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GMAT Prep problem - Number of positive factors

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GMAT Prep problem - Number of positive factors

by sreak1089 » Sat Jan 16, 2010 9:44 am
45) If k is a positive integer, then 20k is divisible by how many different positive integers?
a. k is prime
b. k is 7

IMO ans is D.. However, in Zuleron's doc, it is marked as B.

20k can be expressed as 2^2*5*k

Number of positive factors of 20K is 3*2*(exponent of k + 1)

Now, if k is prime or k is 7, the exponent of k will be 1. Hence the Ans should have been D right?
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by going4gmat » Sat Jan 16, 2010 9:58 pm
answer will be B ....

IN THE FIRST OPTION U HV NO IDEA WAT THE VALUE OF K IS?

SUPPOSE K IS 2 or 5 then it will hv only 3 factors- 1, 2, 5,

and if k is any other positive prime number like 11, then it will hv more factors - 1, 2, 5, 11

so the number of factors is not constsnt...

however, 2nd option states dat it is 7, so we can calculate the exact number of factors- 1,2,5, 7, hence 4 factors....answer is b
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by sreak1089 » Sat Jan 16, 2010 10:50 pm
Got it. Thank you so much. Shuks, such a silly thing, I did not realize.
sreak1089 wrote:45) If k is a positive integer, then 20k is divisible by how many different positive integers?
a. k is prime
b. k is 7

IMO ans is D.. However, in Zuleron's doc, it is marked as B.

20k can be expressed as 2^2*5*k

Number of positive factors of 20K is 3*2*(exponent of k + 1)

Now, if k is prime or k is 7, the exponent of k will be 1. Hence the Ans should have been D right?
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by Anaira Mitch » Wed Dec 28, 2016 2:35 am
1). K is prime, 20*K=2^2*5*K, k could be 2, 5, or other prime, so, number of the different prime factors of 20*k can not be determined.

2). K=7, 20*k = 2^2*5*7, has 3 different prime factors.
Answer is B
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by Brent@GMATPrepNow » Thu Dec 29, 2016 9:06 am
sreak1089 wrote:45) If k is a positive integer, then 20k is divisible by how many different positive integers?

(1) k is prime
(2) k is 7
BACKGROUND INFO:
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40

-----------------------------------
Now onto the question....

Target question: 20k is divisible by how many different positive integers?

Statement 1: k is prime
There are several values of k that satisfy statement 1. Here are two:
Case a: k = 2, in which case 20k = (20)(2) = 40 = (2^3)(5^1). So, the number of divisors = (3+1)(1+1) = (4)(2) = 8. In other words, 20k is divisible by 8 positive integers
Case b: k = 3, in which case 20k = (20)(3) = 60 = (2^2)(3^1)(5^1). So, the number of divisors = (2+1)(1+1)(1+1) = (3)(2)(2) = 12. In other words, 20k is divisible by 12 positive integers
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: k is 7
This means that 20k = (20)(7) = 140
Since we know the EXACT value of 20k, we COULD (very easily) list and count all of positive divisors of 140.
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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