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

It is currently 18 Sep 2018, 20:33

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

Which of the following integers can be written as both the

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

Hide Tags

Manager
Manager
avatar
Joined: 29 Mar 2010
Posts: 124
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q28 V38
GPA: 2.54
WE: Accounting (Hospitality and Tourism)
GMAT ToolKit User
Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 25 Apr 2012, 22:56
6
12
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

56% (02:05) correct 44% (01:57) wrong based on 419 sessions

HideShow timer Statistics

Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers?

A. 49
B. 70
C. 140
D. 215
E. 525

_________________

4/28 GMATPrep 42Q 36V 640

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49208
Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 25 Apr 2012, 23:12
8
10
hfbamafan wrote:
Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers?

A. 49
B. 70
C. 140
D. 215
E. 525


First of all notice that both the sum of 5 consecutive odd integers and the sum of 7 consecutive odd integers must be odd. Eliminate B, and C right away.

Next the sum of 5 consecutive odd integers can be written as: (x-4)+(x-2)+x+(x+2)+(x+4)=5x, so the sum must be odd multiple of 5;

Similarly, the sum of 7 consecutive odd integers can be written as: (y-6)+(y-4)+(y-2)+y+(y+2)+(y+4)+(y+6)=7y, so the sum must be odd multiple of 7;

So, the sum must be odd multiple of 5*7=35. Only option E meets this conditions.

Answer: E.
_________________

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

General Discussion
Intern
Intern
avatar
Joined: 12 Sep 2012
Posts: 25
GMAT 1: 550 Q49 V17
Re: Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 16 May 2014, 08:53
Hello,
Bunuel one thing I couldn't understand that how the sum is becoming a multiple of 5 & 7. The required sum = 5x + 7x + something. It is not clear to me. Kindly elaborate.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49208
Re: Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 16 May 2014, 09:43
2
deya wrote:
Hello,
Bunuel one thing I couldn't understand that how the sum is becoming a multiple of 5 & 7. The required sum = 5x + 7x + something. It is not clear to me. Kindly elaborate.


I think that you misunderstood the question.

We should be able to write one of the options as the sum of 5 consecutive odd integers. Also, we should be able to write the same options as the sum of 7 consecutive odd integers.

525 = 101 + 103 + 105 + 107 + 109.
525 = 69 + 71 + 73 + 75 + 77 + 79 + 81.

As for 5x and 7y:

The sum of 5 consecutive odd integers can be written as: (x-4)+(x-2)+x+(x+2)+(x+4)=5x --> 5x IS a multiple of 5.
The sum of 7 consecutive odd integers can be written as: (y-6)+(y-4)+(y-2)+y+(y+2)+(y+4)+(y+6)=7y --> 7y IS a multiple of 7.

Thus the integer which is both the sum of 5 consecutive odd integers AND the sum of 7 consecutive odd integers, must be multiple of both 5 and 7, so a multiple of 35
_________________

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
Joined: 19 Oct 2013
Posts: 17
Location: India
Concentration: General Management, Operations
WE: Engineering (Other)
Which of the following integers can be written as both the  [#permalink]

Show Tags

New post Updated on: 18 Jun 2014, 18:46
hfbamafan wrote:
Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers?

A. 49
B. 70
C. 140
D. 215
E. 525


This is how I approached the problem.

Sum of 5 consecutive numbers: x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 5x + 20 --- (1)
Sum of 7 consecutive numbers: y + (y + 2) + (y + 4) + (y + 6) + (y + 8) + (y + 10) + (y + 12) = 7y + 42 --- (2)

Then, equate each of the answer choices with the 2 equations and find out for which Answer Choice you get an ODD VALUE for both 'x' & 'y'.

* Choices (A), (B) & (D) give non-integer values for either x & y on substitution.

* Be careful of Choice (C), as the integer values are EVEN. Not the right answer!! We need ODD consecutive integers.

5x + 20 = 120 ----> x = 24 !!
7y + 42 = 120 ----> y = 14 !!

* Only Choice (E) gives ODD INTEGER values for both x & y.

5x + 20 = 525 ----> x = 101
7y + 42 = 525 ----> y = 69

Hence, (E) is the right answer.

Originally posted by shaderon on 16 May 2014, 22:20.
Last edited by shaderon on 18 Jun 2014, 18:46, edited 1 time in total.
Current Student
avatar
B
Joined: 23 May 2013
Posts: 188
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M)
GMAT 1: 760 Q49 V45
GPA: 3.5
GMAT ToolKit User
Re: Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 18 Jun 2014, 08:52
hfbamafan wrote:
Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers?

A. 49
B. 70
C. 140
D. 215
E. 525


Similar method, just using brute force.

Let's look at the possible values of the sum of 5 consecutive odd integers:

\(1+3+5+7+9 = 10 + 10 + 5 = 5*5 = 25\)
\(3+5+7+9+11 = 25 - 1 + 11 = 25 + 10 = 35\)
\(-3.......+13 = 35 + 10 = 45.\)

We see that each time, the net effect of subtracted and adding will increase the sum by 10. Thus, our sum must be an odd multiple of 5. Our only options are D & E.

Using the same approach for multiples of 7:

\(1+3+5+7+9+11+13 = 49\)
\(3+5+7+9+11+13+15= 49 - 1 + 15 = 49 + 14 = 63\)
\(5+7+9+11+13+15+17= 64-3+17= 63+14 = 77\)

Thus, our number must also be a(n odd) multiple of 7.

D) 215 is clearly not a multiple of 7. Thus, E) 525 (7*75) is our answer.

Answer: E
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 19 Jun 2014, 02:40
1
LCM of 5 & 7 = 35

Answer should be divisible by 35

Option A & D are cancelled out

Addition of 5 & 7 consecutive odd's would always return an odd number

Option B & C are cancelled out

Answer = E = 525
_________________

Kindly press "+1 Kudos" to appreciate :)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49208
Re: Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 19 Jun 2014, 04:26
arindamsur wrote:
Why not option B.?

Bunuel wrote:
deya wrote:
Hello,
Bunuel one thing I couldn't understand that how the sum is becoming a multiple of 5 & 7. The required sum = 5x + 7x + something. It is not clear to me. Kindly elaborate.


I think that you misunderstood the question.

We should be able to write one of the options as the sum of 5 consecutive odd integers. Also, we should be able to write the same options as the sum of 7 consecutive odd integers.

525 = 101 + 103 + 105 + 107 + 109.
525 = 69 + 71 + 73 + 75 + 77 + 79 + 81.

As for 5x and 7y:

The sum of 5 consecutive odd integers can be written as: (x-4)+(x-2)+x+(x+2)+(x+4)=5x --> 5x IS a multiple of 5.
The sum of 7 consecutive odd integers can be written as: (y-6)+(y-4)+(y-2)+y+(y+2)+(y+4)+(y+6)=7y --> 7y IS a multiple of 7.

Thus the integer which is both the sum of 5 consecutive odd integers AND the sum of 7 consecutive odd integers, must be multiple of both 5 and 7, so a multiple of 35


Because 70 is not an ODD multiple of 35.
_________________

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
User avatar
B
Joined: 27 Jul 2018
Posts: 7
Location: India
Concentration: International Business, Strategy
GPA: 3.82
WE: Information Technology (Computer Software)
Re: Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 12 Aug 2018, 13:43
In this question, we need to understand that, sum of five consecutive odd numbers will give you an odd number which should end with 5.
So, we are left with options D&E.
Now, as we can see sum of consecutive seven odd numbers(that number) should at least have a factor as 7, which (D) 215 is not.
So, we are left with (525) E.It is our answer.
Manager
Manager
User avatar
S
Joined: 24 Dec 2016
Posts: 90
Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)
Re: Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 19 Aug 2018, 22:41
Bunuel wrote:
deya wrote:
Hello,
Bunuel one thing I couldn't understand that how the sum is becoming a multiple of 5 & 7. The required sum = 5x + 7x + something. It is not clear to me. Kindly elaborate.


I think that you misunderstood the question.

We should be able to write one of the options as the sum of 5 consecutive odd integers. Also, we should be able to write the same options as the sum of 7 consecutive odd integers.

525 = 101 + 103 + 105 + 107 + 109.
525 = 69 + 71 + 73 + 75 + 77 + 79 + 81.

As for 5x and 7y:

The sum of 5 consecutive odd integers can be written as: (x-4)+(x-2)+x+(x+2)+(x+4)=5x --> 5x IS a multiple of 5.
The sum of 7 consecutive odd integers can be written as: (y-6)+(y-4)+(y-2)+y+(y+2)+(y+4)+(y+6)=7y --> 7y IS a multiple of 7.

Thus the integer which is both the sum of 5 consecutive odd integers AND the sum of 7 consecutive odd integers, must be multiple of both 5 and 7, so a multiple of 35




Hi Bunuel,

I followed the same process as mentioned by you, except instead of taking x and y, I took (2x+1) and (2y+1) as the middle terms to ensure that the nos. are odd.
That gave me equations of the form 10x+1 = 525 and 14x+1 = 525, neither of which result in a whole no.
Could you please suggest what's going wrong with this logic?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49208
Re: Which of the following integers can be written as both the  [#permalink]

Show Tags

New post 19 Aug 2018, 23:52
Shruti0805 wrote:
Bunuel wrote:
deya wrote:
Hello,
Bunuel one thing I couldn't understand that how the sum is becoming a multiple of 5 & 7. The required sum = 5x + 7x + something. It is not clear to me. Kindly elaborate.


I think that you misunderstood the question.

We should be able to write one of the options as the sum of 5 consecutive odd integers. Also, we should be able to write the same options as the sum of 7 consecutive odd integers.

525 = 101 + 103 + 105 + 107 + 109.
525 = 69 + 71 + 73 + 75 + 77 + 79 + 81.

As for 5x and 7y:

The sum of 5 consecutive odd integers can be written as: (x-4)+(x-2)+x+(x+2)+(x+4)=5x --> 5x IS a multiple of 5.
The sum of 7 consecutive odd integers can be written as: (y-6)+(y-4)+(y-2)+y+(y+2)+(y+4)+(y+6)=7y --> 7y IS a multiple of 7.

Thus the integer which is both the sum of 5 consecutive odd integers AND the sum of 7 consecutive odd integers, must be multiple of both 5 and 7, so a multiple of 35




Hi Bunuel,

I followed the same process as mentioned by you, except instead of taking x and y, I took (2x+1) and (2y+1) as the middle terms to ensure that the nos. are odd.
That gave me equations of the form 10x+1 = 525 and 14x+1 = 525, neither of which result in a whole no.
Could you please suggest what's going wrong with this logic?


(2x - 3) + (2x - 1) + (2x +1) + (2x + 3) + (2x + 5) = 525 --> x = 52 --> 2x + 1 = 105
_________________

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

Re: Which of the following integers can be written as both the &nbs [#permalink] 19 Aug 2018, 23:52
Display posts from previous: Sort by

Which of the following integers can be written as both the

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

Events & Promotions

PREV
NEXT


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®.