February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th. February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 839
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
25 Jun 2015, 10:54
Question Stats:
49% (02:12) correct 51% (02:08) wrong based on 250 sessions
HideShow timer Statistics
A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q? A. 20 B. 19 C. 18 D. 17 E. 16
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.




Intern
Joined: 30 Sep 2013
Posts: 20

A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
01 Sep 2015, 09:31
Lets Q's first number be 14 As per question, Q contains 9 multiples of 14 , so let Q's last number be 126. \((14 * 9)\) We have, \(a_n\) = \(a + (n1)d\)
Then
126 = 14 + (n1)7
Solving for n , we get n = 17




Manager
Joined: 27 Dec 2013
Posts: 234

Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
26 Jun 2015, 05:03
I am getting the answer 17. Let A=14 and B= 154. Q= {15,16, 17...................153} The nine multiples of Q are {28......140}. The number of multiples of 7 between {28......................140} N=17. option d. reto wrote: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?
A. 20 B. 19 C. 18 D. 17 E. 16
_________________
Kudos to you, for helping me with some KUDOS.



Intern
Joined: 28 Nov 2012
Posts: 28

Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
22 Nov 2015, 06:26
Hey As per your approach you are missing 2 numbers here i.e. 21 and 147, both will be in the set and divisible by 7, hence the answer should be 19. Thank you shriramvelamuri wrote: I am getting the answer 17. Let A=14 and B= 154. Q= {15,16, 17...................153} The nine multiples of Q are {28......140}. The number of multiples of 7 between {28......................140} N=17. option d. reto wrote: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?
A. 20 B. 19 C. 18 D. 17 E. 16



Math Expert
Joined: 02 Aug 2009
Posts: 7334

Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
22 Nov 2015, 07:20
rsaahil90 wrote: Hey As per your approach you are missing 2 numbers here i.e. 21 and 147, both will be in the set and divisible by 7, hence the answer should be 19. Thank you shriramvelamuri wrote: I am getting the answer 17. Let A=14 and B= 154. Q= {15,16, 17...................153} The nine multiples of Q are {28......140}. The number of multiples of 7 between {28......................140} N=17. option d. reto wrote: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?
A. 20 B. 19 C. 18 D. 17 E. 16 Hi, the Q has a straight logic.. 7 is an odd number so its consecutives multiples will be even, odd, even,odd and so on.. and even multiple of 7 will mean multiple of 14.. now we have two ends of the set which are multiples of 14 or in other words even multiple of 7... and between each set of consecutive even multiple of 7, there will be 1 odd multiple of 7.. so even multiple=9 odd multiple=91=8.. total 17 ans D
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Senior Manager
Joined: 03 Apr 2013
Posts: 275
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
01 Jul 2016, 23:01
reto wrote: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?
A. 20 B. 19 C. 18 D. 17 E. 16 Visualization question... Let's try 2 small values..two multiples and three multiples..I will write multiples of 14(which are also multiples of 7) in boldface.. 1421 28 number of multiples of 7? 2 + 1 = 3 Three multiples 1421 2835 42 number of multiples of 7? 3 + 2 = 5 So imagine all multiples of 14 written with blanks in between them..multiples of 7 will be (number of mutiples of 14) + (number of blanks between them) Thus, 9 + 8 = 17 (D).
_________________
Spread some love..Like = +1 Kudos



Manager
Joined: 16 Mar 2016
Posts: 129
Location: France
GPA: 3.25

Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
02 Jul 2016, 00:48
First multiple of Q : 14 x 1 = 14 Last multiple of Q : 14 x 9 = 126
So, 126  14 = 122, and 122/7 = 16 We add + 1 since elements are inclusive
17



Manager
Status: GMAT Coach
Joined: 05 Nov 2012
Posts: 141
Location: Peru
GPA: 3.98

Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
17 Oct 2016, 08:06
reto wrote: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?
A. 20 B. 19 C. 18 D. 17 E. 16 When we include both endpoints, we add one (1 for every 14 + the other end) So, if we have nine we have (8 + the other end) 7 is 14/2 so we have 2 multiples of 7 for every multiple of 14 + the other end => 2x8 + 1 = 17 Choice D
_________________
Clipper Ledgard GMAT Coach



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
26 Oct 2017, 14:27
reto wrote: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?
A. 20 B. 19 C. 18 D. 17 E. 16 Since Q is the set of consecutive integers between A and B, inclusive, we can let A = 1 x 14 = 14 and B = 9 x 14 = 126. Thus, the number of multiples of 7 in Q is: (126  14)/7 + 1 = 112/7 + 1 = 17 Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 9878

Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
Show Tags
04 Nov 2018, 02:46
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A and B are two multiples of 14, and Q is the set of consecutive integ
[#permalink]
04 Nov 2018, 02:46






