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The “primeness” of a positive integer x is defined as

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The “primeness” of a positive integer x is defined as  [#permalink]

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New post 05 Jul 2018, 23:38
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E

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Question Stats:

81% (00:55) correct 19% (01:12) wrong based on 57 sessions

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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
Spoiler: OA

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Re: The “primeness” of a positive integer x is defined as  [#permalink]

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New post 06 Jul 2018, 01:17
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GyMrAT 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


Greatest primeness=Largest prime factor-smallest prime factor.

Among the options,14 has the largest prime factor as 7 & smallest prime factor as 2

So, greatest primeness=7-2=5

Ans. (C)

A quick check,
A. 5-2=3
B.3-2=1
C.7-2=5
D.5-2=3
E.3-2=1
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Re: The “primeness” of a positive integer x is defined as the positive dif  [#permalink]

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New post 13 Jun 2019, 00:35
Bunuel 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


(A) 10-5*2
(B) 12-3*2^2
(C) 14-7*2
(D) 15-5*3
(E) 18-3^2*2

IMO C
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Re: The “primeness” of a positive integer x is defined as the positive dif  [#permalink]

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New post 13 Jun 2019, 01:12
A:10=5*2 , Primeness = 3
B:12=3*2² , Primeness = 1
C:14=7*2 , Primeness = 4
D:15=5*3 , Primeness = 2
E:18=3²*2, Primeness = 1

Hence, Answer must be C

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Re: The “primeness” of a positive integer x is defined as the positive dif  [#permalink]

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New post 13 Jun 2019, 09:46
Bunuel 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


factorize given no in prime we get option C has primeness as 5
IMO C
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Re: The “primeness” of a positive integer x is defined as  [#permalink]

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New post 27 Nov 2019, 11:57
GyMrAT 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


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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Re: The “primeness” of a positive integer x is defined as   [#permalink] 27 Nov 2019, 11:57
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