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The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

(A) 440 (b) 512 (C) 620 (D) 700 (E) 750

Problem Solving Question: 78 Category:Arithmetic Properties of numbers Page: 71 Difficulty: 600

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Re: The "prime sum" of an integer n greater than 1 is the sum of [#permalink]

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07 Feb 2014, 14:59

5

3

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

(A) 440 (b) 512 (C) 620 (D) 700 (E) 750

Before getting down to solving on careful observation B(2^9, So sum is 18),D(7*100----> 7*2^2*5^2) and E(250*3---->5^3*2*3) can be ruled out

C looked good cause 620 is multiple of 31 so ideally should be the closest one.Always start with C and then decide to move on.

Ans is C
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Re: The "prime sum" of an integer n greater than 1 is the sum of [#permalink]

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05 Feb 2014, 02:27

2

SOLUTION

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

(A) 440 (B) 512 (C) 620 (D) 700 (E) 750

Start by testing the middle option:

(C) 620 = 2*2*5*31, hence the "prime sum" of 620 is 2 + 2 + 5 + 31 = 40 > 35. Since there can be only one correct answer, then it must be C.

Re: The "prime sum" of an integer n greater than 1 is the sum of [#permalink]

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07 Feb 2014, 13:28

1

I'd say (C) too, solved by the same method (took 1:14), might be time-consuming if the answer was D, or E for example. I hope that a faster approach exists.

Re: The "prime sum" of an integer n greater than 1 is the sum of [#permalink]

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08 Feb 2014, 03:58

SOLUTION

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

(A) 440 (B) 512 (C) 620 (D) 700 (E) 750

Start by testing the middle option:

(C) 620 = 2*2*5*31, hence the "prime sum" of 620 is 2 + 2 + 5 + 31 = 40 > 35. Since there can be only one correct answer, then it must be C.

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

(A) 440 (b) 512 (C) 620 (D) 700 (E) 750

Problem Solving Question: 78 Category:Arithmetic Properties of numbers Page: 71 Difficulty: 600

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

we can see all options are even so 2 is common in all of them . only option B looks promising as 2*310 , 31 itself is very close to 35 . answer should be C.
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The "prime sum" of an integer n greater than 1 is the sum of [#permalink]

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19 Apr 2015, 05:57

4

Ergenekon wrote:

Bunuel, you wrote that we shoud start by middle option. Can you explain the reason? Thanks.

Good question. +1.

On the GMAT, answer choices are always in ascending/descending order, so trying option C firsts gives an idea which direction to go next if C is not correct.
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Re: The "prime sum" of an integer n greater than 1 is the sum of [#permalink]

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18 May 2015, 03:27

Bunuel wrote:

Ergenekon wrote:

Bunuel, you wrote that we shoud start by middle option. Can you explain the reason? Thanks.

Good question. +1.

On the GMAT, answer choices are always in ascending/descending order, so trying option C firsts gives an idea which direction to go next if C is not correct.

I always thought it would be good to start with B and then with D with ascending / descending order choices?

That is exactly what I did and what took forever, because both B and D did not work...

Re: The "prime sum" of an integer n greater than 1 is the sum of [#permalink]

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27 Mar 2016, 12:47

Bunuel wrote:

Ergenekon wrote:

Bunuel, you wrote that we shoud start by middle option. Can you explain the reason? Thanks.

Good question. +1.

On the GMAT, answer choices are always in ascending/descending order, so trying option C firsts gives an idea which direction to go next if C is not correct.

Hello, except that we should have a way to assess in which direction to go, had C not worked... In such case, we should go toward the direction of the number having the bigger prime, or a repetition of prime high enough to increase "prime sum", which seems fairly difficult to assess (at least to me...)

So should we not, because the question stem is structured with a " Which of the following", start with E upwards ?

The assumption is that GMAT could be nasty enough to make us test more than 3 options... Indeed, we would stop at the first answer choice that works.

Re: The "prime sum" of an integer n greater than 1 is the sum of [#permalink]

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12 Mar 2018, 07:05

Bunuel wrote:

SOLUTION

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

(A) 440 (B) 512 (C) 620 (D) 700 (E) 750

Start by testing the middle option:

(C) 620 = 2*2*5*31, hence the "prime sum" of 620 is 2 + 2 + 5 + 31 = 40 > 35. Since there can be only one correct answer, then it must be C.

Answer: C.

Bunuel any idea how can I approximately eliminate other answer choices before I start doing prime factorization ? to save time I mean

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

(A) 440 (b) 512 (C) 620 (D) 700 (E) 750

This question requires us to find the prime factorization of the answer choices

A. 440 = (2)(2)(2)(5)(11). PRIME SUM = 2 + 2 + 2 + 5 + 11 = 22

B. 512 = (2)(2)(2)(2)(2)(2)(2)(2)(2) PRIME SUM = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18

C. 620 = (2)(2)(5)(31) PRIME SUM = 2 + 2 + 5 + 31 = 40

STOP

We've found the number that has a prime sum that's greater than 35.

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

(A) 440 (b) 512 (C) 620 (D) 700 (E) 750

Scanning our answer choices we want to find the number that contains a large prime factor. Thus, considering answer choice C, we have:

620 = 62 x 10 = 31 x 2 x 2 x 5

The sum is 31 + 5 + 2 + 2 = 40.

Answer: C
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