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

 It is currently 21 Oct 2018, 16:18

### 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

# Can the positive integer p be expressed as the product of

Author Message
TAGS:

### Hide Tags

Intern
Joined: 24 Apr 2013
Posts: 4
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

30 Sep 2013, 21:36
Bunuel wrote:
abhisheksharma wrote:
What if i say that P = 33 x 1.

So it implies that surely one of the integer is greater than 1 but other one is 1 itself ?

Mental block..!!!

33 also can be expressed as 3*11, so the answer to the question "can the positive integer P be expressed as a product of two integers, each of which is greater than 1?" is still YES.

I agree, but then I came across this question.

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

and I am confused again.

In both questions we know that the number is an integer,
let's suppose the number is 33 for both questions(for easier calculation)
33 can be 33 x 1 or 11 x 3. (can be true)
& 33 can be 31 + 2 or 27 + 6 (can be true) than why is the answer E in this particular case ??

Math Expert
Joined: 02 Sep 2009
Posts: 50009
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

01 Oct 2013, 00:30
abhisheksharma wrote:
Bunuel wrote:
abhisheksharma wrote:
What if i say that P = 33 x 1.

So it implies that surely one of the integer is greater than 1 but other one is 1 itself ?

Mental block..!!!

33 also can be expressed as 3*11, so the answer to the question "can the positive integer P be expressed as a product of two integers, each of which is greater than 1?" is still YES.

I agree, but then I came across this question.

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

and I am confused again.

In both questions we know that the number is an integer,
let's suppose the number is 33 for both questions(for easier calculation)
33 can be 33 x 1 or 11 x 3. (can be true)
& 33 can be 31 + 2 or 27 + 6 (can be true) than why is the answer E in this particular case ??

For original question, EVERY possible value of p (32, 33, 34, 35, and 36) CAN be written as the product of two integers, each of which is greater than 1. Thus answer B.

For the other question, SOME possible values of n (for example n=5) CAN be written as the sum of two different positive prime numbers and others cannot (for example n=11). Thus answer E.

The second question is discussed here: can-the-positive-integer-n-be-written-as-the-sum-of-two-126725.html

Hope it helps.
_________________
Intern
Status: Do or Die!!
Joined: 29 Jul 2013
Posts: 13
Location: India
Concentration: Technology
GMAT 1: 630 Q49 V27
GPA: 3.86
WE: Information Technology (Computer Software)
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

29 Apr 2015, 19:58
Bunuel wrote:
abhisheksharma wrote:
What if i say that P = 33 x 1.

So it implies that surely one of the integer is greater than 1 but other one is 1 itself ?

Mental block..!!!

33 also can be expressed as 3*11, so the answer to the question "can the positive integer P be expressed as a product of two integers, each of which is greater than 1?" is still YES.

Hi Bunuel,
Thanks for the explanation, but still there is some doubt I have:
What if I change range in point (1) as to contain few prime numbers as well. So now will the answer change to E (Both insuff)? Lets say range is 40<p<49

Senior Manager
Joined: 21 Jan 2015
Posts: 346
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

29 Apr 2015, 22:04
This cannot be 600-700 level question.
It simply ask for factor of these numbers (a*b) where a and b are > 1.
1. there is no prime number between 31 and 37 so : Sufficient
2. there are so many prime numbers to take the value of P. : not sufficent

Ans: A
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Thanks

Senior Manager
Joined: 21 Jan 2015
Posts: 346
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

29 Apr 2015, 22:07
sandeep1756 wrote:
Hi Bunuel,
Thanks for the explanation, but still there is some doubt I have:
What if I change range in point (1) as to contain few prime numbers as well. So now will the answer change to E (Both insuff)? Lets say range is 40<p<49

: To answer your question if you include any prime number between the range than yes ans will be E, as you won't be able to give specific values for a and b ; (P=a*b)
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Thanks

Manager
Joined: 17 Jun 2015
Posts: 220
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

20 Dec 2015, 10:30
The question means

Is p=ab where a and b>1

P, a, b are all integers

Statement 1:
31 < p <37 => p = 32, 33, 34, 35, 36

All of these can be. 1 is sufficient

Statement 2: P is odd. It could be an odd prime or a composite odd
Insuff.

Hence, A
_________________

Fais de ta vie un rêve et d'un rêve une réalité

SVP
Joined: 06 Nov 2014
Posts: 1883
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

06 Jun 2016, 21:04
1
Required: Can p be expressed as the product of two integers, each of which is greater than 1
Or is p = x*y, where x and y are greater than 1.
This means p can have the numbers that are not prime, since a prime number has only 2 factors: 1 and the number itself.

Statement 1: 31 < p < 37
Values of p can be = 32, 33, 34, 35, 36
None of these is prime, hence p can be written as a product of x and y
SUFFICIENT

Statement 2: p is odd.
Odd numbers can both be prime and non prime
INSUFFICIENT

Correct Option: A
CEO
Joined: 12 Sep 2015
Posts: 3024
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

18 Jan 2018, 10:43
Top Contributor
Minotaur wrote:
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

1) 31 < p < 37
2) p is odd

Target question: Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

This question is a great candidate for rephrasing the target question.
If an integer p can be expressed as the product of two integers, each of which is greater than 1, then that integer is a composite number (as opposed to a prime number). So . . . .

REPHRASED target question: Is integer p a composite number?

Aside: We have a video with tips on rephrasing the target question (below)

Statement 1: 31 < p < 37
There are 5 several values of p that meet this condition. Let's check them all.
p=32, which means p is a composite number
p=33, which means p is a composite number
p=34, which means p is a composite number
p=35, which means p is a composite number
p=36, which means p is a composite number
Since the answer to the REPHRASED target question is the SAME ("yes, p IS a composite number") for every possible value of p, statement 1 is SUFFICIENT

Statement 2: p is odd
There are several possible values of p that meet this condition. Here are two:
Case a: p = 3 in which case p is not a composite number
Case b: p = 9 in which case p is a composite number
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

RELATED VIDEO

_________________

Brent Hanneson – GMATPrepNow.com

Intern
Joined: 06 Aug 2017
Posts: 21
Location: India
GMAT 1: 660 Q47 V34
Re: Can the positive integer p be expressed as the product of  [#permalink]

### Show Tags

18 Jan 2018, 11:00
1
Need to find if p is prime or not.
As non prime numbers can be expressed as product of two factors.

Between 31 and 37 :
These are the numbers
32,33,34,35,36 : All of these numbers are not prime. So it can be expressed as product of two factors.

p is odd.
All odd numbers are not always prime.
Re: Can the positive integer p be expressed as the product of &nbs [#permalink] 18 Jan 2018, 11:00

Go to page   Previous    1   2   [ 29 posts ]

Display posts from previous: Sort by

# Can the positive integer p be expressed as the product of

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.