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# What is the greatest integer that is the sum of two different prime nu

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Math Expert
Joined: 02 Sep 2009
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What is the greatest integer that is the sum of two different prime nu  [#permalink]

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22 May 2020, 10:51
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15% (low)

Question Stats:

79% (00:53) correct 21% (01:09) wrong based on 90 sessions

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What is the greatest integer that is the sum of two different prime numbers, each of which is less than 50 ?

A. 47
B. 90
C. 94
D. 96
E. 99

PS20428

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Re: What is the greatest integer that is the sum of two different prime nu  [#permalink]

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22 May 2020, 11:01
Two prime no. Just next to Less than 50 are
43 & 47
There sum will be 90.

Posted from my mobile device
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Posts: 44
Re: What is the greatest integer that is the sum of two different prime nu  [#permalink]

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22 May 2020, 11:05
Bunuel wrote:
What is the greatest integer that is the sum of two different prime numbers, each of which is less than 50 ?

A. 47
B. 90
C. 94
D. 96
E. 99

PS20428

For the sum to be maximum, the prime numbers must be maximum possible.
Prime numbers must be less different and less than 50.
Two maximum prime numbers which are less than 50 are 47 and 43
47+43 = 90.
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Re: What is the greatest integer that is the sum of two different prime nu  [#permalink]

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22 May 2020, 19:24
Bunuel wrote:
What is the greatest integer that is the sum of two different prime numbers, each of which is less than 50 ?

A. 47
B. 90
C. 94
D. 96
E. 99

PS20428

prime number can be checked ; 6n+/-1 ;
n=8 ; 47 and n=7 ; 43
47+43 ; 90
OPTION B
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Re: What is the greatest integer that is the sum of two different prime nu  [#permalink]

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23 May 2020, 16:25
B?

47 + 43 = 90

Greatest sum: when two numbers added are greatest.

Both are the greatest prime number < 50
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NJ
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Re: What is the greatest integer that is the sum of two different prime nu  [#permalink]

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24 May 2020, 08:14
1
Top Contributor
Bunuel wrote:
What is the greatest integer that is the sum of two different prime numbers, each of which is less than 50 ?

A. 47
B. 90
C. 94
D. 96
E. 99
PS20428

To maximize the sum, we need to find the biggest prime numbers less than 50.
Those primes are: 43 and 47

So the greatest sum = 43 + 47 = 90

Cheers,
Brent
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What is the greatest integer that is the sum of two different prime nu  [#permalink]

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Updated on: 31 May 2020, 07:42

Solution

To Find
• Greatest value of the sum of two different prime numbers, each of which <50.

Approach and Working Out
Let’s consider the two numbers be ‘a’ and ‘b’.
• Sum = a+b. Both a and b must be prime and must be <50.
• For sum to be greatest, both a and b should be maximum.
o Thus we need to find two distinct prime numbers which are immediately less than 50
.
We know that all prime numbers greater than 3 are of the form 6k +1 or 6k-1 and are thus odd as well.
• Checking for 49, $$49 = 7^2$$, thus is not a prime number.
• Checking for 47, we cannot prime factorize it to any prime factor <47. Thus it is prime.
• Checking for 45, $$45 = 5*3^2$$, thus is not a prime.
• Checking for 43, we cannot prime factorize it to any prime factor <43. Thus it is prime.

Thus the two greatest primes which are less than 50 are 43 and 47.
Sum = 47 + 43 = 90

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Originally posted by EgmatQuantExpert on 30 May 2020, 21:20.
Last edited by EgmatQuantExpert on 31 May 2020, 07:42, edited 1 time in total.
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Posts: 608
Re: What is the greatest integer that is the sum of two different prime nu  [#permalink]

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31 May 2020, 02:38
how to find if a number is a prime number?
check divisibility for all nos till the closest perfect sq of that number
for eg: to check if 47 has any factor check all nos from 1 to 7 and 7^2 =49 (closest sq to 47)
no number between 1 to 7 is divisible by 47; hence no need to check further. 47 is a Prime.
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Re: What is the greatest integer that is the sum of two different prime nu  [#permalink]

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31 May 2020, 07:35

Solution

To Find
• Greatest value of the sum of two different prime numbers, each of which <50.

Approach and Working Out
Let’s consider the two numbers be ‘a’ and ‘b’.
• Sum = a+b. Both a and b must be prime and must be <50.
• For sum to be greatest, both a and b should be maximum.
o Thus we need to find two distinct prime numbers which are immediately less than 50
.
We know that all prime numbers greater than 3 are of the form 6k +1 or 6k-1 and are thus odd as well.
• Checking for 49, $$49 = 7^2$$, thus is not a prime number.
• Checking for 47, we cannot prime factorize it to any prime factor <47. Thus it is prime.
• Checking for 45, $$45 = 5*3^2$$, thus is not a prime.
• Checking for 43, we cannot prime factorize it to any prime factor <43. Thus it is prime.

Thus the two greatest primes which are less than 50 are 43 and 47.
Sum = 47 + 43 = 90

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Re: What is the greatest integer that is the sum of two different prime nu  [#permalink]

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31 May 2020, 08:03
43+47=90
Re: What is the greatest integer that is the sum of two different prime nu   [#permalink] 31 May 2020, 08:03