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Manager  Joined: 30 Mar 2010
Posts: 71
Shortcut: Divisible by 7 ?  [#permalink]

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8
4
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.
Manager  Joined: 16 Mar 2010
Posts: 91
Schools: Dalhousie School of Business (Corporate Residency MBA)
Re: Shortcut: Divisible by 7 ?  [#permalink]

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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: 145
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
Re: Shortcut: Divisible by 7 ?  [#permalink]

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2
2
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 stand-alone number. So you don't subtract 12 from 2016, or from 2010. You subtract 12 from 201 to get 189.

4. Repeat steps 1-3 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 non-multiple 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: 1358-14 = 1344
1. Separate: 134 and 4
2. Double the 4: 8
3. Subtract: 134-8 = 126
Recognize 126 as 14 less than 140, i.e. a multiple of 7.

Conclusion: 13,587 is a multiple of 7.
Manhattan Prep Instructor Joined: 27 Aug 2009
Posts: 145
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
Re: Shortcut: Divisible by 7 ?  [#permalink]

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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?
Manager  Joined: 08 May 2010
Posts: 115
Re: Shortcut: Divisible by 7 ?  [#permalink]

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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.

Thanks,
Skip
Intern  Joined: 04 Aug 2009
Posts: 2
Re: Shortcut: Divisible by 7 ?  [#permalink]

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Its absolutely not required to remember this formula. Just divide as you do normal division. It will be much faster.
Director  B
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 600
Re: Shortcut: Divisible by 7 ?  [#permalink]

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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
GMAT Tutor P
Joined: 24 Jun 2008
Posts: 2308
Re: Shortcut: Divisible by 7 ?  [#permalink]

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I agree with Dabral above - divisibility tests for numbers like 7 and 11 aren't useful unless you're testing six-digit 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.
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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

# Shortcut: Divisible by 7 ?   