BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Unable to understand this DS problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Tue Feb 02, 2010 12:24 pm

Unable to understand this DS problem

by manjus_mailme » Wed Apr 14, 2010 8:10 am
If P has a total of 8 positive factors, including 1 and P, what is the value of P? Positive integer
P has 2 positive prime factors, 5 and 11.

1. 125 is a factor of P.
2. 121 is not a factor of P.

I can understand that statement 1 is sufficient to answer the question because we can determine the 8 positive factors as follows :

statement 1: 125 can be written as 5^3 .So 5^2 ,5 ,11,11*5,11*5^2,11*5^3,1 are all factors of P.Since p is a factor of itself P=11*5^3.

But the answer says that statement 2 is also sufficient.How to determine that?

Thanks for your help.
Last edited by manjus_mailme on Wed Apr 14, 2010 12:22 pm, edited 1 time in total.
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 435
Joined: Mon Mar 15, 2010 6:15 am
Thanked: 32 times
Followed by:1 members

by eaakbari » Wed Apr 14, 2010 10:30 am
manjus_mailme wrote:If P has a total of 8 positive factors,.....
P has exactly 2 positive prime factors, 5 and 11.
Please correct the question
Whether you think you can or can't, you're right.
- Henry Ford
Top
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Tue Feb 02, 2010 12:24 pm

by manjus_mailme » Wed Apr 14, 2010 12:24 pm
eaakbari wrote:
manjus_mailme wrote:If P has a total of 8 positive factors,.....
P has exactly 2 positive prime factors, 5 and 11.
Please correct the question
Does the question make sense now.The question from the source itself was wrong.I edited it as it is now.
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Wed Apr 14, 2010 12:33 pm
Let's start by fixing up the problem:
If P has a total of 8 positive factors, including 1 and P, what is the value of P? Positive integer
P has 2 positive prime factors, 5 and 11.


becomes:
Positive integer P has only 2 distinct prime factors, 5 and 11. If P has a total of 8 positive factors, what's the value of P?
Step 1 of the Kaplan Method for DS: Analyze the stem

We know that 4 of the factors of P are 1, 5, 11 and P. We also know that P has no other primes factors other than 5 and 11; what we don't know is how many 5s and 11s P contains.

Step 2 of the Kaplan Method for DS: Evaluate the Statements

(1) 125 is a factor of P.

Therefore, P has at least 3 "5"s among it's primes.

So, we have 1, 5, 11, 25, 55, 125, 25*11, 125*11 as our 8 factors. Therefore, P = 125*11... sufficient.

(2) 121 is NOT a factor of P.

Therefore, P has exactly 1 factor of 11; the other factors all have to be 5s.

Well, the only way to generate 8 factors for P is if we have 3 "5"s among the factors; as above, P = 125*11... sufficient.

Each of (1) and (2) is sufficient alone, choose (D).
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Legendary Member
Posts: 610
Joined: Fri Jan 15, 2010 12:33 am
Thanked: 47 times
Followed by:2 members

by kstv » Wed Apr 14, 2010 9:02 pm
P has 8 factors
1, 5 , 11 , a, b, c , d, P
(1) 125 is a factor of P.
so a, b, c or d can be 125
so possible values of a,b and c are
25, 55, 125, 25*11
( but does it have to be 55 or 25*11 can it not be 121 )
since there are 4 more factors a to d, does it restrict the existence of 11*11 as one of the factors
till (2) 121 is NOT a factor of P clears the air.
and if it does restrict the existence of 121 then is (2) really necessary.

What am I missing ?
Top
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Mon Jul 13, 2009 4:25 pm
Thanked: 1 times

by ymach3 » Thu Apr 15, 2010 4:08 am
If a Number P is factorized in the format P= a^m * b^n.

and a , b are two prime factors of a number, then the number of factors is given by = (m+1)*(n+1).

For example, No of factors of 6 = 2^1*3^1 = (1+1)*(1+1)=2*2=4 ----> 1,2,3,6.

From the Question,

we have 5 and 11 as prime factors.... 5^m * 11^n ...

And Number of factors=8

From (i)

125 is factor of P---> 125=5^3 and P=5^3 * 11^n

Number of factors = (3+1)*(n+1)=8---> n=1.

S(i) is Sufficient.



From (ii)

121 is not a factor of P.

Only possibility=5^3*11---> Sufficient.

Hence D.

Thx Stuart.
Top
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Tue Feb 02, 2010 12:24 pm

by manjus_mailme » Thu Apr 15, 2010 5:18 am
Thank you so much for explaning the problem .It was very helpful.
Top
Post new topic Post Reply
• Page 1 of 1