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stonecold
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if P represents the number of prime numbers between 1 and 102 then wha 07 Apr 2016, 23:20
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Difficulty:

65% (hard)

Question Stats:

53% (01:32) correct 47% (02:12) wrong based on 260 sessions

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if P represents the number of prime numbers between 1 and 102 then what is the value of P?
[A] 25
[B] 26
[C] 27
[D] 28
[E] 29
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B
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Abhishek009
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if P represents the number of prime numbers between 1 and 102 then wha 21 Apr 2016, 12:58
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stonecold
if P represents the number of prime numbers between 1 and 102 then what is the value of P?
[A] 25
26
[C] 27
[D] 28
[E] 29
Show more

All prime numbers except 2 and 3 can be expressed as -

6n + 1

and

6n - 1


Find the value of n -

n can be 100/6 = 16

Now form a table -

Attachment:
Capture.PNG
Capture.PNG [ 7.95 KiB | Viewed 5830 times ]

So we have 23 numbers between 5 to 97 and 3 more numbers (2, 3 and 101 )

[b]Hence total we have 26 numbers in the given range... :-D :lol: :x
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mikemcgarry
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if P represents the number of prime numbers between 1 and 102 then wha 11 Apr 2016, 16:28
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stonecold
if P represents the number of prime numbers between 1 and 102 then what is the value of P?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
Show more
Dear stonecold,
I'm happy to respond. :-)

My friend, where on earth did you get this question? This is, in many ways, a tedious counting question in which we just have to list out the individual cases. It helps, of course, to be conversant in the primes from one to 100. There's really no other way to answer this besides listing all the examples. This is not particularly GMAT-like: I am not familiar with any GMAT question which cannot be solved in any shortcut way and which requires writing out a tedious list.

Here's the list, grouped in sets of five for easy counting
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
101

That's 26 prime numbers. Answer = (B)

Incidentally, it's helpful to note that {101, 103, 107, 109} are all prime. In other words, all the odds except the multiple of 5 are prime between 100 and 110, as is true between 10 and 20. This is also true between 190 and 200.

Does all this make sense?
Mike :-)
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stonecold
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if P represents the number of prime numbers between 1 and 102 then wha 21 Apr 2016, 12:30
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stonecold
if P represents the number of prime numbers between 1 and 102 then what is the value of P?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
Dear stonecold,
I'm happy to respond. :-)

My friend, where on earth did you get this question? This is, in many ways, a tedious counting question in which we just have to list out the individual cases. It helps, of course, to be conversant in the primes from one to 100. There's really no other way to answer this besides listing all the examples. This is not particularly GMAT-like: I am not familiar with any GMAT question which cannot be solved in any shortcut way and which requires writing out a tedious list.

Here's the list, grouped in sets of five for easy counting
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
101

That's 26 prime numbers. Answer = (B)

Incidentally, it's helpful to note that {101, 103, 107, 109} are all prime. In other words, all the odds except the multiple of 5 are prime between 100 and 110, as is true between 10 and 20. This is also true between 190 and 200.

Does all this make sense?
Mike :-)
Show more


Can you please post a question based on odds are prime except the multiple of 5 are prime between 100 and 110, as is true between 10 and 20. This is also true between 190 and 200.
Sounds very interesting.
Do share the link if it already exists.
Thanks
Stone Cold
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stonecold
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Schools: Boston U '20 (M)
GRE 1: Q169 V154
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if P represents the number of prime numbers between 1 and 102 then wha 21 Apr 2016, 13:09
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Abhishek009
stonecold
if P represents the number of prime numbers between 1 and 102 then what is the value of P?
[A] 25
26
[C] 27
[D] 28
[E] 29

All prime numbers except 2 and 3 can be expressed as -

6n + 1

and

6n - 1


Find the value of n -

n can be 100/6 = 16

Now form a table -

Attachment:
Capture.PNG

So we have 23 numbers between 5 to 97 and 3 more numbers (2, 3 and 101 )

[b]Hence total we have 26 numbers in the given range... :-D :lol: :x
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Excellent Solution...!!
Unfortunately 5 kudos limit has been already surpassed.

StoneCold
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Abhishek009
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Posts: 5,903
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 [1]
if P represents the number of prime numbers between 1 and 102 then wha 21 Apr 2016, 13:18
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Excellent Solution...!!
Unfortunately 5 kudos limit has been already surpassed.

StoneCold
Show more

A different approach without use of 6n+1 and 6n -1

Units digit of a prime number except 2 will always be odd ( 1,3 , 5 , 7 , 9 )

So start working around.

01 - 09 = 2, 3 ,5 , 7
10 - 19 = 11, 13 , 17 , 19
20 - 29 = 23 , 29
30 - 39 = 31 , 37
40 - 49 = 41 , 43 , 47
50 - 59 = 53 , 59
60 - 69 = 61 , 67
70 - 79 = 71 , 73 , 79
80 - 89 = 83 , 87 , 89
90 - 99 = 97
100 - 102 = 101

Count you will get 26 Prime numbers

[b]stonecold no issues Austin Bro :-D :lol: , the satisfaction of helping someone > Kudos!! ( Expression in Mathematical form because I am posting in Quants Section ) :lol:


Would love to have someone with any alternative solution to the same question, indeed its a beautiful question.
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if P represents the number of prime numbers between 1 and 102 then wha 21 Apr 2016, 13:49
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stonecold
Can you please post a question based on odds are prime except the multiple of 5 are prime between 100 and 110, as is true between 10 and 20. This is also true between 190 and 200.
Sounds very interesting.
Do share the link if it already exists.
Thanks
Stone Cold
Show more
Dear Stone Cold,
My friend, I was inspired by this question and this discussion, and I posted a related question here:
how-many-integers-n-are-prime-numbers-in-the-range-200-n-217055.html
That one can be solved very systematically without a calculator.
Mike :-)
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stonecold
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if P represents the number of prime numbers between 1 and 102 then wha 02 May 2016, 21:05
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Abhishek009
stonecold


Excellent Solution...!!
Unfortunately 5 kudos limit has been already surpassed.

StoneCold

A different approach without use of 6n+1 and 6n -1

Units digit of a prime number except 2 will always be odd ( 1,3 , 5 , 7 , 9 )

So start working around.

01 - 09 = 2, 3 ,5 , 7
10 - 19 = 11, 13 , 17 , 19
20 - 29 = 23 , 29
30 - 39 = 31 , 37
40 - 49 = 41 , 43 , 47
50 - 59 = 53 , 59
60 - 69 = 61 , 67
70 - 79 = 71 , 73 , 79
80 - 89 = 83 , 87 , 89
90 - 99 = 97
100 - 102 = 101

Count you will get 26 Prime numbers

[b]stonecold no issues Austin Bro :-D :lol: , the satisfaction of helping someone > Kudos!! ( Expression in Mathematical form because I am posting in Quants Section ) :lol:


Would love to have someone with any alternative solution to the same question, indeed its a beautiful question.
Show more


Kudos Visible ..!!
:)
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if P represents the number of prime numbers between 1 and 102 then wha 12 Jun 2025, 07:27
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