joined: 12 Oct 2011
Posts: 20
Location: United States
GMAT 1: 720 Q50 V36
Followers: 0

Kudos [?]: 17 [1] , given: 5

GMAT Tests User Reviews Badge
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 11:34
1
This post received
KUDOS
4. What is the value of 5+4*5+4*5^2+4*5^3+4*5^4+4*5^5?
A. 5^6
B. 5^7
C. 5^8
D. 5^9
E. 5^10


a(r^n - 1) / (r-1)
5+4*5+4*5^2+4*5^3+4*5^4+4*5^5
1+4+4*5+4*5^2+4*5^3+4*5^4+4*5^5
1 + 4(5^6 -1)/4
5^6

Option
[Reveal] Spoiler:
A
1 KUDOS received
Intern
Intern
avatar
Joined: 12 Oct 2011
Posts: 20
Location: United States
GMAT 1: 720 Q50 V36
Followers: 0

Kudos [?]: 17 [1] , given: 5

GMAT Tests User Reviews Badge
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 11:36
1
This post received
KUDOS
5. If x=23^2*25^4*27^6*29^8 and is a multiple of 26^n, where n is a non-negative integer, then what is the value of n^26-26^n?
A. -26
B. -25
C. -1
D. 0
E. 1

n=0 because x is not a multiple of 26

n^26 - 26^n = 0-1 = -1

Option
[Reveal] Spoiler:
C
2 KUDOS received
Intern
Intern
avatar
Joined: 12 Oct 2011
Posts: 20
Location: United States
GMAT 1: 720 Q50 V36
Followers: 0

Kudos [?]: 17 [2] , given: 5

GMAT Tests User Reviews Badge
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 11:44
2
This post received
KUDOS
6. If x=\sqrt[5]{-37} then which of the following must be true?
A. \sqrt{-x}>2
B. x>-2
C. x^2<4
D. x^3<-8
E. x^4>32


x^5 = -37

-2^5 = -32
-3<x<-2

A. Eliminated
B. Eliminated
C. x^2<4 = -2<x<2 Eliminated
D. x^3<-8 Correct


Option
[Reveal] Spoiler:
D
1 KUDOS received
Intern
Intern
avatar
Joined: 12 Oct 2011
Posts: 20
Location: United States
GMAT 1: 720 Q50 V36
Followers: 0

Kudos [?]: 17 [1] , given: 5

GMAT Tests User Reviews Badge
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 11:51
1
This post received
KUDOS
8. If x is a positive number and equals to \sqrt{6+{\sqrt{6+\sqrt{6+\sqrt{6+...}}}}}, where the given expression extends to an infinite number of roots, then what is the value of x?
A. \sqrt{6}
B. 3
C. 1+\sqrt{6}
D. 2\sqrt{3}
E. 6



x= √(6+√(6+√(6+...
x^2 = 6 + x
x^2-x-6=0
(x-3)(x+2) = 0
x = 3 or -2
Value of sqrt cant be -ve
Option
[Reveal] Spoiler:
B
Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
GMAT 1: 690 Q47 V38
Followers: 11

Kudos [?]: 119 [0], given: 72

GMAT ToolKit User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 12:01
10. Given that 5x=125-3y+z and \sqrt{5x}-25-\sqrt{z-3y}=0, then what is the value of \sqrt{\frac{45(z-3y)}{x}}?
A. 5
B. 10
C. 15
D. 20
E. Can not be determined

5x-125=z-3y

sqrt{5x}-25=\sqrt{z-3y}
(sqrt{5x}-25)^2=z-3y

(sqrt{5x}-25)^2=5x-125
\sqrt{5x}=15
x=5*9=45

so the expression \sqrt{\frac{45(z-3y)}{x} = \sqrt{45(15-25)/45}=\sqrt{-10}

E is the answ
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
GMAT 1: 690 Q47 V38
Followers: 11

Kudos [?]: 119 [0], given: 72

GMAT ToolKit User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 12:07
7. If x=\sqrt{10}+\sqrt[3]{9}+\sqrt[4]{8}+\sqrt[5]{7}+\sqrt[6]{6}+\sqrt[7]{5}+\sqrt[8]{4}+\sqrt[9]{3}+\sqrt[10]{2}, then which of the following must be true:
A. x<6
B. 6<x<8
C. 8<x<10
D. 10<x<12
E. x>12

my answ to this q is intuitive.

everyone knows that sqroot10=3.16
\sqrt[3]{9} is approx \sqrt[3]{2^3} >2 (but less than 3)
the rest of roots are more than 1 and less than 2

so we have 3.16+2,..+1+1+1+1+1+1+1 = approx 12.16

E is the answ
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
GMAT 1: 690 Q47 V38
Followers: 11

Kudos [?]: 119 [0], given: 72

GMAT ToolKit User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 12:17
9. If x is a positive integer then the value of \frac{22^{22x}-22^{2x}}{11^{11x}-11^x} is closest to which of the following?
A. 2^{11x}
B. 11^{11x}
C. 22^{11x}
D. 2^{22x}*11^{11x}
E. 2^{22x}*11^{22x}


let 11=a

so we have

(2a^(2ax)-2a^2x)/(a^(ax)-a^x)=2*((a^(ax)-a^x)*(a^(ax)+a^x))/(a^(ax)-a^x)=2(a^(ax)+a^x)

2(a^(ax)+a^x)=2*(11^(11x)+11^x)
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

1 KUDOS received
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 967
Location: Toronto
Followers: 243

Kudos [?]: 618 [1] , given: 3

GMAT Tests User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 12:18
1
This post received
KUDOS
Bunuel wrote:



3. If 5^{10x}=4,900 and 2^{\sqrt{y}}=25 what is the value of \frac{5^{(x-1)^5}}{4^{-\sqrt{y}}?
A. 14/5
B. 5
C. 28/5
D. 13
E. 14


5. If x=23^2*25^4*27^6*29^8 and is a multiple of 26^n, where n is a non-negative integer, then what is the value of n^26-26^n?
A. -26
B. -25
C. -1
D. 0
E. 1



Welcome back Bunuel! :)

Some nice questions. A couple of comments:

Q5 has a typo at the end: n^26-26^n. I think you need to include the exponent 26 in braces {26} to get n^{26}-26^n

In Q3, unless I'm making some kind of stupid mistake, the value of the expression in the question is close to 600 (so isn't among the answers). I'm wondering if you meant the question to instead read something more like:


3. If 5^{10x}=4,900 and 4^{\sqrt{y}}=25 what is the value of \frac{5^{5x-1}}{2^{\sqrt{y}}?
A. 14/5
B. 5
C. 28/5
D. 13
E. 14

In that case, I get one of the five answer choices (A).
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

1 KUDOS received
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 967
Location: Toronto
Followers: 243

Kudos [?]: 618 [1] , given: 3

GMAT Tests User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 12:27
1
This post received
KUDOS
LalaB wrote:
9. If x is a positive integer then the value of \frac{22^{22x}-22^{2x}}{11^{11x}-11^x} is closest to which of the following?
A. 2^{11x}
B. 11^{11x}
C. 22^{11x}
D. 2^{22x}*11^{11x}
E. 2^{22x}*11^{22x}


let 11=a

so we have

(2a^(2ax)-2a^2x)/(a^(ax)-a^x)=2*((a^(ax)-a^x)*(a^(ax)+a^x))/(a^(ax)-a^x)=2(a^(ax)+a^x)

2(a^(ax)+a^x)=2*(11^(11x)+11^x)


And it looks as though every other question has been solved except for this one. I won't solve it completely, but I'll help people get started. Here, since we are asked for an approximation only, we don't need to compute an exact value. You might notice that if x is a positive integer, 22^{22x} is vastly bigger than 22^{2x}. Since that's true, if we only need to estimate, we can ignore the small term. We can do the same thing in the denominator.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
GMAT 1: 690 Q47 V38
Followers: 11

Kudos [?]: 119 [0], given: 72

GMAT ToolKit User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 12:40
yep, if the 3d q is -If 5^{10x}=4,900 and 4^{\sqrt{y}}=25 what is the value of \frac{5^{5x-1}}{2^{\sqrt{y}}?
A. 14/5
B. 5
C. 28/5
D. 13
E. 14""

then

5^{10x}=70^2
(5^{5x})2=70^2
5^{5x}=70

4^{\sqrt{y}}=25
2^{\sqrt{y}}=5

70/5*5=14/5 ans is A
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
GMAT 1: 690 Q47 V38
Followers: 11

Kudos [?]: 119 [0], given: 72

GMAT ToolKit User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 12:48
IanStewart wrote:

And it looks as though every other question has been solved except for this one. I won't solve it completely, but I'll help people get started. Here, since we are asked for an approximation only, we don't need to compute an exact value. You might notice that if x is a positive integer, 22^{22x} is vastly bigger than 22^{2x}. Since that's true, if we only need to estimate, we can ignore the small term. We can do the same thing in the denominator.


2a^(2ax)/a^(ax)=2*a^(ax)=2*11^(11x)

ans is
[Reveal] Spoiler:
B
?
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

1 KUDOS received
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 967
Location: Toronto
Followers: 243

Kudos [?]: 618 [1] , given: 3

GMAT Tests User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 13:31
1
This post received
KUDOS
LalaB wrote:
IanStewart wrote:

And it looks as though every other question has been solved except for this one. I won't solve it completely, but I'll help people get started. Here, since we are asked for an approximation only, we don't need to compute an exact value. You might notice that if x is a positive integer, 22^{22x} is vastly bigger than 22^{2x}. Since that's true, if we only need to estimate, we can ignore the small term. We can do the same thing in the denominator.


2a^(2ax)/a^(ax)=2*a^(ax)=2*11^(11x)

ans is
[Reveal] Spoiler:
B
?


Your substitution might be making things more difficult. If we want to estimate the value of

\frac{22^{22x}-22^{2x}}{11^{11x}-11^x}

then we can ignore the comparatively small values in the numerator and denominator; this is roughly equal to


\frac{22^{22x}}{11^{11x}}

which is equal to

\frac{22^{22x}}{11^{11x}} = \frac{2^{22x} 11^{22x}}{11^{11x}} = 2^{22x} 11^{11x}
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18532
Followers: 3197

Kudos [?]: 21480 [0], given: 2547

Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 17:00
Expert's post
IanStewart wrote:
Bunuel wrote:



3. If 5^{10x}=4,900 and 2^{\sqrt{y}}=25 what is the value of \frac{5^{(x-1)^5}}{4^{-\sqrt{y}}?
A. 14/5
B. 5
C. 28/5
D. 13
E. 14


5. If x=23^2*25^4*27^6*29^8 and is a multiple of 26^n, where n is a non-negative integer, then what is the value of n^26-26^n?
A. -26
B. -25
C. -1
D. 0
E. 1



Welcome back Bunuel! :)

Some nice questions. A couple of comments:

Q5 has a typo at the end: n^26-26^n. I think you need to include the exponent 26 in braces {26} to get n^{26}-26^n

In Q3, unless I'm making some kind of stupid mistake, the value of the expression in the question is close to 600 (so isn't among the answers). I'm wondering if you meant the question to instead read something more like:


3. If 5^{10x}=4,900 and 4^{\sqrt{y}}=25 what is the value of \frac{5^{5x-1}}{2^{\sqrt{y}}?
A. 14/5
B. 5
C. 28/5
D. 13
E. 14

In that case, I get one of the five answer choices (A).


Hello Ian. Glad to be back!

Thanks for your comments. Yes, there were 2 typos:
For Q5: included the exponent 26 in braces {26} to avoid confusion;
For Q3: added the brackets which were lost in copy/past, it should read \frac{(5^{(x-1)})^5}{4^{-\sqrt{y}}.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 17 [0], given: 1

GMAT Tests User
Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 12 Jan 2012, 20:22
Hi,
My answers are:
1 - C
2 - E
3 - E
4 - A
5 -
6 - B
7 - E
8 - B
9 -
10 - E
11 - E

Unable to solve for 5th & 9th :(
Manager
Manager
User avatar
Joined: 23 Oct 2011
Posts: 85
Followers: 0

Kudos [?]: 15 [0], given: 34

Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 13 Jan 2012, 13:39
LalaB wrote:
2. What is the units digit of (17^3)^4-1973^{3^2}?
A. 0
B. 2
C. 4
D. 6
E. 8

7^12-3^9
11-3=8

ANS IS E


Bunuel wrote:
2. What is the units digit of (17^3)^4-1973^{3^2}?
A. 0
B. 2
C. 4
D. 6
E. 8


i believe the answer is : 7^12-3^6 ---> 11-9= 2 ---> B

note: I believe the part I wrote (which i colored red) is wrong. Can someone explain why? when an exponent is raised to another exponent then what operation should we do first? - Okey! Just read the rules about routs that Bunuel posted and found my mistake! (exponentiation by stacked symbols)

Last edited by SonyGmat on 13 Jan 2012, 23:11, edited 6 times in total.
Manager
Manager
User avatar
Joined: 23 Oct 2011
Posts: 85
Followers: 0

Kudos [?]: 15 [0], given: 34

Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 13 Jan 2012, 15:09
LalaB wrote:
10. Given that 5x=125-3y+z and \sqrt{5x}-25-\sqrt{z-3y}=0, then what is the value of \sqrt{\frac{45(z-3y)}{x}}?
A. 5
B. 10
C. 15
D. 20
E. Can not be determined

5x-125=z-3y

sqrt{5x}-25=\sqrt{z-3y}
(sqrt{5x}-25)^2=z-3y

(sqrt{5x}-25)^2=5x-125
\sqrt{5x}=15
x=5*9=45

so the expression \sqrt{\frac{45(z-3y)}{x} = \sqrt{45(15-25)/45}=\sqrt{-10}

E is the answ


bunuel wrote:
10. Given that 5x=125-3y+z and \sqrt{5x}-25-\sqrt{z-3y}=0, then what is the value of \sqrt{\frac{45(z-3y)}{x}}?
A. 5
B. 10
C. 15
D. 20
E. Can not be determined


We know that:

5x=125-3y+z ---> [highlight]z-3y=5x-125 (1)[/highlight]

and that:

\sqrt{5x}-25-\sqrt{z-3y}=0 ---> \sqrt{5x}-25=\sqrt{z-3y} ----> [\sqrt{5x}-25]^2=[\sqrt{z-3y}]^2 ----> using (1): [\sqrt{5x}-25]^2=[\sqrt{5x-125}]^2 --->

5x-50\sqrt{5x}+625=5x-125 ---> 50\sqrt{5x}=750 ---> \sqrt{5x}=15 ---> 5x=15*15--->[[highlight]x=45 (2)[/highlight]

(1), (2) ---> z-3y=5*45-125--->[highlight]z-3y=100 (3)[/highlight]

therefore: \sqrt{\frac{45(z-3y)}{x}} ---->using (2),(3) :\sqrt{\frac{45*100}{45}} ---> 10 ---->B
Manager
Manager
User avatar
Status: Employed
Joined: 17 Nov 2011
Posts: 101
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 4

Kudos [?]: 74 [0], given: 10

Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 13 Jan 2012, 18:42
IanStewart wrote:
Bunuel wrote:



3. If 5^{10x}=4,900 and 2^{\sqrt{y}}=25 what is the value of \frac{5^{(x-1)^5}}{4^{-\sqrt{y}}?
A. 14/5
B. 5
C. 28/5
D. 13
E. 14


5. If x=23^2*25^4*27^6*29^8 and is a multiple of 26^n, where n is a non-negative integer, then what is the value of n^26-26^n?
A. -26
B. -25
C. -1
D. 0
E. 1



Welcome back Bunuel! :)

Some nice questions. A couple of comments:

Q5 has a typo at the end: n^26-26^n. I think you need to include the exponent 26 in braces {26} to get n^{26}-26^n

In Q3, unless I'm making some kind of stupid mistake, the value of the expression in the question is close to 600 (so isn't among the answers). I'm wondering if you meant the question to instead read something more like:


3. If 5^{10x}=4,900 and 4^{\sqrt{y}}=25 what is the value of \frac{5^{5x-1}}{2^{\sqrt{y}}?
A. 14/5
B. 5
C. 28/5
D. 13
E. 14

In that case, I get one of the five answer choices (A).


The answer should be E. 14

Here is how:

5^{10x}=4900
so {(5^{5x})}^2=70^2

Take square root of both sides >

so 5^{5x}=70

Also from question stem:

2^{\sqrt{y}} = 5^2

So (from the question stem)

4^{-\sqrt{y}} = \frac{1}{4^{\sqrt{y}}}
4^{-\sqrt{y}} = (\frac{1}{2^{\sqrt{y}}})^2 = \frac{1}{5^4}

Now 5^{(x-1)^5}

Should be \frac{5^{5x}}{5^5}

We know 5^{10x}=4900

so 5^{10x}=70^2

so 5^{5x}=70

So \frac{(5^{(x-1)})^5}{4^{-\sqrt{y}}

is basically \frac{5^x}{5^5}*5^4

We already know the value of 5^x which is 70

So now it becomes \frac{70}{5^5}*5^4

Which should resolve to 14

Hence Answer = E = 14
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

1 KUDOS received
Manager
Manager
User avatar
Status: Employed
Joined: 17 Nov 2011
Posts: 101
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 4

Kudos [?]: 74 [1] , given: 10

Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 13 Jan 2012, 20:05
1
This post received
KUDOS
Q1.

\sqrt{25+10\sqrt{6}}+\sqrt{25-10\sqrt{6}}

First look and we know that this is of the type:

let a = \sqrt{25+10\sqrt{6}}

Let b = \sqrt{25-10\sqrt{6}}

let a+b=x

Then (a+b)^2=x^2

So a^2+b^2+2ab=x^2

So a^2 = {25+10\sqrt{6}}
So b^2 = {25-10\sqrt{6}}
So a^2+b^2=50

Now on to 2ab

a=\sqrt{25+10\sqrt{6}}
b=\sqrt{25-10\sqrt{6}}

let ab=y

then \sqrt{25+10\sqrt{6}}*\sqrt{25-10\sqrt{6}}=y
So ({25+10\sqrt{6}})*({25-10\sqrt{6}})=y^2
so 625-600=y^2
so y=5
so 2ab=2y=10
so x^2=a^2+b^2+2ab=50+10=60
so x^2=60
so x=\sqrt{4*15}
so x=2\sqrt{15}

Hence Answer is C. 2\sqrt{15}
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

1 KUDOS received
Manager
Manager
User avatar
Status: Employed
Joined: 17 Nov 2011
Posts: 101
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 4

Kudos [?]: 74 [1] , given: 10

Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 13 Jan 2012, 20:35
1
This post received
KUDOS
Q2. What is the units digit of (17^3)^4-1973^{3^2}?[/b]

Now we know that:

(17^3)^4 = (17^6)^2

So the expression now becomes

(17^6)^2 - (1973^3)^2

Now we know that a^2-b^2 can be written as (a+b)*(a-b)

Let a=17^6 and b=1973^3

Now on to (a+b)*(a-b)

(17^6+1973^3)*(17^6-1973^3)

Lets see what the units digit of 17^6 is:
We are only concerned with 7:
7*7*7*7*7*7= ..........9 unit digit of 9

Lets see what the units digit of 1973^3 is:
We are only concerned with 3:
3*3*3= ..........7 unit digit of 7

Lets translate this into our expression for (a+b)*(a-b)

(17^6+1973^3)*(17^6-1973^3)

Should in digit terms give:

(9+7)*(9-7)
(6)*(2)

Should Yield a units digit of 2.

Hence Answer = 2
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

1 KUDOS received
Manager
Manager
User avatar
Status: Employed
Joined: 17 Nov 2011
Posts: 101
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 4

Kudos [?]: 74 [1] , given: 10

Re: NEW!!! Tough and tricky exponents and roots questions [#permalink] New post 13 Jan 2012, 20:45
1
This post received
KUDOS
Q3.

5^{10x}=4900
so {(5^{5x})}^2=70^2

Take square root of both sides >

so 5^{5x}=70

Also from question stem:

2^{\sqrt{y}} = 5^2

So (from the question stem)

4^{-\sqrt{y}} = \frac{1}{4^{\sqrt{y}}}
4^{-\sqrt{y}} = (\frac{1}{2^{\sqrt{y}}})^2 = \frac{1}{5^4}

Now 5^{(x-1)^5}

Should be \frac{5^{5x}}{5^5}

We know 5^{10x}=4900

so 5^{10x}=70^2

so 5^{5x}=70

So \frac{(5^{(x-1)})^5}{4^{-\sqrt{y}}

is basically \frac{5^x}{5^5}*5^4

We already know the value of 5^x which is 70

So now it becomes \frac{70}{5^5}*5^4

Which should resolve to 14

Hence Answer = E = 14
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Re: NEW!!! Tough and tricky exponents and roots questions   [#permalink] 13 Jan 2012, 20:45
    Similar topics Author Replies Last post
Similar
Topics:
75 Experts publish their posts in the topic NEW!!! Tough and tricky exponents and roots questions Bunuel 60 12 Jan 2012, 02:50
1 A tricky question about Exponents Lstadt 4 26 Jul 2011, 11:31
2 Tricky Exponents Question tonebeeze 6 13 Apr 2011, 12:23
Experts publish their posts in the topic Important question on roots and exponents benjiboo 5 02 Nov 2009, 10:52
Tricky Exponents Question lfox2 3 27 Jun 2006, 02:21
Display posts from previous: Sort by

NEW!!! Tough and tricky exponents and roots questions

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   3   4   5   6   7   8    Next  [ 151 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.