If k is divisible by 10 and 12, is k divisible by 24? (BTW,

Question

If k is divisible by 10 and 12, is k divisible by 24? (BTW, I hate this kinda questions...

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smcgrath12 · Answer

If you select number 60 (divisible by 10 and 12), but it is not divisible by 24. But if you select 120 (again divisible by 10 and 12), it is divisible by 24. So, what is the standard method to solve this kinda problems?

SigEpUCI · Answer

To solve this, you factor out the number.

10 = 2 * 5
12 = 2 * 2 * 3

24 = 2 * 2 * 2 * 3

since 24 has '2' three times, it is not always a multiple of 12 and 10. ( you dont sum the factors, you merely take the highest occurences of the numbers.

60 on the other hand is always a multiple

60 = 2 * 2 * 3 * 5

lastochka · Answer

good explanation sig

ian7777 · Answer

this is exactly right.

let's not underestimate the power of prime factors. Prime factors are the greatest tool you have on the test. They work for these questions, and pretty much any question that deals with factors, multiples, divisors, products... they're great for figuring out lowest common multiples and lowest common denominators, they kick ass when it comes to finding the square root of a big number. 

If you've ever read the Hitchhiker's Guide to the Galaxy, prime numbers are the GMAT taker's towel. They'll get you through many sticky situations.

smcgrath12 · Answer

Thanks for everybody's response. Sometimes the easy questions trips you, while the difficult questions can seem simple.

ywilfred · Answer

If k is divisible by 10 and 12, is k divisible by 24? 

I'll try by picking some numbers:

k=120 -- divisible by 10 and 12 and 24
k=60 -- disivible by 10 and 12 but not 24

So is K divisible by 24 ? Maybe, maybe not.

What are we trying to solve here ? If it's a DS question, I'll say not sufficient.

Anonymous · Answer

I have a question about this method. Actually Iâ€™m not too clear about how it works, but here are my thoughts.

If K is divisible by 10, the it must be a multiple of 10. So we can write k = 10n where n = 1,2,3,4â€¦ etc
So k = 10n = (2)(5)n

Similarly, since k is divisible by 12, then k must be a multiple of 12. So k=12n=(2^2)(3)n

Now we want to know if k is a multiple of 24, so k=24n=(2^3)(3)n. However, this can only be achieved by multiplying k=(2^2)(3)n by 2, to give (2^3)(3)n. There is no way that (2)(5)n can be made to be a multiple of 24. So k is divisible by 12 and 24, but not by 10. Is that how this method works ? I think itâ€™s a fantastic way to solve such questions instead of plugging numbers. When you plug numbers, you spend time thinking about possibilities that can make and break the logic.

ywilfred · Answer

Sorry guys, forgot to log in. The guest was actually me.

ian7777 · Answer

ywilfred,

you're almost there. I'll explain it as simply as I can, because it is definately hard to wrap your head around, but once you do, it'll open many doors of opportunity.

We know that it's divisible by 10 and 12, right? Let's break both of them down to their primes: 2x5 and 2x2x3. In your algebraic method, you wrote that k=2x5xn and k=2x2x3xn. But that's not true, because it's the same k, so it can't be the same n. It's more correct to say that k=2x2x3xm.

Think about how we use primes to get the lowest common multiple. We have to take each prime that's in both numbers, and each one has to occur the maximum number of times possible. So the lowest common multiple of 10 and 12 is 2x2x3x5 = 60. So whatever your k is, it is actually a multiple of 60.

In your method, it would have to be 2x2x3x5xnxm.

Now, try to divide that by 24. You can't, because 24 is 2x2x2x3 - it's got too many 2's in it.

There are definately ways to make this number a multiple of 24. You can make n or m a 2, and you'll have it. But you can't be positive about that. As long as 60 isn't multiplied by another even number, the product will never be divisible by 24.

I hope this helps. I'm rereading it and it seems a little convoluted. If I had you sitting in my classroom, I'd explain it on the board in 5 minutes, and you'd walk away sold. Let me know if I need to be more specific.

If k is divisible by 10 and 12, is k divisible by 24? (BTW,

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