Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 30 Mar 2010
Posts: 84

Shortcut: Divisible by 7 ? [#permalink]
Show Tags
21 May 2010, 09:17
8
This post received KUDOS
5
This post was BOOKMARKED
We all know the rules for 2,3,4,5,6,8,9 and 10. But what is less talked about is the number 7. Here is the shortcut to see whether the number is divisible by 7 or not. Step1: Take a number and multiply each of the digit beginning on the right hand side by 1,3,2,6,4,5 (repeat the pattern if the number is large enough) Step 2: Add the product of the numbers. If the sum is divisible by 7  so is the number. e.g. Check for number 133 3(1) + 3(3) + 1(2) = 14 > which is divisible by 7. So, 133 is divisible by 7. Another example: check for no. 2016 6(1) + 1(3) + 0(2) + 2(6) = 21 > which is also divisible by 7. So, the no. 2016 is divisible by 7.
_________________
Click on kudos, if you like my post!



Manager
Joined: 16 Mar 2010
Posts: 118
Location: Halifax, Canada
Schools: Dalhousie School of Business (Corporate Residency MBA)

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
21 May 2010, 10:16
That is totally weird. I can't be bothered to check if it's true (I assume it is)... I'd love to see the proof as to why it works. Not because I'm that big of a math geek, but because I'm sure it would boggle my mind even further.



Manhattan Prep Instructor
Joined: 27 Aug 2009
Posts: 152
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
21 May 2010, 10:24
1
This post received KUDOS
2
This post was BOOKMARKED
Here's another one: 1. Lop off the last digit of the number in question. For 2016, that would be 6. 2. Double that number. Double the 6 to get 12. 3. Subtract that number from the remaining digits of the number in question, as if they were a standalone number. So you don't subtract 12 from 2016, or from 2010. You subtract 12 from 201 to get 189. 4. Repeat steps 13 until you get to a number you recognize as either a multiple of 7 or not. If you get a multiple of 7 after step 3, the original number was a multiple of 7. If you get a nonmultiple of 7 after step 3, the original number was not a multiple of 7. Take 189, lop of the 9, double to get 18, and subtract 18 from the 18 we got when we took 9 off the end of 189. Result 0 is divisible by 7, so 2016 also was. Another example: 13,587 1. Separate: 1358 and 7 2. Double the 7: 14 3. Subtract: 135814 = 1344 1. Separate: 134 and 4 2. Double the 4: 8 3. Subtract: 1348 = 126 Recognize 126 as 14 less than 140, i.e. a multiple of 7. Conclusion: 13,587 is a multiple of 7.
_________________
Emily Sledge  Manhattan GMAT Instructor  St. Louis
Manhattan GMAT Discount  Manhattan GMAT Course Reviews  Manhattan GMAT Reviews



Manhattan Prep Instructor
Joined: 27 Aug 2009
Posts: 152
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
21 May 2010, 10:32
dalmba wrote: That is totally weird. I can't be bothered to check if it's true (I assume it is)... I'd love to see the proof as to why it works. Not because I'm that big of a math geek, but because I'm sure it would boggle my mind even further. I totally agree! Both of these methods are so wacky, unlike the more intuitive tests for divisibility by other single digit numbers. I have to wonder, wouldn't simple long division by 7 be fastest?
_________________
Emily Sledge  Manhattan GMAT Instructor  St. Louis
Manhattan GMAT Discount  Manhattan GMAT Course Reviews  Manhattan GMAT Reviews



Manager
Joined: 08 May 2010
Posts: 140

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
21 May 2010, 10:43
I have book for my kids that gives the rules for divisibility by 7 as: Multiply the final digit by 5 and then add the answer to the number preceding it. If the answer is divisible by 7 then the whole number is divisible by 7. (the book is called Speed Math for Kids by Bill Handley)
So for your example 13587. 1358 +35=1393. 1393 is divisible by 7 (=199.) so the larger number is.
Ultimately I do not see this speeding you up at all. It is absolutely slower AND more error prone for me. I would just divide it out. Not thinking this will be very relevant on the GMAT anyway.
If you found my comments helpful, please give kudos. ( only need a few more) Thanks, Skip



Intern
Joined: 04 Aug 2009
Posts: 3

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
27 May 2010, 07:00
Its absolutely not required to remember this formula. Just divide as you do normal division. It will be much faster.



NonHuman User
Joined: 09 Sep 2013
Posts: 13817

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
07 Jan 2015, 02:16
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



Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 607

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
11 Jan 2015, 09:23
Yes, no need to learn the divisibility rule for 7 as far as the GMAT is concerned. For every single computation I have seen on the GMAT, it would be faster to just divide by 7 than resorting to these rules.
Dabral



NonHuman User
Joined: 09 Sep 2013
Posts: 13817

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
07 Apr 2016, 07:29
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



NonHuman User
Joined: 09 Sep 2013
Posts: 13817

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
17 Aug 2017, 13:53
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



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

Re: Shortcut: Divisible by 7 ? [#permalink]
Show Tags
17 Aug 2017, 14:13
I agree with Dabral above  divisibility tests for numbers like 7 and 11 aren't useful unless you're testing sixdigit numbers for divisibility by 7 or 11, which you never need to do on the GMAT. If you see a smaller number like 1785 and wanted to know if it's divisible by 7, you can just take out obvious multiples of 7 until you get down to familiar numbers: 1785 = 1400 + 385 = 1400 + 350 + 35 and since we have no remainder, 1785 is divisible by 7. That's much faster, for small numbers, than any divisibility 'trick' I've ever seen, and it works for any number at all (not only for 7), so you don't need to learn different 'tricks' for different numbers. One other advantage of doing this is you can work out what 1785/7 is equal to, if you need to: 1785 = 1400 + 350 + 35 = 7(200 + 50 + 5) = 7*255 Of course long division will also work, but there are alternatives that can be faster.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com




Re: Shortcut: Divisible by 7 ?
[#permalink]
17 Aug 2017, 14:13






