GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Nov 2018, 03:26

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

November 18, 2018

November 18, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Jul 2018
Posts: 38
Location: India
GMAT 1: 560 Q47 V28
GMAT 2: 560 Q47 V28
GMAT 3: 560 Q47 V28
GMAT 4: 560 Q47 V28
GPA: 3.88
The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

Updated on: 12 Jul 2018, 08:26
2
00:00

Difficulty:

85% (hard)

Question Stats:

44% (01:40) correct 56% (01:57) wrong based on 68 sessions

### HideShow timer Statistics

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, 06:49.
Last edited by chetan2u on 12 Jul 2018, 08:26, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 03 Mar 2018
Posts: 179
Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

12 Jul 2018, 08:02
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.
_________________

Manager
Joined: 06 May 2018
Posts: 59
Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

12 Jul 2018, 08:21
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?
Math Expert
Joined: 02 Aug 2009
Posts: 7035
The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

12 Jul 2018, 08:25
3
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
_________________

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

GMAT online Tutor

Manager
Joined: 03 Mar 2018
Posts: 179
Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

13 Jul 2018, 11:36
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.
_________________

Intern
Joined: 15 May 2017
Posts: 29
Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

13 Jul 2018, 13:50
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?
Math Expert
Joined: 02 Aug 2009
Posts: 7035
Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

13 Jul 2018, 18:27
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
_________________

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

GMAT online Tutor

Director
Joined: 09 Mar 2017
Posts: 516
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

14 Jul 2018, 02:42
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.
_________________

------------------------------
"Trust the timing of your life"
Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

Math Expert
Joined: 02 Aug 2009
Posts: 7035
Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which  [#permalink]

### Show Tags

14 Jul 2018, 03:48
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
_________________

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

GMAT online Tutor

Re: The product of all prime numbers from 2 to 29 plus 1 equals K. Which &nbs [#permalink] 14 Jul 2018, 03:48
Display posts from previous: Sort by