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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
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Difficulty:   15% (low)

Question Stats: 84% (01:57) correct 16% (02:18) wrong based on 1386 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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.

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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.

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Math Expert V
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Posts: 58402
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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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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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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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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.

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Posts: 224
Location: India
Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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Ans C

Solved it the prime factorization way
440= 2*2*2*5*11 Sum=22
512= 2^6 Sum=2*6=12
620=2*2*5*31 Sum=40>35
Hence 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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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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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.

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GMAT 1: 630 Q49 V27 Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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

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Bunuel, you wrote that we shoud start by middle option. Can you explain the reason? Thanks.
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Director  Joined: 19 Apr 2013
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Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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Thanks a lot. Makes sense now.
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Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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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...
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Joined: 18 Jan 2016
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GMAT 1: 640 Q47 V28 GMAT 2: 680 Q50 V31 GMAT 3: 700 Q49 V35 GMAT 4: 740 Q49 V41 GPA: 3.1
Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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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.
VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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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.

Bunuel any idea how can I approximately eliminate other answer choices before I start doing prime factorization ? to save time I mean GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4007
Re: The "prime sum" of an integer n greater than 1 is the sum of  [#permalink]

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Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

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

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

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

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Hi dave13

All the answer choices except for 512 have a units digit of 0 right?

so you can try to factorize it in a way that helps you. I tried to factorize it into 10 times another factor

for example 440 = 10 * 44 = 10 * 22 * 2

512 is just 2^9

620 = 10 * 62 = 10 * 31 * 2

700 = 10 * 70 = 10 * 2 * 35

750 = 10 * 75 = 10 * 3 * 25

From there you can notice faster. Re: The "prime sum" of an integer n greater than 1 is the sum of   [#permalink] 22 Oct 2018, 11:01
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