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What is the smallest integer that is the sum of 2 distinct

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What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 07 Aug 2014, 10:34
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What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 80 ?

A. 170
B. 172
C. 173
D. 199
E. 186

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What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 07 Aug 2014, 21:42
5
3
IMO B
Remember following chart:
There is a pattern in following list.. try to compare pattern and repetition after rows.
2 3 5 7
11 13 17 19
23 29
31 37

41 43 47
53 59
61 67

71 73 79
83 89
97

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Re: What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 07 Aug 2014, 18:30
1
I didn't memorize the list of primes, so, is there any other way of solving this out going through the list and finding the next 2 smallest primes?
81 - Divisible by 3
82 - Divisible by 2
83 - Prime
84 - Divisible by 2
85 - Divisible by 5
86 - Divisible by 2
87 - Divisible by 3
88 - Divisible by 2
89 - Prime

83+89=172
Answer is B
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Re: What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 07 Aug 2014, 22:50
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Gnpth wrote:
What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 80 ?

A. 170
B. 172
C. 173
D. 199
E. 186


First of all, discard 173 and 199 since they are odd. Sum of two primes greater than 2 will always be even because both primes will be odd.

Both numbers need to be greater than 80 i.e. their sum needs to be greater than 160. Since two of the given sums, 170 and 172, are quite close to 160, it should be fair to assume that if they can be written as sum of two primes, we will find the primes between 80 to 90.

Between 80 and 90, there are only 2 primes: 83 and 89 (if you don't remember this, you just need to check for 81, 83, 87 and 89)

83+89 = 172 so answer is (B)
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Re: What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 07 Aug 2014, 23:41
Above 80, the first prime number = 83

Next to 83, the prime number = 89

83 + 89 = 172

Answer = B
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Re: What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 08 Apr 2015, 06:39
2
PiyushK wrote:
IMO B
Remember following chart:
There is a pattern in following list.. try to compare pattern and repetition after rows.
2 3 5 7
11 13 17 19
23 29
31 37

41 43 47
53 59
61 67

71 73 79
83 89
97


Another way to catch prime numbers fast is to do the following:

If number is less than 100 check for divisibility of all prime numbers less than 10.
If numbers is less than 144 check all prime numbers under 12 and so on...
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What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 08 Feb 2016, 20:03
1.create set of numbers

2. remove all even numbers

3. remove all multiples of 3,5,7, 11 (should know divisibility)

81,82,83,84,85,86,87,88,89,90

only 83 and 89 remain, so B
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Re: What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 02 Dec 2016, 07:47
Gnpth wrote:
What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 80 ?

A. 170
B. 172
C. 173
D. 199
E. 186


the fastest way to identify prime numbers that are less than 100, is to divide by the first prime numbers: 2, 3, 5, 7. If the number is not divisible by these prime numbers, then the number is a prime one.

81 - not prime, divisible by 3
82 - not prime, divisible by 2
83 - is a prime number
84 - not prime, divisible by 2
85 - not prime, divisible by 5
86 - not prime, divisible by 2
87 - not prime, divisible by 3
88 - not prime, divisible by 2
89 - is a prime number

89+83 = XX2. units digit is 2. Only B has the units digit 2. B must be the answer.
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Re: What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 17 Jul 2018, 15:40
Gnpth wrote:
What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 80 ?

A. 170
B. 172
C. 173
D. 199
E. 186



The smallest integer that is the sum of 2 distinct prime integers, each greater than 80, is the sum of the two prime integers right after 80. Those two integers are 83 and 89. Thus, the sum is 83 + 89 = 172.

Answer: B
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Re: What is the smallest integer that is the sum of 2 distinct  [#permalink]

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New post 20 Nov 2018, 09:15
The question is testing whether we understand the concept of prime numbers. To find the smallest integer that is the sum of 2 different prime numbers greater than 80, we need to add the 2 smallest prime numbers greater than 80. Count up from 80 by the odd numbers, since 2 is the only even prime number.

81 is not prime. The sum of the digits of 81 is 8 + 1 = 9, which is a multiple of 3. So 81 is a multiple of 3.

83 is prime.

85 is a multiple of 5, not prime.

87 is not prime. The sum of the digits of 87 is 8 + 7 = 15, which is a multiple of 3. So 87 is a multiple of 3.

89 is prime.

83 + 89 = 172, which is the answer.

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Re: What is the smallest integer that is the sum of 2 distinct &nbs [#permalink] 20 Nov 2018, 09:15
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