Last visit was: 17 Jul 2024, 11:56 It is currently 17 Jul 2024, 11:56
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94383
Own Kudos [?]: 641738 [3]
Given Kudos: 85693
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13796 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
User avatar
Manager
Manager
Joined: 13 May 2011
Posts: 170
Own Kudos [?]: 180 [2]
Given Kudos: 93
Concentration: Strategy, Technology
GMAT 1: 750 Q49 V42
GPA: 3.2
WE:Accounting (Consulting)
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13796 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
1
Kudos
Expert Reply
GMAT questions don't come with information just to confuse the test takers. So please understand that if GMAT gives an information then it's either to define the question within the acceptable boundaries or to use for solving the question. It's never to confuse the test takers.
User avatar
Manager
Manager
Joined: 13 May 2011
Posts: 170
Own Kudos [?]: 180 [0]
Given Kudos: 93
Concentration: Strategy, Technology
GMAT 1: 750 Q49 V42
GPA: 3.2
WE:Accounting (Consulting)
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
GMATinsight wrote:
GMAT questions don't come with information just to confuse the test takers. So please understand that if GMAT gives an information then it's either to define the question within the acceptable boundaries or to use for solving the question. It's never to confuse the test takers.


Could you please help me with why the information about X being > 2 was given? I might be missing something. I mean, it doesn't confuse you, but you don't need it to solve the question.
User avatar
SDA Bocconi Thread Master
Joined: 27 Dec 2012
Posts: 26
Own Kudos [?]: 29 [0]
Given Kudos: 34
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q48 V33
GMAT 2: 730 Q49 V40
WE:Engineering (Energy and Utilities)
Send PM
x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
I selected option D based on the usage of the word any

Statement 2 is straightforward so there is no need for any elaboration on that.

The sum of any prime factor of x and x is even

I read it like this: If a number has three prime factors, the three sums, i.e sum of each prime factor of x taken one at a time and the number x is even. This can only happen if the number are odd. So this statement is also sufficient.
Hence D.

DJ
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13796 [0]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
Expert Reply
kvazar wrote:
GMATinsight wrote:
GMAT questions don't come with information just to confuse the test takers. So please understand that if GMAT gives an information then it's either to define the question within the acceptable boundaries or to use for solving the question. It's never to confuse the test takers.


Could you please help me with why the information about X being > 2 was given? I might be missing something. I mean, it doesn't confuse you, but you don't need it to solve the question.


Hi kvazar,
I am not saying you are wrong. The comment I mention was a general understanding about GMAT questions so that the message goes right to the readers that "any information of question that you are not able to relate isn't to confuse you, it's to help you understand/solve the question better and without using it your answer has very high potential to be incorrect". Also, this question hasn't come from GMAC so it may have have such flaws but not the questions of GMAC. ;)
User avatar
Manager
Manager
Joined: 13 May 2011
Posts: 170
Own Kudos [?]: 180 [0]
Given Kudos: 93
Concentration: Strategy, Technology
GMAT 1: 750 Q49 V42
GPA: 3.2
WE:Accounting (Consulting)
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
akashganga wrote:
I selected option D based on the usage of the word any

Statement 2 is straightforward so there is no need for any elaboration on that.

The sum of any prime factor of x and x is even

I read it like this: If a number has three prime factors, the three sums, i.e sum of each prime factor of x taken one at a time and the number x is even. This can only happen if the number are odd. So this statement is also sufficient.
Hence D.

DJ


And this is the trap I was talking about!
If X = 8, then it has only one prime factor = 2, and 2 + 8 = 10 (EVEN). It is not necessary for X to have odd prime factors!
User avatar
Manager
Manager
Joined: 13 May 2011
Posts: 170
Own Kudos [?]: 180 [0]
Given Kudos: 93
Concentration: Strategy, Technology
GMAT 1: 750 Q49 V42
GPA: 3.2
WE:Accounting (Consulting)
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
GMATinsight wrote:
kvazar wrote:
GMATinsight wrote:
GMAT questions don't come with information just to confuse the test takers. So please understand that if GMAT gives an information then it's either to define the question within the acceptable boundaries or to use for solving the question. It's never to confuse the test takers.


Could you please help me with why the information about X being > 2 was given? I might be missing something. I mean, it doesn't confuse you, but you don't need it to solve the question.


Hi kvazar,
I am not saying you are wrong. The comment I mention was a general understanding about GMAT questions so that the message goes right to the readers that "any information of question that you are not able to relate isn't to confuse you, it's to help you understand/solve the question better and without using it your answer has very high potential to be incorrect". Also, this question hasn't come from GMAC so it may have have such flaws but not the questions of GMAC. ;)


I agree! My experience is that if you didn't use ALL the information, then chances are you're missed something. But in my reasoning for this question I just focused on what I have at hand, not what GMAC had at it's mind. But I'm pretty sure are numerous other questions with excess information on the forum. I won't be surprised if they are not GMAC created. Maybe Bunuel can shed some light, if he ever met questions like this created by GMAC.
Math Expert
Joined: 02 Sep 2009
Posts: 94383
Own Kudos [?]: 641738 [0]
Given Kudos: 85693
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
Expert Reply
Bunuel wrote:
x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x – 3) an odd number?

(1) The sum of any prime factor of x and x is even
(2) 3x is an even number


Source: Platinum GMAT
Kudos for a correct solution.


Platinum GMAT Official Solution:

In order to solve this question efficiently, it is necessary to begin with number properties. For a product of any number of terms to be odd, all the terms must be odd. If there is but one even term, the product will be even. To see this, consider the following examples:
All Terms Odd --> Odd Product
3*7*9*5 = 945
7*9*3 = 189
1*3*5 = 15

But: One or More Even Terms --> Even Product
3*7*9*2 = 378
7*9*4 = 252
1*3*5*6 = 90

In order for (x^3 + 19837)(x^2 + 5)(x – 3) to be an odd number, all the terms must be odd.

To determine under what conditions each term will be odd, it is important to remember the following relationships:
odd + odd = even
odd - odd = even

even + even = even
even - even = even

even + odd = odd
even - odd = odd
odd + even = odd
odd - even = odd

The only way for each term of (x^3 + 19837)(x^2 + 5)(x – 3) to be odd is if an even and an odd number are added or subtracted together within the parenthesis of each term. In other words:
even + odd = odd: For (x^3 + 19837) to be odd, since 19837 is odd, x^3 will need to be even. This will happen only when x is even.

even + odd = odd: For (x^2 + 5) to be odd, since 5 is odd, x^2 will need to be even. This will happen only when x is even.

even - odd = odd: For (x – 3) to be odd, since 3 is odd, x will need to be even.

When combining the results from the analysis of the three terms above, the only way for (x^3 + 19837)(x^2 + 5)(x – 3) to be odd is if each term is odd. This will only happen if x is even. Consequently, the original question can be simplified to: is x even? Another version of the simplified question is: what is the parity of x?

Evaluate Statement (1) alone.

In order for the sum of any prime factor of x and x to be even, it must follow one of two patterns:
Pattern (1): even + even = even
Pattern (2): odd + odd = even

There are two possible cases:

Case (1): x is even. In this case, Pattern (1) must hold. Since x is even in Case (1), any and every prime factor of x must be even (otherwise we could choose an odd prime factor of x and the sum of x and the odd prime factor would be odd). Let's consider some examples:
Let x = 12: However, x cannot equal 12 since one prime factor of 12 is 3 and 12 + 3 = odd number.
Let x = 26: However, x cannot equal 26 since one prime factor of 26 is 13 and 26 + 13 = odd number.
Let x = 14: However, x cannot equal 14 since one prime factor of 14 is 7 and 14 + 7 = odd number.
Let x = 16: x can equal 16 since every prime factor of 16 is even and as a result we know that and 16 + any prime factor = even number.
It is clear that Statement (1) allows x to be even (e.g., 16 is a possible value of x).

Case (2): x is odd. In this case, Pattern (2) must hold. Since x is odd in Case (2), any and every prime factor of x must be odd (otherwise we could choose an even prime factor of x and the sum of x and the even prime factor would be odd). Since all the prime factors of x are odd, x must be odd in Case (2). Let's consider some examples:
Let x = 11: Every prime factor of 11 is odd, so: 11 + prime factor of 11 = even number.
Let x = 15: Every prime factor of 15 is odd, so: 15 + prime factor of 15 = even number.
Since Statement (1) allows x to be either even (e.g., 16) or odd (e.g., 15), we cannot determine the parity of x.

Statement (1) is NOT SUFFICIENT.

Evaluate Statement (2) alone.
3x = Even Number
(odd)(x)=(even)
x must be even because, as shown above, if x were odd, 3x would be odd.

Statement (2) is SUFFICIENT since it definitively tells the parity of x.

Since Statement (1) alone is NOT SUFFICIENT but Statement (2) alone is SUFFICIENT, answer B is correct.
Manager
Manager
Joined: 26 Dec 2012
Posts: 132
Own Kudos [?]: 51 [0]
Given Kudos: 4
Location: United States
Concentration: Technology, Social Entrepreneurship
WE:Information Technology (Computer Software)
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
X>2, positive integer; Is (X^3+oddnumber)(X^2+Odd)(X-Odd) = odd?
If X= even , then expression will be (e+o)(e+o)(e-o) =o*o =Odd
If X= odd , then expression will be (o+o)(o+o)(o-o) = there is one even, so entire expression will be Even

1. X can be 4, so prime factors of 4 will 2 +4=Even, then expression will be Odd. But when X=5 sum of prime factor will be 5+5=even, but expression will be Even. So insufficient
2. 3X is even, that means X must be even. So expression will be Odd. Sufficient

Hence answer is B
Thanks,
Senior Manager
Senior Manager
Joined: 02 Apr 2014
Posts: 369
Own Kudos [?]: 493 [0]
Given Kudos: 1227
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Send PM
x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
Simplifying big question: \((x^3 + 19837)(x^2 + 5)(x – 3)\) = odd?
\((x^3 + odd)(x^2 + odd)(x - odd)\) = odd?
basically question is x even ?

Statement 1: The sum of any prime factor of x and x is even
x can be square of odd prime, say 49, prime factor 7 + 49 = 56 (even) => x is odd
or x can be any power of 2, say 64, prime factor 2 + 64 = 66 (even) => x is even

x can be odd or even -> Not Sufficient

Statement 2: 3x is even
since x is integer, x must be even integer, to make 3x even -> Sufficient.

Answer (B)
Senior Manager
Senior Manager
Joined: 31 Jan 2019
Posts: 368
Own Kudos [?]: 730 [0]
Given Kudos: 67
Location: Switzerland
Concentration: General Management
GPA: 3.9
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
Hi everyone,

x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x – 3) an odd number?

The hidden question is x=even? If X is not even then the multiplication above cannot be odd

(1) The sum of any prime factor of x and x is even
This is valid for both 4 and 9

Hence We can't establish whether X is even or odd

Insuff.


(2) 3x is an even number

Clearly X=even

Suff

B
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33999
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x [#permalink]
Moderator:
Math Expert
94383 posts