The prime sum of a number is the sum of all its prime factors,

Question

The prime sum of a number is the sum of all its prime factors, including repetition. For example, prime sum of 12 is 7, since 12=2*2*3. Which of the following has a prime sum greater than 30?

(A) 880

(B) 1,024

(C) 1,430

(D) 1,440

(E) 1,500

Shovan01 · Answer

1430=5*286=5*2*143=5*2*11*13
Now, 5+2+11+13=31
Therefore, right answer is (C).

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • The prime sum of a number is the sum of all its prime factors, including repetition

To find  
We need to determine
 • Among the given numbers, which one has a prime sum greater than 30

Approach and Working out  
 880 = 2^4 * 5 * 11 
 • Prime sum of 880 = (2 x 4) + 5 + 11 = 24

1024 = 2^{10} 
 • Prime sum of 1024 = 2 x 10 = 20

1430 = 2 * 5 * 11 * 13 
 • Prime sum of 1430 = 2 + 5 + 11 + 13 = 31

1440 = 2^5 * 3^2 * 5 
 • Prime sum of 1440 = (2 x 5) + (3 x 2) + 5 = 21

1500 = 2^2 * 3 * 5^3 
 • Prime sum of 1500 = (2 x 2) + 3 + (5 x 3) = 22

Thus, option C is the correct answer.

Correct Answer: Option C

Nipungupta9081 · Answer

IMO C

Option A = 880 - 2^4 * 5 * 11 = 2+2+2+2+5+11 = 24

Option B = 1024 = 2^10 = 2 * 10 = 20

Option C = 1,430 = 2 + 5+11 + 13 = 31

Option D - 2^5 * 3^2 * 5 = 2+2+2+2+2+3+3+5 = 21

Option E = 2^2 * 3 * 5^3 = 2+2+3+5+5+5 = 22

Thelionking1234 · Answer

IMO C

1430= 2X5X11X13

Hence

Prime sum of 1430 = 2 + 5 + 11 + 13 = 31

Posted from my mobile device

Fdambro294 · Answer

Always seems like a few common Numbers keep showing up throughout all the problems. May be worth remembering:

143 = 11 * 13

119 is NOT a Prime Number ----- 119 = 7 * 17

91 is NOT a Prime Number ---- 91 = 13 * 7

2^10th = 1024 (and remember the First 10 Powers of 2 as well as the First 5 Powers of 3)

1, 001 = Product of 3 Consecutive Prime Numbers = 7 * 11 * 13

Just something I noticed, may or may not be worth remembering these few little Number Properties.

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The prime sum of a number is the sum of all its prime factors,

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