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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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Bunuel
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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GyMrAT
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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GyMrAT
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

\(5-2=3\)

B) 12

\(3-2=1\)

C) 14

\(7-2=5\)

D) 15

\(5-3=2\)

E) 18

\(3-2=1\)


The highest value is for C, which is our choice.
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