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If \(n\) is multiple of \(5\), and \(n = p^2q\) where \(p\) and \(q\) are prime, which of the following must be a multiple of \(25\)?
A \(p^2\) B. \(q^2\) C. \(pq\) D. \(p^2q^2\) E. \(p^3q\)
\(n=5k\) and \(n=p^2p\), (\(p\) and \(q\) are primes). Q: \(25m=?\)
Well obviously either \(p\) or \(q\) is \(5\). As we are asked to determine which choice MUST be multiple of \(25\), right answer choice must have BOTH, \(p\) and \(q\) in power of 2 or higher to guarantee the divisibility by \(25\). Only D offers this.
If n is a multiple of 5 and n = p^2*q, where p and q are prime numbers which of the following must be a multiple of 25
n is a multiple of 5 and p and q are prime numbers. the only prime number which multiple of 5 i s5 itself so either p or q is 5 This is why we can surely say that p^2*q^2 is the multiple of 25 since one of thme is 5 and 5^2 = 25 so d is the answer
n is a multiple of 5 n = pq^2 and p and q are primes numbers... so either p or q is 5 or both are 5
A. p^2 -- q could be 5, so this might not be a multiple of 25 B. q^2 -- p could be 5, so this might not be a multiple of 25 C. pq -- p could be 5 and q some other prime number,so this might not be a multiple of 25 D. p^2q^2 -- bingo, either p or q has to be 5, and this one sure will be a multiple of 25 E.p^3q - q could be 5, so this might not be a multiple of 25
Sorry (in advance) if I'm not posting this in the right place. Not sure I quite figured what to post where... Could someone help me with this question? TIA!
If n is a multiple of 5 and \(n=p^2q\), where p and q are prime numbers, which of the following must be a multiple of 25? a) \(p^2\) b) \(q^2\) c) \(pq\) d) \(p^2q^2\) e) \(p^3q\)
if n is a multiple of 5, it means [/m]p^2q[/m]is multiple of 5. Now both p and q are prime, so atleast one of them should be 5.
let say if p=5, then and q=3, (n=75) ,then option b is out. >>> [/m]3^2[/m] is not a multiple of 25. let say if p=3, then and q=5, (n=45) ,then option a is out. >>> [/m]3^2[/m] is not a multiple of 25. let say if p=3, then and q=5, (n=45) ,then option c is out. >>> 3 * 5 is not a multiple of 25. let say if p=3, then and q=5, (n=135) ,then option e is out. >>>[/m]3^3 * 5[/m] is not a multiple of 25.
Let see option D.
Both p or q can be 5, and if any one of them is squared, the result will be divisible by 5...!!
For this question, it's best to look at the equation and the conditions together. Here's what we know: 1. n must be a multiple of 5 2. n=p^2*q 3. p and q are prime numbers.
For n to be a multiple of 5, either p or q has to be 5. They can't be 10, 15, 25, etc. since they have to be prime numbers. As long as one of the two is 5, the other can be any prime number. Knowing this, take a look at the answer choices:
A. p^2 B. q^2 C. pq D.p^2*q^2 E.p^3*q
A and B should be eliminated, because the question asks "which of the following MUST be a multiple of 25", which means for whatever values we put in that fulfill the conditions in the stem, the correct answer choice should be 25. A and B are both at risk of either p or q being the "other" prime number (p=5 and q=3, p=3 and q=5) in which case 9 won't be divisible by 25.
C is also out-- we can finagle p and q into both being 5 to make this true, but it will not be true for every case, since p or q can just as easily be 3, and 15 won't be divisible by 25.
D is the correct answer because regardless of what p or q may be individually, the fact is that one of them will always have to be 5 and thus the result of p^2*q^2 will always be divisible by 25, which is what we're looking for in the correct answer.
E is incorrect because it's actually very similar to C, where we can potentially make it divisible by 25, but it won't be true for every case.
I hope that helps, feel free to let me know if you have any other questions!
Re: If is n is multiple of 5, and n=p^2*q where p and q are [#permalink]
15 Jan 2012, 16:45
D is the correct answer. Tip - whenever given like n = 5k, and n = pq, always check the possibility of both p and Q as 5. I did only for 1 variable and got the answer wrong then later Bunnel post helped.
Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink]
21 Dec 2015, 03:12
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