Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 Mar 2010
Posts: 124
Location: United States
Concentration: Finance, International Business
GPA: 2.54
WE: Accounting (Hospitality and Tourism)

Which of the following integers can be written as both the
[#permalink]
Show Tags
25 Apr 2012, 22:56
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
4/28 GMATPrep 42Q 36V 640




Math Expert
Joined: 02 Sep 2009
Posts: 49208

Which of the following integers can be written as both the
[#permalink]
Show Tags
25 Apr 2012, 23:12
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: (x4)+(x2)+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: (y6)+(y4)+(y2)+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? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 12 Sep 2012
Posts: 25

Re: Which of the following integers can be written as both the
[#permalink]
Show Tags
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
Joined: 02 Sep 2009
Posts: 49208

Re: Which of the following integers can be written as both the
[#permalink]
Show Tags
16 May 2014, 09:43
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: (x4)+(x2)+x+(x+2)+(x+4)=5x > 5x IS a multiple of 5. The sum of 7 consecutive odd integers can be written as: (y6)+(y4)+(y2)+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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 19 Oct 2013
Posts: 17
Location: India
Concentration: General Management, Operations
Schools: Kelley '17, Georgia Tech '17, Merage '17, Mays '17, Fisher '17, Krannert '17, Olin '17, Simon '17, Carlson '17, Terry '17, UrbanaChampaign '17, Melbourne '17, AGSM '16, Neeley '17
WE: Engineering (Other)

Which of the following integers can be written as both the
[#permalink]
Show Tags
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 noninteger 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
Joined: 23 May 2013
Posts: 188
Location: United States
Concentration: Technology, Healthcare
GPA: 3.5

Re: Which of the following integers can be written as both the
[#permalink]
Show Tags
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: \(1+3+5+7+9+11+13 = 49\) \(3+5+7+9+11+13+15= 49  1 + 15 = 49 + 14 = 63\) \(5+7+9+11+13+15+17= 643+17= 63+14 = 77\) 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
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
19 Jun 2014, 02:40
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 numberOption B & C are cancelled out Answer = E = 525
_________________
Kindly press "+1 Kudos" to appreciate



Math Expert
Joined: 02 Sep 2009
Posts: 49208

Re: Which of the following integers can be written as both the
[#permalink]
Show Tags
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: (x4)+(x2)+x+(x+2)+(x+4)=5x > 5x IS a multiple of 5. The sum of 7 consecutive odd integers can be written as: (y6)+(y4)+(y2)+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? Extrahard Quant Tests with Brilliant Analytics



Intern
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
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
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
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: (x4)+(x2)+x+(x+2)+(x+4)=5x > 5x IS a multiple of 5. The sum of 7 consecutive odd integers can be written as: (y6)+(y4)+(y2)+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
Joined: 02 Sep 2009
Posts: 49208

Re: Which of the following integers can be written as both the
[#permalink]
Show Tags
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: (x4)+(x2)+x+(x+2)+(x+4)=5x > 5x IS a multiple of 5. The sum of 7 consecutive odd integers can be written as: (y6)+(y4)+(y2)+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? Extrahard Quant Tests with Brilliant Analytics




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






