GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Nov 2018, 17:46

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     November 18, 2018

     November 18, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

M26-28

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
M26-28  [#permalink]

Show Tags

New post 16 Sep 2014, 00:26
2
25
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (01:59) correct 55% (01:58) wrong based on 191 sessions

HideShow timer Statistics

If \(x=\frac{(8!)^{10}-(8!)^6}{(8!)^{5}-(8!)^3}\), what is the product of the tens and the units digits of \(\frac{x}{(8!)^3}-39\)?

A. 0
B. 6
C. 7
D. 12
E. 14

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
Re M26-28  [#permalink]

Show Tags

New post 16 Sep 2014, 00:26
10
1
5
Official Solution:

If \(x=\frac{(8!)^{10}-(8!)^6}{(8!)^{5}-(8!)^3}\), what is the product of the tens and the units digits of \(\frac{x}{(8!)^3}-39\)?

A. 0
B. 6
C. 7
D. 12
E. 14


Apply \(a^2-b^2=(a-b)(a+b)\): \(x=\frac{(8!)^{10}-(8!)^6}{(8!)^{5}-(8!)^3}=\frac{((8!)^{5}-(8!)^3)((8!)^{5}+(8!)^3)}{(8!)^{5}-(8!)^3}=(8!)^{5}+(8!)^3\).

Next, \(\frac{x}{(8!)^3}-39=\frac{(8!)^{5}+(8!)^3}{(8!)^3}=\frac{(8!)^{5}}{(8!)^3}+\frac{(8!)^{3}}{(8!)^3}-39=(8!)^2+1-39=(8!)^2-38\).

Now, since \(8!\) has 2 and 5 as its multiples, then it will have 0 as the units digit, so \((8!)^2\) will have two zeros in the end, which means that \((8!)^2-38\) will have \(00-38=62\) as the last digits: \(6*2=12\).


Answer: D
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
Joined: 17 May 2016
Posts: 67
Concentration: Finance, International Business
GMAT 1: 720 Q49 V39
GPA: 3.7
WE: Analyst (Investment Banking)
Re: M26-28  [#permalink]

Show Tags

New post 22 May 2016, 10:23
Would anyone perhaps have any similar questions for practice? Many many thanks!
_________________

Please kindly +Kudos if my posts or questions help you!

My debrief: Self-study: How to improve from 620(Q39,V36) to 720(Q49,V39) in 25 days!

Intern
Intern
avatar
B
Joined: 08 Apr 2017
Posts: 6
Reviews Badge
Re M26-28  [#permalink]

Show Tags

New post 01 Oct 2017, 21:47
How do we arrive at 00-32=62 in the above given solution
Intern
Intern
avatar
B
Joined: 08 Apr 2017
Posts: 6
Reviews Badge
Re: M26-28  [#permalink]

Show Tags

New post 01 Oct 2017, 21:51
In the above given solution how do we arrive at 00-38=62 ? Please help.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
Re: M26-28  [#permalink]

Show Tags

New post 01 Oct 2017, 21:57
Intern
Intern
avatar
B
Joined: 08 Apr 2017
Posts: 6
Reviews Badge
Re: M26-28  [#permalink]

Show Tags

New post 01 Oct 2017, 22:02
Got it. Thanks a lot.
Intern
Intern
avatar
B
Joined: 13 Oct 2017
Posts: 39
Re: M26-28  [#permalink]

Show Tags

New post 28 Feb 2018, 02:26
Hi Bunuel,

I have a two part question:

1. How did you know to use a^2 - b^2 ...plus also how come the powers reduced by half when you used difference of squares i.e. from 8!^10 to *8!^5

2. I understand how the tens digit and the units digit will both be zero...and thus how 8!^2 - 38 = 00-38...I just don't know how you get 62...leading to 6*2=12.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
M26-28  [#permalink]

Show Tags

New post 28 Feb 2018, 04:48
1
ttaiwo wrote:
Hi Bunuel,

I have a two part question:

1. How did you know to use a^2 - b^2 ...plus also how come the powers reduced by half when you used difference of squares i.e. from 8!^10 to *8!^5

2. I understand how the tens digit and the units digit will both be zero...and thus how 8!^2 - 38 = 00-38...I just don't know how you get 62...leading to 6*2=12.


Consider easier examples:

1. \(x^{10} - y^{10} = (x^5)^2 - (y^5)^2 = (x^5 - y^5)(x^5 + y^5)\)

2. 100 - 38 = 62.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 13 Oct 2017
Posts: 39
Re: M26-28  [#permalink]

Show Tags

New post 28 Feb 2018, 09:44
Bunuel wrote:
ttaiwo wrote:
Hi Bunuel,

I have a two part question:

1. How did you know to use a^2 - b^2 ...plus also how come the powers reduced by half when you used difference of squares i.e. from 8!^10 to *8!^5

2. I understand how the tens digit and the units digit will both be zero...and thus how 8!^2 - 38 = 00-38...I just don't know how you get 62...leading to 6*2=12.


Consider easier examples:

1. \(x^{10} - y^{10} = (x^5)^2 - (y^5)^2 = (x^5 - y^5)(x^5 + y^5)\)

2. 100 - 38 = 62.


I should've seen 2....but I've genuinely haven't come across 1. before ...thanks :)
Manager
Manager
avatar
S
Joined: 05 Nov 2016
Posts: 88
GMAT ToolKit User
Re: M26-28  [#permalink]

Show Tags

New post 24 Aug 2018, 19:00
Thanks @Bunnel for the great solution.

To elaborate further on the (8!)\(2\)−38 = 62. As mentioned earlier (8!)\(2\)has 00 in the end(i.e., units and tens are zeroes). We do have no concern for the third digit(so lets take it as x. where x lies from 0 - 9). So any combination gives the last two digits as 62. (200-38 = 162 or 500-38=462). Since we were asked only to find the product of last two digits its 6*2 = 12
_________________

Kudos are always welcome ... as well your suggestions

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
Re: M26-28  [#permalink]

Show Tags

New post 25 Aug 2018, 03:17
umadurga wrote:
Thanks @Bunnel for the great solution.

To elaborate further on the (8!)\(2\)−38 = 62. As mentioned earlier (8!)\(2\)has 00 in the end(i.e., units and tens are zeroes). We do have no concern for the third digit(so lets take it as x. where x lies from 0 - 9). So any combination gives the last two digits as 62. (200-38 = 162 or 500-38=462). Since we were asked only to find the product of last two digits its 6*2 = 12

__________________
Yes, that's correct.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 29 May 2017
Posts: 103
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: M26-28  [#permalink]

Show Tags

New post 26 Aug 2018, 07:00
Bunuel wrote:
GeetikaR wrote:
How do we arrive at 00-32=62 in the above given solution


(8!)^2 = (1*2*3*4*5*6*7*8)^2 will have two zeros at the end. So, ...00 - 38 = ...62.


Hi...

can you point me to where i can learn about multiples giving trailing zeros?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
Re: M26-28  [#permalink]

Show Tags

New post 26 Aug 2018, 11:00
Mansoor50 wrote:
Bunuel wrote:
GeetikaR wrote:
How do we arrive at 00-32=62 in the above given solution


(8!)^2 = (1*2*3*4*5*6*7*8)^2 will have two zeros at the end. So, ...00 - 38 = ...62.


Hi...

can you point me to where i can learn about multiples giving trailing zeros?


Everything about Factorials on the GMAT
Power of a Number in a Factorial Problems
Trailing Zeros Problems

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: M26-28 &nbs [#permalink] 26 Aug 2018, 11:00
Display posts from previous: Sort by

M26-28

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel



Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.