Is the number of different prime factors of the positive integer p mor

Question

Competition Mode Question

Is the number of different prime factors of the positive integer p more than 3?

(1) The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10

(2) The number of distinct prime factor of  (4p)^3  is 3 more than that of 18

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exc4libur · Accepted Answer

(1) The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10   insufic

dist.pf(10)=(2,5)=2
dist.pf(10p)=2+dist.pf(10)=2+2=4
p=2,5,7,11; dist.pf(10p)=2,5,7,11=4; answer yes
p=7,11; dist.pf(10p)=2,5,7,11=4; answer no

(2) The number of distinct prime factor of (4p)^3 is 3 more than that of 18   sufic

dist.pf(18)=(3^2,2)=(3,2)=2
dist.pf(2^3p^3)=3+dist.pf(18)=3+2=5
dist.pf(2^3p^3)=5
4≤dist.pf(p^3)≤5

Ans (B)

madgmat2019 · Answer

(1) The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10............for 10...its 2,5.....so for p its just 2.....Sufficient to say that its < 3

(2) The number of distinct prime factor of (4p)^3 is 3 more than that of 18.......for 18 its 2,3....for 4^3 its only 2......so the left number of distinct prime factor of p^3 is 2...so its the same for p.....SUFFICIENT

OA:D

Archit3110 · Answer

#1
The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10
10 has 2 prime factors
so 10p will have 4 distinct prime factors ; may or may not be true
insufficient
#2
The number of distinct prime factor of (4p)3 is 3 more than that of 18
18 has = 2*3^2 ; 2 prime factors 
and 64 p^3 has 5 ; 64 = 2^6 * p^3 ; p can have atleast 2 more distinct prime factors
sufficient
IMO B

Is the number of different prime factors of the positive integer p more than 3?

(1) The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10

(2) The number of distinct prime factor of (4p)3 is 3 more than that of 18

unraveled · Answer

Is the number of different prime factors of the positive integer p more than 3?
Let number of prime factors of p = n(p)
n(p) > 3

(1) The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10
10p has primes 2, 5 and others as per p. Here p must have 2 more different prime factors so that 10p has factors 2, 5, p1 and p2 which is two more than 2 and 5 for 10.
Hence n(p) = 4
SUFFICIENT.

(2) The number of distinct prime factor of  (4p)^3  is 3 more than that of 18
18 has two prime factors i.e. 2 and 3
 (4p)^3  has factors as 2 and others as per p such that  (4p)^3  has 3 more than that of 18.
Hence p must be having at least 4 different prime factors so that 5 - 2 = 3 more factors than that of 18.
SUFFICIENT.

Answer D.

freedom128 · Answer

(1) The number of distinct prime factors of 2*5*p =2+2 =4 (including 2 and 5). So the number of distinct prime factor of p varies from 2 to 4 .
NOT SUFFICIENT

(2) The number of distinct prime factor of 64p^3 =2+3=5. So the number of distinct prime factors of p is from 4 to 5.
SUFFICIENT

FINAL ANSWER IS (B)

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CrackverbalGMAT · Answer

The question statement gives us a hint that p is a composite number. Therefore, we are working with a question testing us on composite number concepts.

From statement I alone, we know that 10p has 2 more distinct prime factors than 10 has. Let us look at 10.

10 = 2*5, which means 10 has 2 distinct prime factors. Therefore, we can conclude that 10p has 4 distinct prime factors. Of these 4, 2 and 5 are from the 10; therefore, the p should be contributing the remaining 2 distinct prime factors.

Knowing that p has 2 distinct prime factors, we can answer the question with a NO. Statement I alone is sufficient. The possible answers at this stage are A or D. Answer options B, C and E can be eliminated.

From statement II alone, we know that  (4p)^3  has 3 more distinct prime factors than 18 has. Let us analyse 18.

18 = 2 *  3^2 , which means 18 also has 2 distinct prime factors. 
Now, let us look at  (4p)^3 .  (4p)^3  is nothing but  2^6  *  p^3 . Clearly, 2 is one of the distinct prime factors. But, as per the data given in statement II,  2^6  *  p^3  should have 5 distinct prime factors (3 more distinct prime factors than the ones in 18). This can only happen when p has 4 distinct prime factors.

Knowing that p has 4 distinct prime factors, we can answer the question with a YES. Statement II alone is sufficient. Answer option A can be eliminated.
 The correct answer option is D .
 
Hope that helps!

lacktutor · Answer

Is the number of different prime factors of the positive integer p more than 3?

(Statement1): The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10.
—>the # of distinct prime factors of 10 — 2 and 5 
10p should have 4 distinct prime factors.

a) if p= 21, then 10p= 210. —> 210 = 2*3*5*7 (4 distinct prime factors)
—> p has 2 distinct prime factors (No)

b) if p = 210, then 10p= 2100.—> 2100 = 2^{2}*3*5^{2}*7  ( 4 distinct prime factors) 
—> p has also 4 distinct prime factors. (Yes) 
Insufficient

(Statement2): The number of distinct prime factor of  (4p)^{3}  is 3 more than that of 18. 
—> the # of distinct prime factors of 18 ( 2*3^{2} ) — 2 and 3. 
 (4p)^{3}  should have 5 distinct prime factors.

—> if 4p has 5 distinct prime factors, p should have 4 distinct prime factors( Always YES) 
Sufficient

The answer is B

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eakabuah · Answer

Given that p is a positive integer, Is the number of prime integers of p more than 3?

Statement 1: The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10.
10 has two prime factors. 2 and 5. So, if we are given that 10P has 2 more than the number of distinct prime factors of 10, then for this to be satisfied, p must have 2 distinct prime factors. We can boldly say that p has less than 3 prime factors.

Statement 2: The number of distinct prime factor of (4p)^3 is 3 more than that of 18
The number of prime factors of 4p is the same as the number of prime factors of (4p)^3
Prime factors of 18: 2 and 3.
So if (4p)^3 has three more prime factors than that of 18, then p must have four prime factors, since 4 has only one prime factor. Therefore we can conclude that p has more than 3 factors based on statement 2.

The right answer is puton.

chaitralirr · Answer

Is the number of different prime factors of the positive integer p more than 3?

(1) The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10

(2) The number of distinct prime factor of (4p)3(4p)3 is 3 more than that of 18

Statement 1: The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10

10 distinct prime factors are 5 and 2 p can have 2 distinct prime factors or can have 3, 2, 7 also hence statement 1 is insufficient

Statement 2: The number of distinct prime factor of (4p)3(4p)3 is 3 more than that of 18

18 prime factors are 2,3 the prime factors for 4p is 3 more one prime factor is 2 therefore p has more than 3 prime factors because total prime factors of 4p is 5

Hence statement 2 is sufficient

IMO B

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