Hello everybody!
I'm having some problems with divisibility problem such as this:
If n is a positive integer, is n+4 divisible by 8?
(1) n+12 is divisible by 8
(2) n is divisible by 12
Anybody can tell me what is the correct way to attack this kind of problem? And how to solve this one specifically?
Thanks,
Divisibility problems
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about this particular problem
is n+4 divisible by 8
(1) n+12=8k, n=8k-12, 8k-12+4=8k-8=8(k-1)-always divisible by 8, so suff
(2)n=12m, does 12m+4 divisible by 8
m=1, 12+4=16 divisible by 8
m=2, 24+4=28, not divisible by 8
as we have both yes and no answer, insuff
imo A
is n+4 divisible by 8
(1) n+12=8k, n=8k-12, 8k-12+4=8k-8=8(k-1)-always divisible by 8, so suff
(2)n=12m, does 12m+4 divisible by 8
m=1, 12+4=16 divisible by 8
m=2, 24+4=28, not divisible by 8
as we have both yes and no answer, insuff
imo A
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Hi!
You can certainly solve this type of problem by applying divisibility rules, but like almost all data sufficiency yes-no number property problems, picking numbers is also an excellent approach.
When you pick numbers in data sufficiency, it's vital to follow 2 steps:
1) pick a number (or numbers) that are "legal" (i.e. follow all the rules provided); and then
2) plug the number (or numbers) back into the question, trying to get both a yes and a no answer.
Since we need to get both a yes and a no to show that a statement is insufficient, you'll always have to pick at least 2 sets of numbers.
Applying picking numbers to this question:
1) 16 is divisible by 8, so let's pick n=4 so that n+12 is divisible by 8.
If n=4, is n+4 divisible by 8? YES
Now we pick another value for n to try to get a "no" answer.
24 is the next number divisible by 8, so let's pick n=12 so that n+12 is divisible by 8.
If n=12, is n+4 divisible by 8? YES
We've gotten a yes answer for 2 consecutive values of n; at this point we can probably deduce that n+4 will always be divisible by 8: sufficient.
(If we're still not convinced, we would try one more value for n).
(2) n is divisible by 12.
Let's start with the obvious choice, n=12. If n=12, is n+4 divisible by 8? YES.
The next possible value of n is 24. If n=24, is n+4 divisible by 8? NO.
We've gotten a yes and a no answer, so (2) is insufficient - no further work required.
(1) is sufficient, (2) isn't, choose (A).
* * *
Here's a good general rule for attacking DS number property questions:
if the applicable rules jump out at you, then apply them to solve the question; and
if after 3-5 seconds of thought the rules aren't jumping out at you, dive in and pick numbers.
The one thing you can NEVER afford to do on test day is stare at the screen, hoping to have an epiphany - quite literally, every second you spend waiting for inspiration your score is going down.
You can certainly solve this type of problem by applying divisibility rules, but like almost all data sufficiency yes-no number property problems, picking numbers is also an excellent approach.
When you pick numbers in data sufficiency, it's vital to follow 2 steps:
1) pick a number (or numbers) that are "legal" (i.e. follow all the rules provided); and then
2) plug the number (or numbers) back into the question, trying to get both a yes and a no answer.
Since we need to get both a yes and a no to show that a statement is insufficient, you'll always have to pick at least 2 sets of numbers.
Applying picking numbers to this question:
From the stem, we know that n is a positive integer, but nothing else. To the statements:andersonlgb wrote: If n is a positive integer, is n+4 divisible by 8?
(1) n+12 is divisible by 8
(2) n is divisible by 12
1) 16 is divisible by 8, so let's pick n=4 so that n+12 is divisible by 8.
If n=4, is n+4 divisible by 8? YES
Now we pick another value for n to try to get a "no" answer.
24 is the next number divisible by 8, so let's pick n=12 so that n+12 is divisible by 8.
If n=12, is n+4 divisible by 8? YES
We've gotten a yes answer for 2 consecutive values of n; at this point we can probably deduce that n+4 will always be divisible by 8: sufficient.
(If we're still not convinced, we would try one more value for n).
(2) n is divisible by 12.
Let's start with the obvious choice, n=12. If n=12, is n+4 divisible by 8? YES.
The next possible value of n is 24. If n=24, is n+4 divisible by 8? NO.
We've gotten a yes and a no answer, so (2) is insufficient - no further work required.
(1) is sufficient, (2) isn't, choose (A).
* * *
Here's a good general rule for attacking DS number property questions:
if the applicable rules jump out at you, then apply them to solve the question; and
if after 3-5 seconds of thought the rules aren't jumping out at you, dive in and pick numbers.
The one thing you can NEVER afford to do on test day is stare at the screen, hoping to have an epiphany - quite literally, every second you spend waiting for inspiration your score is going down.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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One of the most important (and simplest) facts about number theory is that multiples are equally spaced. If, say, x is a multiple of 5, then so are x+5, x+10, x+15 and so on (as are x-5, x-10, and so on).andersonlgb wrote:Hello everybody!
I'm having some problems with divisibility problem such as this:
If n is a positive integer, is n+4 divisible by 8?
(1) n+12 is divisible by 8
(2) n is divisible by 12
Anybody can tell me what is the correct way to attack this kind of problem? And how to solve this one specifically?
Thanks,
Applying this to Statement 1, if n+12 is a multiple of 8, then if we subtract 8 from n+12 we must get another multiple of 8, so n+4 is a multiple of 8, and Statement 1 is sufficient.
For Statement 2, I'd find it easiest to look at two consecutive multiples of 12 - 12 and 24, say - to see that n+4 is sometimes a multiple of 8 and sometimes not, so Statement 2 is not sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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