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The “primeness”

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by BTGmoderatorDC » Sun Sep 24, 2017 4:02 am
The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness?

A) 10
B) 12
C) 14
D) 15
E) 18

How will i start to solve this? Can any experts help me?

OA C
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by Jay@ManhattanReview » Sun Sep 24, 2017 4:21 am
lheiannie07 wrote:The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness?

A) 10
B) 12
C) 14
D) 15
E) 18

How will i start to solve this? Can any experts help me?

OA C
A) 10:

Factors of 10 are: 1, 2, 4, 5, and 10; the largest prime factor = 5 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 5 – 2 = 3.

B) 12:

Factors of 12 are: 1, 2, 3, 4, 6, and 12; the largest prime factor = 3 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 3 – 2 = 1.

C) 14:

Factors of 14 are: 1, 2, 7, and 14; the largest prime factor = 7 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 7 – 2 = 5.

D) 15:

Factors of 15 are: 1, 3, 5, and 15; the largest prime factor = 5 and the smallest prime factor = 3; thus, the difference between the largest and the smallest prime factors = 5 – 3 = 2.

E) 18:

Factors of 18 are: 1, 2, 3, 6, 9, and 18; the largest prime factor = 3 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 3 – 2 = 1.

The greatest difference is 5 for number 14 (option C).

The correct answer: C

Hope this helps!

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by [email protected] » Mon Sep 25, 2017 3:52 pm
Hi lheiannie07,

This question literally tells you to use prime factorization on the each of the 5 answer choices - as we're looking for the answer with the largest DIFFERENCE between its largest and smallest prime factors.

Answer A: 10 = (2)(5)
Answer B: 12 = (2)(2)(3)
Answer C: 14 = (2)(7)
Answer D: 15 = (3)(5)
Answer E: 18 = (2)(3)(3)

Looking at these options, the largest difference isn't hard to spot...

Final Answer: C

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by Matt@VeritasPrep » Tue Sep 26, 2017 5:18 pm
Find the prime factorization, then do largest prime - smallest prime.

A: 10 = 2 * 5, largest - smallest = 5 - 2 = 3

B: 12 = 2 * 2 * 3, largest - smallest = 3 - 2 = 1

C: 14 = 2 * 7, largest - smallest = 7 - 2 = 5

etc. etc. You get the idea :)
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by EconomistGMATTutor » Fri Oct 13, 2017 10:56 am
The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness?

A) 10
B) 12
C) 14
D) 15
E) 18

How will i start to solve this? Can any experts help me?
Hi lheiannie07,
Let's take a look at your question.
The question states that the “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors.
To find the greatest primeness, we will find the primeness of each number given one by one by finding its factors.

Primeness of 10:
Factors of 10 = 1, 2, 5, 10
Smallest prime factor = 2
Largest prime factor = 5
Primeness of 10 = 5 - 2 = 3

Primeness of 12:
Factors of 12 = 1, 2, 3, 4, 6, 12
Smallest prime factor = 2
Largest prime factor = 3
Primeness of 12 = 3 - 2 = 1

Primeness of 14:
Factors of 14 = 1, 2, 7, 14
Smallest prime factor = 2
Largest prime factor = 7
Primeness of 14 = 7 - 2 = 5

Primeness of 15:
Factors of 15 = 1, 2, 3, 5, 15
Smallest prime factor = 2
Largest prime factor = 5
Primeness of 15 = 5 - 2 = 3

Primeness of 18:
Factors of 18 = 1, 2, 3, 6, 9, 18
Smallest prime factor = 2
Largest prime factor = 3
Primeness of 18 = 3 - 2 = 1

We can see that 14 has the largest primeness, i.e. 5.

Therefore, Option C is correct.
Hope this helps.

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by Scott@TargetTestPrep » Fri Nov 22, 2019 11:48 am
BTGmoderatorDC wrote:The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness?

A) 10
B) 12
C) 14
D) 15
E) 18

How will i start to solve this? Can any experts help me?

OA C
We have to prime factorize each number and find the difference between the largest and smallest prime factors of each number.

A) 10 = 2 x 5

primeness of 10 = 5 - 2 = 3

B) 12 = 2^2 x 3

primeness of 12 = 3 - 2 = 1

C) 14 = 2 x 7

primeness of 14 = 7 - 2 = 5

D) 15 = 3 x 5

primeness of 15 = 5 - 3 = 2

E) 18 = 2 x 3^2

primeness of 18 = 3 - 2 = 1

We see that 14 has the greatest primeness.

Answer: C

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