2 Quick Questions

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2 Quick Questions

by javzprobz » Wed Aug 07, 2013 8:29 am
Hi Brent,

I would appreciate it if you answer these two questions.

First one: In the video 12 of Integer Properties, you mention one useful rule for divisors. "If jk is a divisor of N, then j is a divisor of N and k is a divisor of N."

Just a few days ago, I came across this DS question, which belongs to Manhattan:

"Is n divisible by 108? 1)n is divisible by 12 2)n is divisible by 9 "

I started solving this q by saying that statement 1 is insufficient and statement 2 is also insufficient, then I said wait a minute if I consider both statements together, I can say that if n is divisible by j and if n is divisible by k, then n is divisible by j*k too.

So, I said since 12*9 is equal to 108, then the answer to the above question should be C!

However, when I read the answer explanation for this q, I saw that the correct answer is E. The explanation said that from the q we can get this, "is n=(2^2)*(3^3)*?", and from the first statement we can get this, "n=(2^2)*3*", and from the second statement we can get this, "n=3^2". The explanation said that when combining statement 1 and 2, we can't say with certainty whether the 3 factor in the first statement is one of the two 'threes' in the second statement or it is a new 3. If it is a new 3, then n will be divisible by 108. But if it is not a new 3 (meaning it is one of those threes in the second statement), then we're not sure whether n is divisible by 108. Hence E. While I really understand the given explanation by Manhattan, I would like to know whether I used that 'Divisor Rule' in the video 12 in a wrong way to get to C or if there's a sort-of limitation or consideration when using that divisor rule.

And my second question is that, again, somewhere in Manhattan I saw this DS question:

"Is p an odd integer? 1)p^2 is odd 2)root(p) is odd"

I solved this question by saying that OK p^2=p*p=odd and we know that only the product of 2 odd numbers can be odd, so p should be odd. And root(p)*root(p)=p, since root(p) is odd and odd*odd=odd, then p should be odd. Hence D. But the given correct answer was B! Sorry, I couldn't find any explanations for that B answer. Maybe the given answer by that expert was just a mistake. Do you think my way of solving this super easy question is OK and my answer is correct?

Thank you so much in advance.

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by [email protected] » Wed Aug 07, 2013 2:26 pm
javzprobz wrote:Hi Brent,

I would appreciate it if you answer these two questions.

First one: In the video 12 of Integer Properties, you mention one useful rule for divisors. "If jk is a divisor of N, then j is a divisor of N and k is a divisor of N."

Just a few days ago, I came across this DS question, which belongs to Manhattan:

"Is n divisible by 108? 1)n is divisible by 12 2)n is divisible by 9 "

I started solving this q by saying that statement 1 is insufficient and statement 2 is also insufficient, then I said wait a minute if I consider both statements together, I can say that if n is divisible by j and if n is divisible by k, then n is divisible by j*k too.

So, I said since 12*9 is equal to 108, then the answer to the above question should be C!

However, when I read the answer explanation for this q, I saw that the correct answer is E. The explanation said that from the q we can get this, "is n=(2^2)*(3^3)*?", and from the first statement we can get this, "n=(2^2)*3*", and from the second statement we can get this, "n=3^2". The explanation said that when combining statement 1 and 2, we can't say with certainty whether the 3 factor in the first statement is one of the two 'threes' in the second statement or it is a new 3. If it is a new 3, then n will be divisible by 108. But if it is not a new 3 (meaning it is one of those threes in the second statement), then we're not sure whether n is divisible by 108. Hence E. While I really understand the given explanation by Manhattan, I would like to know whether I used that 'Divisor Rule' in the video 12 in a wrong way to get to C or if there's a sort-of limitation or consideration when using that divisor rule.

And my second question is that, again, somewhere in Manhattan I saw this DS question:

"Is p an odd integer? 1)p^2 is odd 2)root(p) is odd"

I solved this question by saying that OK p^2=p*p=odd and we know that only the product of 2 odd numbers can be odd, so p should be odd. And root(p)*root(p)=p, since root(p) is odd and odd*odd=odd, then p should be odd. Hence D. But the given correct answer was B! Sorry, I couldn't find any explanations for that B answer. Maybe the given answer by that expert was just a mistake. Do you think my way of solving this super easy question is OK and my answer is correct?

Thank you so much in advance.
Hi javzprobz,

I'm happy to answer these questions.

Question #1
The rule " "If jk is a divisor of N, then j is a divisor of N and k is a divisor of N" is true. However, notice that this is an IF...THEN rule.
You have incorrectly used the rule in reverse. You concluded "If "j is a divisor of N and k is a divisor of N then jk is a divisor of N." There is no such rule.


Question #2
Statement 1 tells us that p^2 is odd. However, this does not mean that p is an integer.
For example, if p = √3, then p^2 is odd, but p is not odd.
For that reason, statement 1 is not sufficient.

I hope that helps.

Cheers,
Brent
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by javzprobz » Wed Aug 07, 2013 10:17 pm
I seriously can't thank you enough, Brent. Thanks a million.

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by [email protected] » Thu Aug 08, 2013 6:12 am
You're welcome.

All the best,
Brent
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by JasonBal » Sat Dec 26, 2020 6:40 pm
So I didnt see a thread like this and thought it would be good to have one for the people who just have a quick simple question that needs a quick answer.
Just keep adding questions or answers