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guys ...i just didnt get this problem.... pls can some one tell me what exactly is being asked?? and how to start analysis of such problems... also what difficulty level is this problem at? on a scale of 1 to 5? 5 being most difficult...
and what is the meaning of sentence 1?? it says m has 9 +ve factors. in the stem it says m has 2 prime factors... how can a no. have factors like this?? is it that square and cube of the basic prime nos are also considered?? how do we start thinking abt such problems on the exam day???
well, does'nt look like it is asking that.. it asks if m is divisible by p^2*t. i dont think that is the same thing as is power of p>=2.... right??? or.... wrong
what it looks to be asking is when m/p^2*t, do we get an integer??? but i think that if p and t divide m , then p^2 usually divides right, unless the m itself <p^2*t. eg , take 6. it is divisible by 2 and 3 , but not by 2^2*3, but that is bcos p^2*t>m for this example... but what is the problem asking us?
well, does'nt look like it is asking that.. it asks if m is divisible by p^2*t. i dont think that is the same thing as is power of p>=2.... right??? or.... wrong
I have rephrased the question. Thereby it looks different. If M is divisible by p^2t then of course it means that m has factor of p equal to or more than 2 and also that m has a factor of t.
guys ...i just didnt get this problem.... pls can some one tell me what exactly is being asked?? and how to start analysis of such problems... also what difficulty level is this problem at? on a scale of 1 to 5? 5 being most difficult...
and what is the meaning of sentence 1?? it says m has 9 +ve factors. in the stem it says m has 2 prime factors... how can a no. have factors like this?? is it that square and cube of the basic prime nos are also considered?? how do we start thinking abt such problems on the exam day???
1: to have more than 9 +ve factors, either, at least, p = 4 and t = 1, or p = 1 and t = 4. nsf. 2: m is a multiple of p^3 means m is also a multiple of p^2t. suff
well, does'nt look like it is asking that.. it asks if m is divisible by p^2*t. i dont think that is the same thing as is power of p>=2.... right??? or.... wrong
I have rephrased the question. Thereby it looks different. If M is divisible by p^2t then of course it means that m has factor of p equal to or more than 2 and also that m has a factor of t.
That could be a question, but GMAT questions donot have that pattern.
if m can be written as m = p^x * q^y * r ^z where p, q and r are distinct prime numbers number for total +ve factors = (1+x)(1+y)(1+z)
question : m = p^x * t^y is m a mutiple of p^2 * t --> is x >=2
statement 1 : (1+x)(1+y) > 9 .... x,y = 1,4 Or 3,3 Not suff statement 2 : m = k * p^3 ----> x >=3 .. Suff
why this combination?? how did u arrive at that combo of 1,4 or 3,3? why not 2,5 or something like that?
we have to see if (1+x)(1+y) > 9 is enough to prove that x >= 2 or not , so i took two examples with x < 2 and x > 2. Since both cases are possible, the statement is not suff.
guys ...i just didnt get this problem.... pls can some one tell me what exactly is being asked?? and how to start analysis of such problems... also what difficulty level is this problem at? on a scale of 1 to 5? 5 being most difficult...
and what is the meaning of sentence 1?? it says m has 9 +ve factors. in the stem it says m has 2 prime factors... how can a no. have factors like this?? is it that square and cube of the basic prime nos are also considered?? how do we start thinking abt such problems on the exam day???
given that : Only two prime factors are p,t of m question : m=p^2 * t *n n is any integer n is again product of p,t only since p,t are only prime factors
(1) says m has > 9 positive factors => t^8.p or p^8.t or t^2*p^7 etc hence when m=p*t^8 then its not the multiple of p^2 *t when m = p^8.t then its the multiple of p^2 *t INSUFFI
(2) says m is multiple of p^3 also only two prime factors of m are p,t hence p^3 * p^k * t^l is possible hence always multiple of p^2*t
I will first take the example and then i will explain it... Say m = 36. So m has 9 factors: 1 2 3 4 6 9 12 18 36. Now only two numbers are prime in this: 2 and 3. say p and t. so p^2*t^2 = m. so, A is definately the answer, because p^2 *t is factor of m, obviously.
Further, in general, we have (a + 1)(b+1)(c+1) factors of a number where a, b, c are powers of prime number in the factors of number....
see, example, 36 has 9 factors....(3)(3)=9. so a = 2, b = 2. because there are only two primes 2, 3.
guys ...i just didnt get this problem.... pls can some one tell me what exactly is being asked?? and how to start analysis of such problems... also what difficulty level is this problem at? on a scale of 1 to 5? 5 being most difficult...
and what is the meaning of sentence 1?? it says m has 9 +ve factors. in the stem it says m has 2 prime factors... how can a no. have factors like this?? is it that square and cube of the basic prime nos are also considered?? how do we start thinking abt such problems on the exam day???
It is B)
Suppose there is a number 12, now it has only two prime factors 2 and 3
Statement 1) is insuff. because you can have \(3^9*2\) and it is not multiple of \(2^2 * 3\) Statement 2) if m is multiple of \(p^3\) then it will be multiple of \(p^2\) as well and t is already another prime factor so multiple of \(p^2 * t\)