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Difficulty:
5%
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Question Stats:
87% (00:53) correct
13%
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wrong
based on 161
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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
A) 10
B) 12
C) 14
D) 15
E) 18
GyMrAT
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
Bunuel
(A) 10-5*2
(B) 12-3*2^2
(C) 14-7*2
(D) 15-5*3
(E) 18-3^2*2
IMO C
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
Posted from my mobile device
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
Posted from my mobile device
Archit3110
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Bunuel
factorize given no in prime we get option C has primeness as 5
IMO C
ScottTargetTestPrep
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Joined: 14 Oct 2015
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Expert reply
Posts: 22,736
GyMrAT
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
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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