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A k-almost prime number is defined as a positive integer with exactly

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A k-almost prime number is defined as a positive integer with exactly  [#permalink]

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New post 14 Sep 2015, 23:00
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  95% (hard)

Question Stats:

45% (02:53) correct 55% (02:27) wrong based on 145 sessions

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Re: A k-almost prime number is defined as a positive integer with exactly  [#permalink]

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New post 15 Sep 2015, 03:42
6
anudeep133 wrote:
Bunuel wrote:
A k-almost prime number is defined as a positive integer with exactly k prime factors that are not necessarily distinct. The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number is

A. 6
B. 8
C. 16
D. 24
E. 28

Kudos for a correct solution.


Solution: 3-almost prime numbers : 8(as 8 = 2*2*2) , 12 (2*2*3) , 18 (2*3*3) , 20 (2*2*5)....
4-almost prime numbers : 16(as 8 = 2*2*2*2) , 24 (2*2*2*3) , 36 (2*2*3*3)...
The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number = 36-20 = 16.



Option C.

Bunuel I almost took 5 min to solve this. Is there a easier method?



The term “k-almost prime” is defined: the number has exactly k prime factors (including repeats).
Let’s try making some of these numbers out of small integers, starting low: the smallest 3-almost prime, for instance, would be 2 × 2 × 2 = 8. Keep going by increasing the primes: the second smallest 3-almost prime is 2 × 2 × 3 = 12.
The third smallest 3-almost prime is 2 × 3 × 3. The fourth smallest is 2 × 2 × 5 = 20. That’s one of the numbers we want.
Now find the pattern with 4-almost primes. The smallest is 2 × 2 × 2 × 2 = 16. The second smallest is 2 × 2 × 2 × 3 = 24, and the third smallest is 2 × 2 × 3 × 3 = 36.
36 – 20 = 16.
answer C.
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Re: A k-almost prime number is defined as a positive integer with exactly  [#permalink]

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New post 15 Sep 2015, 02:58
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Bunuel wrote:
A k-almost prime number is defined as a positive integer with exactly k prime factors that are not necessarily distinct. The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number is

A. 6
B. 8
C. 16
D. 24
E. 28

Kudos for a correct solution.


Solution: 3-almost prime numbers : 8(as 8 = 2*2*2) , 12 (2*2*3) , 18 (2*3*3) , 20 (2*2*5)....
4-almost prime numbers : 16(as 8 = 2*2*2*2) , 24 (2*2*2*3) , 36 (2*2*3*3)...
The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number = 36-20 = 16.

Option C.

Bunuel I almost took 5 min to solve this. Is there a easier method?
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Re: A k-almost prime number is defined as a positive integer with exactly  [#permalink]

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New post 15 Sep 2015, 04:12
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1
1st 3 almost prime = 2*2*2 = 8
2nd 3 almost prime = 2*2*3 = 12
3rd 3 almost prime = 2*3*3 = 18
4th 3 almost prime = 2*2*5 = 20

1st 4th almost prime = 2*2*2*2 = 16
2nd 4th almost prime = 2*2*2*3 = 24
3rd 4th almost prime = 2**2*3*3 = 36

Difference between 3rd 4th almost prime & 4th 3 almost prime = 36-20 = 16
Answer:C
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Re: A k-almost prime number is defined as a positive integer with exactly  [#permalink]

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New post 20 Sep 2015, 21:25
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2
Bunuel wrote:
A k-almost prime number is defined as a positive integer with exactly k prime factors that are not necessarily distinct. The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number is

A. 6
B. 8
C. 16
D. 24
E. 28

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

The term “k-almost prime” is defined: the number has exactly k prime factors (including repeats).

Let’s try making some of these numbers out of small integers, starting low: the smallest 3-almost prime, for instance, would be 2 × 2 × 2 = 8. Keep going by increasing the primes: the second smallest 3-almost prime is 2 × 2 × 3 = 12.

The third smallest 3-almost prime is 2 × 3 × 3. The fourth smallest is 2 × 2 × 5 = 20. That’s one of the numbers we want.

Now find the pattern with 4-almost primes. The smallest is 2 × 2 × 2 × 2 = 16. The second smallest is 2 × 2 × 2 × 3 = 24, and the third smallest is 2 × 2 × 3 × 3 = 36.
36 – 20 = 16.

The correct answer is C.
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Re: A k-almost prime number is defined as a positive integer with exactly  [#permalink]

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New post 30 Nov 2018, 02:26
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Re: A k-almost prime number is defined as a positive integer with exactly   [#permalink] 30 Nov 2018, 02:26
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