Divisibility by 11

dabral -

While it is true that the GMAT may not necessarily test the divisibility by 7 and 11 rules directly, they do come in handy when determining whether a number is prime.

Dennis,

Based on my experience with a large number of gmat problems, I have found that the test writers only expect students to be able to recognize prime numbers up to 100. There was one case where one was required to know if 131(if i remember correctly) was prime or not. In any case, to test prime numbers in this range one only need to test divisibility by 2, 3, 5, 7, and 11, and in all cases doing direct division by 7 and 11 would be faster.

In cases where gmat is testing whether a large number is prime or not, it will likely be a conceptual question which will not require tedious division or application of a complicated divisibility rule.

Dabral

Dabral --

I agree with you to a certain extent - you can and should use reasoning, rather than brute force to tackle problems that ask if a large, unfamiliar item is prime. 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.

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.



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.

i think that this is just an extension of the conventional method of finding div by 11, wherein we used to subtract the sum of odd and even digits resp.