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

It is currently 20 Mar 2019, 10:34

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

If the sum of x distinct, positive integers is less than 75, what is

  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: 53734
If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 19 Feb 2019, 21:57
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:37) correct 22% (01:30) wrong based on 55 sessions

HideShow timer Statistics

SVP
SVP
User avatar
P
Joined: 18 Aug 2017
Posts: 2400
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post Updated on: 21 Feb 2019, 07:32
Bunuel wrote:
If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12


sum of distinct integers < 75
1+2+3... +11;
IMO D ;11 will be the largest integer..
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.


Originally posted by Archit3110 on 20 Feb 2019, 00:48.
Last edited by Archit3110 on 21 Feb 2019, 07:32, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53734
Re: If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 21 Feb 2019, 07:30
Archit3110 wrote:
Bunuel wrote:
If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12


IMO e
12
3+4+5+....+12= 75

Bunuel ; is the given answer option correct? if so please provide solution..


First of all notice that we are told that the sum is LESS than 75. Next, the question asks about the greatest possible NUMBER of distinct, positive integers the sum of which is LESS than 75.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66 < 75. If you add the next one, 12, then the sum would be 78. So, the greatest possible NUMBER of distinct, positive integers the sum of which is LESS than 75 is 11 (from 1 to 11, inclusive).

Answer: D.

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

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4403
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
Re: If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 21 Feb 2019, 08:05
Bunuel wrote:
If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12

\(\frac{n(n+1)}{2} < 75\)

Now check using the given options...

\(11*\frac{12}{2} = 66 < 75\) , Answer ,must be (D)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

VP
VP
User avatar
P
Joined: 31 Oct 2013
Posts: 1269
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 21 Feb 2019, 09:21
Bunuel wrote:
If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12



we are looking for the number of integers whose sum is less then 75.

Number of integers = x. we are asked to maximize x.

All the integers are positive. Thus we must start with 1 and continue the series with lower integers to get the maximum value of x.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66 which is less than 75. It is not possible to add any other integers.

Thus, x =11.

D is the correct answer.
Manager
Manager
User avatar
G
Joined: 13 Jan 2018
Posts: 243
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE: Consulting (Consulting)
Reviews Badge
If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 22 Feb 2019, 09:52
What if the numbers are 2,4,5,6,7,8,9,10,11,12? The sum of these numbers is 74. The question hasn't said the numbers are consecutive? It just said x distinct positive integers, that's it! Why is this case not possible? Why can't E be the choice?
_________________

____________________________
Regards,

Chaitanya


+1 Kudos

if you like my explanation!!!

Manager
Manager
User avatar
G
Joined: 13 Jan 2018
Posts: 243
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE: Consulting (Consulting)
Reviews Badge
Re: If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 22 Feb 2019, 09:53
Quote:
If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12


What if the numbers are 2,4,5,6,7,8,9,10,11,12? The sum of these numbers is 74. The question hasn't said the numbers are consecutive? It just said x distinct positive integers, that's it! Why is this case not possible? Why can't E be the choice?
_________________

____________________________
Regards,

Chaitanya


+1 Kudos

if you like my explanation!!!

Intern
Intern
User avatar
Joined: 22 Nov 2017
Posts: 1
GMAT 1: 620 Q48 V27
Re: If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 22 Feb 2019, 10:07
1
eswarchethu135 wrote:
Quote:
If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12


What if the numbers are 2,4,5,6,7,8,9,10,11,12? The sum of these numbers is 74. The question hasn't said the numbers are consecutive? It just said x distinct positive integers, that's it! Why is this case not possible? Why can't E be the choice?


Because in your explanation the value of x is 10. This is because the question is asking for the maximum numbers of distinct integers that can be added to get a sum<75. The question is not asking for the greatest of those integers.
Manager
Manager
User avatar
G
Joined: 13 Jan 2018
Posts: 243
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE: Consulting (Consulting)
Reviews Badge
Re: If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 22 Feb 2019, 10:10
Shivam710 wrote:
eswarchethu135 wrote:
Quote:
If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12


What if the numbers are 2,4,5,6,7,8,9,10,11,12? The sum of these numbers is 74. The question hasn't said the numbers are consecutive? It just said x distinct positive integers, that's it! Why is this case not possible? Why can't E be the choice?


Because in your explanation the value of x is 10. This is because the question is asking for the maximum numbers of distinct integers that can be added to get a sum<75. The question is not asking for the greatest of those integers.


Got it. Thanks for clarification.

Posted from my mobile device
_________________

____________________________
Regards,

Chaitanya


+1 Kudos

if you like my explanation!!!

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5375
Location: United States (CA)
Re: If the sum of x distinct, positive integers is less than 75, what is  [#permalink]

Show Tags

New post 24 Feb 2019, 06:46
Bunuel wrote:
If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12


Let’s analyze the answer choices in reverse order since we are looking for the greatest possible value of x.

E. 12

Since we want x to be as large as possible, we want the smallest of the x integers to be 1. Therefore, if x = 12, the sum of the first 12 positive integers is:

1 + 2 + 3 + … + 12 = 12 x (1 + 12)/2 = 6 x 13 = 78

This is not less than 75, so x can’t be 12.

D. 11

We see that 1 + 2 + 3 + … + 11 = 78 - 12 = 66.

This is less than 75, thus the greatest possible value of x is 11.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@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

GMAT Club Bot
Re: If the sum of x distinct, positive integers is less than 75, what is   [#permalink] 24 Feb 2019, 06:46
Display posts from previous: Sort by

If the sum of x distinct, positive integers is less than 75, what is

  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®.