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The product of all prime numbers from 2 to 29 plus 1 equals K. Which

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The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post Updated on: 12 Jul 2018, 09:26
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The product of all prime numbers from 2 to 29 plus 1 equals K. Which of the following is true?

I. K is divisible by prime number.
II. K has a prime factor greater than 29.
III. k is divisible by 30

A. I
B. II
C. III
D. I and II
E. I, II and III

Originally posted by shard87 on 12 Jul 2018, 07:49.
Last edited by chetan2u on 12 Jul 2018, 09:26, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post 12 Jul 2018, 09:02
shard87 wrote:
The product of all prime numbers from 2 to 29 plus 1 equals K. Which of the following is true?

I. K is divisible by prime number.
II. K has a prime factor greater than 29.
III. P is divisible by 30

A. I
B. II
C. III
D. I and II
E. I, II and III

This question is definitely not a 600 level GMAT question. However, this question is of moderate difficulty(IMO).
Prime numbers from 2 to 29 are 3 5 7 11 13 17 19 23
Product is a odd number. Hence odd number + 1 = even number(So divisible by a prime number 2). Note that this question is not a must be true question.
Option I satisfies. But, I am skeptical about Option II. If someone explains how it is correct it would be helpful.
Also Option III, the term should be K and it is not divisible by 30. Since the product is added with 1, which doesn't end with a zero.
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Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post 12 Jul 2018, 09:21
itisSheldon wrote:
shard87 wrote:
The product of all prime numbers from 2 to 29 plus 1 equals K. Which of the following is true?

I. K is divisible by prime number.
II. K has a prime factor greater than 29.
III. P is divisible by 30

A. I
B. II
C. III
D. I and II
E. I, II and III

This question is definitely not a 600 level GMAT question. However, this question is of moderate difficulty(IMO).
Prime numbers from 2 to 29 are 3 5 7 11 13 17 19 23
Product is a odd number. Hence odd number + 1 = even number(So divisible by a prime number 2). Note that this question is not a must be true question.
Option I satisfies. But, I am skeptical about Option II. If someone explains how it is correct it would be helpful.
Also Option III, the term should be K and it is not divisible by 30. Since the product is added with 1, which doesn't end with a zero.


Shouldn`t be the number 2 included in the calculation as well?
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The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post 12 Jul 2018, 09:25
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1
shard87 wrote:
The product of all prime numbers from 2 to 29 plus 1 equals K. Which of the following is true?

I. K is divisible by prime number.
II. K has a prime factor greater than 29.
III. P is divisible by 30

A. I
B. II
C. III
D. I and II
E. I, II and III



From 2 to 29 should include both 2 and 29..
so 2*3*5*7*11*13*17*19*23*29... add 1 to it


I. K is divisible by prime number.
Every number is divisible by prime number and so is k divisible by prime numbers ...true

II. K has a prime factor greater than 29.
the product of all prime numbers 2 to 29 will be divisible by all these numbers
so when we add 1 to the product, it will NOT be div by any of these prime numbers and prime number will be > 29...true

III. K is divisible by 30
K is NOT div by any of the prime numbers from 2 to 29 as shown in case II, so it will not be div by 3 and 5 and 2, hence by 30...FALSE

Only I and II

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post 13 Jul 2018, 12:36
Thanks for the clarification chetan2u
I am in the impression that if it is not explicitly mentioned in these type of questions as inclusive of 2 and 29, we should not include both.
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Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post 13 Jul 2018, 14:50
chetan2u wrote:
shard87 wrote:
The product of all prime numbers from 2 to 29 plus 1 equals K. Which of the following is true?

I. K is divisible by prime number.
II. K has a prime factor greater than 29.
III. P is divisible by 30

A. I
B. II
C. III
D. I and II
E. I, II and III



From 2 to 29 should include both 2 and 29..
so 2*3*5*7*11*13*17*19*23*29... add 1 to it


I. K is divisible by prime number.
Every number is divisible by prime number and so is k divisible by prime numbers ...true

II. K has a prime factor greater than 29.
the product of all prime numbers 2 to 29 will be divisible by all these numbers
so when we add 1 to the product, it will NOT be div by any of these prime numbers and prime number will be > 29...true

III. K is divisible by 30
K is NOT div by any of the prime numbers from 2 to 29 as shown in case II, so it will not be div by 3 and 5 and 2, hence by 30...FALSE

Only I and II

D



Every number is divisible by prime number and so is k divisible by prime numbers ...true
chetan2u - Is this a property? Can you please elaborate a lil bit?
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Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post 13 Jul 2018, 19:27
Srajagopal21 wrote:
chetan2u wrote:
shard87 wrote:
The product of all prime numbers from 2 to 29 plus 1 equals K. Which of the following is true?

I. K is divisible by prime number.
II. K has a prime factor greater than 29.
III. P is divisible by 30

A. I
B. II
C. III
D. I and II
E. I, II and III



From 2 to 29 should include both 2 and 29..
so 2*3*5*7*11*13*17*19*23*29... add 1 to it


I. K is divisible by prime number.
Every number is divisible by prime number and so is k divisible by prime numbers ...true

II. K has a prime factor greater than 29.
the product of all prime numbers 2 to 29 will be divisible by all these numbers
so when we add 1 to the product, it will NOT be div by any of these prime numbers and prime number will be > 29...true

III. K is divisible by 30
K is NOT div by any of the prime numbers from 2 to 29 as shown in case II, so it will not be div by 3 and 5 and 2, hence by 30...FALSE

Only I and II

D



Every number is divisible by prime number and so is k divisible by prime numbers ...true
chetan2u - Is this a property? Can you please elaborate a lil bit?


Hi...

Every number is the product of some prime number . Only 1 does not fall into it because all prime numbers are >1..
Take 3... Prime number itself
26=2*13... Product of two prime numbers
43..... Prime number itself
Ans so on
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post 14 Jul 2018, 03:42
chetan2u wrote:

Hi...

Every number is the product of some prime number . Only 1 does not fall into it because all prime numbers are >1..
Take 3... Prime number itself
26=2*13... Product of two prime numbers
43..... Prime number itself
Ans so on

So, doesn't adding 1 impact k's divisibility by a prime number? I was confused solely due to the addition of 1 to the product of primes.
Would you please shed some light?
Thank you.
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Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

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New post 14 Jul 2018, 04:48
1
TaN1213 wrote:
chetan2u wrote:

Hi...

Every number is the product of some prime number . Only 1 does not fall into it because all prime numbers are >1..
Take 3... Prime number itself
26=2*13... Product of two prime numbers
43..... Prime number itself
Ans so on

So, doesn't adding 1 impact k's divisibility by a prime number? I was confused solely due to the addition of 1 to the product of primes.
Would you please shed some light?
Thank you.



When you have a product of two-three numbers and add 1 to it, the new number will not be div by those numbers..
Example...2*3*5=30 add 1 to it 31. So 31 will never be div by 2,3,5 and 31 itself is a prime number greater than the biggest prime in product that is 5
Same thing in this 2*3*5*7*11*13*17*19*23*29.... Adding 1 to it will ensure that the new number is not div by any of these prime numbers BUT the number of course is more than 1, so it has to have some prime factor and this prime factor will be GREATER than 29, the biggest prime in the product
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which &nbs [#permalink] 14 Jul 2018, 04:48
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