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

It is currently 24 Mar 2019, 12:29

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

Set A contains all of the integers from 100 to 200, inclusive. Set B

  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: 53800
Set A contains all of the integers from 100 to 200, inclusive. Set B  [#permalink]

Show Tags

New post 28 Aug 2017, 23:35
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (02:01) correct 25% (02:31) wrong based on 83 sessions

HideShow timer Statistics

Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?

A. 7500
B. 7575
C. 8050
D. 9875
E. 12925

_________________

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

Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2234
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: Set A contains all of the integers from 100 to 200, inclusive. Set B  [#permalink]

Show Tags

New post 29 Aug 2017, 01:49
Bunuel wrote:
Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?

A. 7500
B. 7575
C. 8050
D. 9875
E. 12925


Sum of Set A minus the sum of set B = Sum of integers from 126 to 200 - Sum of integers from 25 to 99 (Since integers 100 to 125 are common in both sets , we exclude them )
= 75/2 * (126+200) - 75/2 *(25+99)
= 75/2 ( 326 - 124)
= 75 * 202/2
= 75*101
= 7575

Answer B
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2572
Set A contains all of the integers from 100 to 200, inclusive. Set B  [#permalink]

Show Tags

New post 29 Aug 2017, 08:52
Bunuel wrote:
Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?

A. 7500
B. 7575
C. 8050
D. 9875
E. 12925

We can exclude common terms (in set A and set B), but I think the arithmetic is easier if we do not do so.
Both sets have the same number of terms. (The difference between largest term and smallest term in each set is the same). Leave the sums of the separate sets UNmultiplied.

(1) Find Sum of Set A (consecutive integers)

Sum = (Average) * (Number of terms)

Average = \(\frac{FirstTerm+LastTerm}{2}=\frac{100+200}{2}\)

Number of terms =
(Last - First) + 1 (add one before you're done):
(200 - 100) + 1 = (100 + 1) = 101 terms

SUM of Set A
\(\frac{200+100}{2}\) * 101 = (150)(101)


(2) Sum of Set B

Average = \(\frac{FirstTerm+LastTerm}{2}=\frac{25+125}{2}\)

Number of terms:
(125 - 25) + 1 = (100 + 1) = 101 terms

SUM of Set B
\(\frac{125+25}{2}\) * 101 = (75)(101)


3) (Sum of A) - (Sum of B) =

(150)(101) - (75)(101)
Factor out 101
101(150 - 75) =
101(75) =
(100 + 1)(75)

7500 + 75 = 7575

Answer B
_________________

Do I dare
Disturb the universe?
(—T. S. Eliot)
Absolutely.

SC Butler (two Sentence Correction questions per day from Nov 7 to Mar 1) is here.

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2825
Re: Set A contains all of the integers from 100 to 200, inclusive. Set B  [#permalink]

Show Tags

New post 01 Sep 2017, 12:02
Bunuel wrote:
Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?

A. 7500
B. 7575
C. 8050
D. 9875
E. 12925


Since we see there is overlap between sets, we can just determine the sum of the integers from 25 to 99 inclusive and 126 to 200 inclusive. Remember average = (first number + last number)/2.

For set B (excluding 100 to 125 inclusive):

sum = avg x quantity

sum = (25 + 99)/2 x (99 - 25 + 1)

sum = 62 x 75

For set A (excluding 100 to 125 inclusive):

sum = avg x quantity

sum = (126 + 200)/2 x (200 - 126 + 1)

sum = 163 x 75

Thus, A - B = 163 x 75 - 62 x 75 = 75(163 - 62) = 75(101) = 7,575.

Alternate solution:

Even though some of the numbers in B overlap with those in A, we can just find the sum of all the numbers in B and subtract that from the sum of all the numbers in A.

We use the formulas sum = average x quantity and average = (first number + last number)/2.

For set B:

sum = avg x quantity

sum = (25 + 125)/2 x (125 - 25 + 1)

sum = 75 x 101

For set A:

sum = avg x quantity

sum = (100 + 200)/2 x (200 - 100 + 1)

sum = 150 x 101

Thus, A - B = 150 x 101 - 75 x 101 = 101(150 - 75) = 101(75) = 7,575.

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Intern
Intern
avatar
B
Joined: 30 Nov 2015
Posts: 23
Location: United States (CO)
WE: Information Technology (Consumer Products)
Premium Member CAT Tests
Set A contains all of the integers from 100 to 200, inclusive. Set B  [#permalink]

Show Tags

New post 09 Mar 2019, 14:21
100 to 200 => 100 & 101 to 200 (100 numbers) ==> total 101 numbers

Sum of numbers from 101 to 200 can be obtained by taking an average of all the terms and then multiplying it by 100.
If you try to use the "mirror approach" to get the average, you will notice 150.5 divides the set of 100 numbers in the middle. So, the total sum is-

\((150.5 * 100) + 100 = 15150\)

25 to 125 => 25 & 26 to 125 (100 numbers) ==> total 101 numbers

Apply the same approach here. Get the average of numbers from 26 to 125 by mirror approach and multiple by 100. Don't forget to add 25 to this number.

\((75.5 * 100) + 25 = 7575\)

Finally, \(15150 - 7575 = 7575\)

Answer is B

Took me 1:48 minutes to get to the answer.
GMAT Club Bot
Set A contains all of the integers from 100 to 200, inclusive. Set B   [#permalink] 09 Mar 2019, 14:21
Display posts from previous: Sort by

Set A contains all of the integers from 100 to 200, inclusive. Set B

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


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®.