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

Redeem

Numbers

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Sun Jun 13, 2010 8:15 pm

Numbers

by ruchisharma » Fri Aug 20, 2010 1:16 am
If the prime numbers, p & t are the only prime factors of the integer m, is m a multiple of (p^2)t?

1.) m has more than 9 positive factors.

2.) m is a multiple of p^3
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 324
Joined: Mon Jul 05, 2010 6:44 am
Location: London
Thanked: 70 times
Followed by:3 members

by kmittal82 » Fri Aug 20, 2010 2:07 am
I have a feeling my answer is incorrect, but it might give you an idea on how to approach :)

Let m = p^x * t ^ y

Question is basically asking is m/(p^2)t an integer.

Rephrasing, this means is p^(x-2) * t ^ (y-1) an integer

(1)

Total number of factors of m > 9
=> (x+1)(y+1) > 9

A variety of values of x and y satisfy this equation. E.g., if x = 3, y =4
then our equation asks is p^(3-2)*t(4-1) an integer = p*t^3 which is an integer

However, if x = 1, y = 11
p^(-1)*t^10 = t^10 / p which is not an integer

Hence insufficient

(2)

Let m = p^3 * K, where K is some constant

Question is now asking:

Is [(p^3) * K] / [(p^2) * t] an integer
= p*K/t

This may or may not be an integer, depending on the value of K. Hence, insufficient.

Combining:

m = p^x * t^y = p^3 * k

=> x = 3
We also know that (x+1)(y+1) > 9, this means 4(y+1)>9 => y + 1 > 2
The minimum value of y + 1 has to be 3 => min. value of y = 2

p^(x-2) * t^(y-1) will thus always be an integer, since x = 3 and minimum value of y is 2

Thus (C)

Can you please confirm the OA?
Top
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Sun Jun 13, 2010 8:15 pm

by ruchisharma » Fri Aug 20, 2010 2:13 am
Answer is B
Top
User avatar
Legendary Member
Posts: 659
Joined: Mon Dec 14, 2009 8:12 am
Thanked: 32 times
Followed by:3 members

by Gurpinder » Fri Aug 20, 2010 8:07 am
ruchisharma wrote:If the prime numbers, p & t are the only prime factors of the integer m, is m a multiple of (p^2)t?

1.) m has more than 9 positive factors.

2.) m is a multiple of p^3
the question is basically asking whether m is divisible by (p^2)t - which would mean whether we get an integer or not

stmt (1)
clearly insufficient. It does not tell us anything about P or T or "prime" factors.

Stmt (2)

if m/P^3 is an integer. clearly, m/p^2 would be an integer. And since T is a prime factor of M, then the result of m/P^2 multiplied by T would also be a factor of M.

this one is like saying if X,Y are factors of Z, then XY would also be factors of Z. This is like going up the prime factorization tree.

Therefore the answer is (B).
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 422
Joined: Mon Aug 09, 2010 11:47 am
Thanked: 22 times
Followed by:1 members
GMAT Score:680

by beatthegmatinsept » Fri Aug 20, 2010 8:28 am
ruchisharma wrote:If the prime numbers, p & t are the only prime factors of the integer m, is m a multiple of (p^2)t?

1.) m has more than 9 positive factors.

2.) m is a multiple of p^3
Asking: if p, p and t, are factors of m.
1) is insufficient because m having more than 9 positive factors doesnt tell us if it has p and p as prime factors.
2) is sufficient because it tells you that p, p and p are factors of m..
Being defeated is often only a temporary condition. Giving up is what makes it permanent.
Top
Post new topic Post Reply
• Page 1 of 1