What is the sum of all numbers less than 200 that are either prime or

Question

What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?

A. 19,900
B. 19,535
C. 19,533
D. 19,523
E. 19,522

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GMATinsight · Answer

Hi

Please check the video explanation here

https://www.youtube.com/watch?v=CNQs4k6735o

Answer: Option E

GMATWhizTeam · Answer

Solution

• Positive number having exactly one factor = 1
• Positive numbers having exactly 2 factors = prime numbers
• Positive numbers having exactly 3 factors = square of prime numbers (i.e.  p^2  where p is a prime number)
• Apart from the above mentioned numbers, all other numbers will have more than 3 factors.
• Therefore, the sum of all numbers less than 200 that are either prime or have more than 3 factors = (sum of all integers from 1 to 199) – (sum of the square of prime numbers which are less than 15) – 1  15^2 = 225 , and number under consideration are less than 200]
 o Thus, required the sum  = \frac{199*(199 +1)}{2} – (2^2 +3^2 + 5^2 +7^2 + 11^2 + 13^2) – 1 = 199*100 – (4+9+25+49+121+169) - 1 = 19,522   
Thus, the correct answer is  Option E.

sambitspm · Answer

See the attachment

ScottTargetTestPrep · Answer

Recall that the number 1 has only 1 factor and all the prime numbers have only 2 factors. All the other positive integers (i.e., composite numbers) have more than 2 factors. Therefore, in order to find the sum of all the numbers less than 200 that are either prime or have more than 3 factors, we must exclude 1 and all the numbers that have exactly 3 factors. The numbers that have exactly 3 factors are those that are squares of a prime (for example, 2^2 = 4 has exactly 3 factors: 1, 2 and 4). The sum of excluded numbers is:

1 + 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 1 + 4 + 9 + 25 + 49 + 121 + 169 = 378

The sum of all positive integers less than 200 is:

1 + 2 + 3 + … + 198 + 199 = 199(199 + 1)/2 = 199(200)/2 = 199(100) = 19,900

Therefore, the sum of all the numbers less than 200 that are either prime or have more than 3 factors is 19,900 - 378 = 19,522.

Answer: E

TarunKumar1234 · Answer

What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?

Numbers having 1 factor = {1} : 1 number

Prime numbers always have 2 factors i.e. 1 & prime number itself.

Numbers less than 200 having 3 factors = {4,9,25,49,121,169} : 6 numbers

Sum of non-prime numbers less than 200 having less than 3 factors = 1 + 4 + 9 + 25 + 49 + 121 + 169 = 378

Sum of all numbers less than 200 = 199*200/2 = 19900

The sum of all numbers less than 200 that are either prime or have more than 3 factors = 19900 - 378 = 19522

IMO E

samarpan.g28 · Answer

Firstly, the sum of the first 199 natural numbers: 199*200/2=19900.
We have to exclude numbers which are either prime or have less than 3 factors. Such numbers are 1 and the square of prime numbers 2,3,5,7,11,13.
So, 19900-(1+4+9+25+49+121+169)=19522(E).

Kinshook · Answer

What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?

Numbers having 1 factor = {1} : 1 number

Prime numbers always have 2 factors i.e. 1 & prime number itself.

Numbers less than 200 having 3 factors = {4,9,25,49,121,169} : 6 numbers

Sum of non-prime numbers less than 200 having less than 3 factors = 1 + 4 + 9 + 25 + 49 + 121 + 169 = 378

Sum of all numbers less than 200 = 199*200/2 = 19900

The sum of all numbers less than 200 that are either prime or have more than 3 factors = 19900 - 378 = 19522

IMO E

What is the sum of all numbers less than 200 that are either prime or

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What is the sum of all numbers less than 200 that are either prime or

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards