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TargetMBA007
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10 Mar 2020, 19:27
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Hi,
Here is a sample question (Modified slightly, hence not to be used as practice question) and I was just keen if there is a faster way to approach questions like this:
* A certain number X is divisible by 14! Which of the following must be a factor of X?
1690
1210
726
625
616
Normally, I would just prime factorize 14! and answer choices and choose the answer that contains all the prime factors of 14!. But its a time consuming process and I wondered if there are any shortcuts that could be deployed here?
Thanks
Here is a sample question (Modified slightly, hence not to be used as practice question) and I was just keen if there is a faster way to approach questions like this:
* A certain number X is divisible by 14! Which of the following must be a factor of X?
1690
1210
726
625
616
Normally, I would just prime factorize 14! and answer choices and choose the answer that contains all the prime factors of 14!. But its a time consuming process and I wondered if there are any shortcuts that could be deployed here?
Thanks
10 Mar 2020, 22:46
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TargetMBA007
Hi,
Here is a sample question (Modified slightly, hence not to be used as practice question) and I was just keen if there is a faster way to approach questions like this:
* A certain number X is divisible by 14! Which of the following must be a factor of X?
1690
1210
726
625
616
Normally, I would just prime factorize 14! and answer choices and choose the answer that contains all the prime factors of 14!. But its a time consuming process and I wondered if there are any shortcuts that could be deployed here?
Thanks
Here is a sample question (Modified slightly, hence not to be used as practice question) and I was just keen if there is a faster way to approach questions like this:
* A certain number X is divisible by 14! Which of the following must be a factor of X?
1690
1210
726
625
616
Normally, I would just prime factorize 14! and answer choices and choose the answer that contains all the prime factors of 14!. But its a time consuming process and I wondered if there are any shortcuts that could be deployed here?
Thanks
The way has to do with factors and it is the way you can manipulate the info you have.
Now 14! tells us that the factors cannot be any prime factor above 14 and with just one power for primes between 7 and 14.
let us check the numbers..
1690=169*10=13*13*10....13^2 is not possible
1210=121*10=11*11*10....11^2 is not possible
726=121*6=11*11*6....11^2 is not possible
625=5^4...There can be only 14/5+14/25=2+0=2 5s, so not possible
616..The only choice left... so has to be the answer, but let us check 616=2*308=2*2*154=2*2*2*77=2^3*7*11..Possible
TargetMBA007
Joined: 22 Nov 2019
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10 Mar 2020, 23:39
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Quote:
Just one power for primes between 7 and 14.
Thanks Chetan,
That is super useful, not something that I intuitively thought of. It definitely makes the calculation a lot quicker.
Open to any more ideas here..
