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# How Well Do You Know Your Factors?

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abhinashgc wrote:
Dont understand how 7^x wil be cancelled out by numerator. let say if i use 7^10.. Please help.
Thanks
Abhinash

It is not required for 7^x to be cancelled.
Since , A=5*p and there is nothing in the denominator (B) to cancel this 5 , we can say that C is divisible by 5.
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abhinashgc wrote:
Bunuel wrote:
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Dont understand how 7^x wil be cancelled out by numerator. let say if i use 7^10.. Please help.
Thanks
Abhinash

I think I have a much simpler explanation. If A=210 and B=7^x, say 7^1, for simplicity sake. than 210 can be factorized in the following manner. 30*7. In other words there is only one 7 in 210.
Now, however you choose these numbers for A and B, You can never cancel out that 30 using 7. 30 by itself is divisible by 5. So for the equality A/B=C/D to hold, C must be also multiple of 30, as D must be equivalent of some power of 7.

I hope this explanation is correct and hope it helps.

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Appreciate the effort but too many jumps in logic which make it hard for a noob to follow... even just reading the start...

"Statement 1: A is divisible by 210

We still have no idea what B is so this statement alone is not sufficient. Let’s take an example of how the value of B could change our answer. Assume A is 210.

If B is 3, AD/B will be divisible by 5."

Why will AD/B be divisible by 5...?
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unicornilove wrote:
Appreciate the effort but too many jumps in logic which make it hard for a noob to follow... even just reading the start...

"Statement 1: A is divisible by 210

We still have no idea what B is so this statement alone is not sufficient. Let’s take an example of how the value of B could change our answer. Assume A is 210.

If B is 3, AD/B will be divisible by 5."

Why will AD/B be divisible by 5...?

­Question: A, B, C and D are positive integers such that A/B = C/D. Is C divisible by 5?

Statement 1: A is divisible by 210
Statement 2: B = 7^x, where x is a positive integer

See, as C=AD/B  B must be completely divisible in AD for C to be an integer.

Statement 1: A is divisible by 210
means A is a multiple of 210
If B is multiple of 7 or 21 or 42 we get C is divisible by 5
but what if B is also a multiple of 210?
So our stem is C divisible by F cant be proved

Statement 2: B = 7^x, where x is a positive integer
B = 7^x so it can be 7, 7^2 ,7^3 etc
But now we don't have any idea about A

Hence after combining both
A is a multiple of 210 and B is a power of 7, so A must be multiple of 210 and you can see that it has 5 in it
hence 3 and 5 will remain anyhow after cancelling out AD/B

hence C is divisible by 5
PS As you said -B cant be 3 as it is given that B = 7^x so it can be 7, 7^2 ,7^3 etc
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