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Divisibility by 11
[#permalink]
02 Aug 2015, 11:43
02 Aug 2015, 11:43
1
Kudos
You can check whether a number is divisible by 11 by the following method
suppose the number is 12323
Sum of digits on odd places O= 3+3+1=7
Sum of digits on even places E= 2+2=4
Remainder= E- O = 4-7 = -3
Thus remainder is 11-3 =8
Ex2
suppose the number is 1232594
Sum of digits on odd places O= 4+5+3+1=13
Sum of digits on even places E= 9+2+2=13
Remainder= E- O= 13-13 = 0
Hence the number is divisible by 11
suppose the number is 12323
Sum of digits on odd places O= 3+3+1=7
Sum of digits on even places E= 2+2=4
Remainder= E- O = 4-7 = -3
Thus remainder is 11-3 =8
Ex2
suppose the number is 1232594
Sum of digits on odd places O= 4+5+3+1=13
Sum of digits on even places E= 9+2+2=13
Remainder= E- O= 13-13 = 0
Hence the number is divisible by 11
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Given Kudos: 91
Q51 V47
Re: Divisibility by 11
[#permalink]
07 Aug 2015, 15:27
07 Aug 2015, 15:27
2
Kudos
Expert Reply
Dabral is right - there will never be a situation on the GMAT where it would be useful to know divisibility tests for 7 or for 11. Those tests are useful if you need to test crazy seven-digit numbers for divisibility by 7 or 11, but that's not the kind of thing the GMAT will ever ask you to do.
However, I have also seen questions such as, "How many prime numbers exist between 200 and 220 inclusive?" or, "What is the sum of all prime numbers between 240 and 260?". In these cases, it helps to use divisibility rules.
Those sound like prep company questions, not official ones. It simply takes too long to prime-test lots of random large-ish numbers that it's not something they can ask you to do on the GMAT. The only way they can ask, about a large number, "is this large number prime?" is if the number has some obvious divisor, and the answer is 'no'. So they can ask "Is 13! + 11 prime?" because you can quickly see the answer is 'no' (we're adding two multiples of 11, so the number is a multiple of 11) but they cannot ask "Is 1009 prime" because it would take far too long to prove that it is.
But if you did, say, need to check if 203 was prime, then since it's not divisible by 2, 3 or 5, you'd next want to check 7. We don't need a divisibility test to do that. We just locate a simple multiple of 7 close to 203, and 210 = 7*30. Since multiples of 7 are equally spaced, then these numbers are multiples of 7:
...196, 203, 210, 217, 224, ....
and we see that 203 is divisible by 7. That's about as fast as any divisibility test, but note the advantage of doing things this way - not only do we answer the question "is 203 divisible by 7?" (as we would using a divisibility test), but we also answer the more GMAT-relevant question: "what is 203/7 equal to?" -- it's equal to 7*29, since it comes just before 7*30 on our list of consecutive multiples of 7.
VeritasPrepDennis wrote:
However, I have also seen questions such as, "How many prime numbers exist between 200 and 220 inclusive?" or, "What is the sum of all prime numbers between 240 and 260?". In these cases, it helps to use divisibility rules.
Those sound like prep company questions, not official ones. It simply takes too long to prime-test lots of random large-ish numbers that it's not something they can ask you to do on the GMAT. The only way they can ask, about a large number, "is this large number prime?" is if the number has some obvious divisor, and the answer is 'no'. So they can ask "Is 13! + 11 prime?" because you can quickly see the answer is 'no' (we're adding two multiples of 11, so the number is a multiple of 11) but they cannot ask "Is 1009 prime" because it would take far too long to prove that it is.
But if you did, say, need to check if 203 was prime, then since it's not divisible by 2, 3 or 5, you'd next want to check 7. We don't need a divisibility test to do that. We just locate a simple multiple of 7 close to 203, and 210 = 7*30. Since multiples of 7 are equally spaced, then these numbers are multiples of 7:
...196, 203, 210, 217, 224, ....
and we see that 203 is divisible by 7. That's about as fast as any divisibility test, but note the advantage of doing things this way - not only do we answer the question "is 203 divisible by 7?" (as we would using a divisibility test), but we also answer the more GMAT-relevant question: "what is 203/7 equal to?" -- it's equal to 7*29, since it comes just before 7*30 on our list of consecutive multiples of 7.
Re: Divisibility by 11
[#permalink]
02 Aug 2015, 22:48
02 Aug 2015, 22:48
1
Kudos
Expert Reply
As far as the GMAT is concerned, memorizing/learning the divisibility rule for 11 is irrelevant. The ones that you do need to know and have been tested are: 3, 4, 6, 8, and 9. In these cases it is valuable to recognize how and why the divisibility rule is related to the place values. Other than that, rules for 7, 11, etc have not been tested on the GMAT and I don't think they are likely to test those.
Dabral
Dabral
