If n = 2pq, where p and q are distinct prime numbers greater

Question

If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight

Bunuel · Accepted Answer

Since we cannot have two correct answers just pick two primes greater than 2, and see how many different positive even divisors will 2pq have. Say p = 3 and q = 5 --> 2pq = 30--> 30 has 4 even divisors: 2, 6, 10 and 30. Answer: C. Similar question to practice from OG: if-n-2pq-where-p-and-q-are-distinct-prime-numbers-greater-148939.html Another similar question: if-n-is-a-prime-number-greater-than-3-what-is-the-remainder-137869.html Hope it helps.

Vinayprajapati · Answer

Total number of divisor of 2pq are (1+1)*(1+1)*(1+1)= 8
Total number of odd divisor of 2pq are (1+1)*(1+1)=4
Total number of even divisor of 2pq are = total divisor- odd divisor=8-4=4
Hence c

gmatgooner · Answer

Answer - 'C' - Four.

For a number 2pq with primes p&q,there will be four even divisors - 2,2*p,2*q,2*p*q

pqhai · Answer

Because p and q are distinct  prime  number > 2, so  p and q are ODD numbers

2pq = 2*odd*odd

There are only four  EVEN  factors of n, including n (because n is even):
2
2*p
2*q
2*pq

C is correct.

Hope it helps.

Temurkhon · Answer

Divisors are:

n, 2, 2p, 2q

C

Shiv2016 · Answer

Even integer multiplied by any number whether odd/even will ALWAYS give even integer.

For example, 2*3*3*3*3*3*3= 1458

Therefore in the above question there will be 4 even positive divisors of n.
n=2*p*q
p,q>2

2 is the only even prime number.
Thus p and q are odd and will be counted under odd divisors. p*q (odd*odd) will also give odd.

Thus the even divisors are: 2, 2p, 2q, and 2pq

ScottTargetTestPrep · Answer

We can let p = 3 and q = 5. Thus, the product of 2pq is 2 x 3 x 5 = 30. The factors of 30 are:

1, 30, 2, 15, 3, 10, 5, 6

Since 30 has 4 even factors, n has 4 even factors.

Alternatively, we can solve the problem algebraically. Keep in mind that p and q will be odd primes since they are greater than 2.

The factors of n are:

1, 2pq, 2, pq, p, 2q, q, 2p

We see that the even factors of n are 2pq, 2, 2q, and 2p, so there are 4 even factors.

Answer: C

medinib · Answer

If n = 2pq, where p and q are distinct prime numbers greater than 2

Pick any two prime numbers greater than prime 2. Say  5  and  7

n = 2 x 5 x 7

Factor of n is n itself -  70

and the even factors of n are   5 x 2 = 10

7 x 2 = 14 and 2

Therefore, total factors of n are  2,10, 14  and  70   - 4 (C)

Kinshook · Answer

n=2pq
Since p & q are odd prime numbers greater than 2, p & q are not even
2, 2p , 2q and 2pq are even divisors.
4 numbers

IMO C

Posted from my mobile device

jim441 · Answer

If n = 2pq, where p and q are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?

Ans:
1. P& q are odd, so pq is odd but when multiplied by 2, it will yield even number, so n is even
2. 2 is also a factor of n
3 2p is also going to be an even factor
3 2q is also going to be an even factor

so answer is four is (C)

messi16 · Answer

Try with example numbes. Make p and q some arbitrary primes. Make them 3 and 5. Thus we get 2(3)(5) = 30. The number of even positive divisors, including 30 is four. Thus our answer is 4.

If n = 2pq, where p and q are distinct prime numbers greater

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If n = 2pq, where p and q are distinct prime numbers greater

Prep Toolkit

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