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

Redeem

number properties

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 344
Joined: Sat Nov 12, 2011 3:21 am
Thanked: 1 times
Followed by:2 members

number properties

by sud21 » Thu Jan 12, 2012 9:32 am
Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2
Top
Source: — Data Sufficiency |
Master | Next Rank: 500 Posts
Posts: 385
Joined: Fri Sep 23, 2011 9:02 pm
Thanked: 62 times
Followed by:6 members

by user123321 » Thu Jan 12, 2012 6:09 pm
sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2
Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321
Just started my preparation :D
Want to do it right the first time.
Top
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Thu Jan 12, 2012 6:56 pm
why you think it's wrong q.?
st(1) implies if x is prime then the only prime factor of x is x itself, and x>sqrt(x). But x as non-prime can have a prime factor equal to srt(x) and/or less (not greater). Ex., x=9, factor=3 and 3=sqrt(9). All other non-primes will contain 2 as a prime as well and will be not suitable here. Hence the answer is Yes, x is prime. Sufficient

st(2) implies if x is prime then x>x/2, which is true. If x is non-prime, then it's possible for prime factors of x to be only less than or equal to x/2. Ex., 3<9/2 or 2=4/2 Sufficient

d
user123321 wrote:
sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2
Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321
Success doesn't come overnight!
Top
User avatar
Legendary Member
Posts: 1239
Joined: Tue Apr 26, 2011 6:25 am
Thanked: 233 times
Followed by:26 members
GMAT Score:680

by sam2304 » Thu Jan 12, 2012 7:03 pm
user123321 wrote:
sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2
Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321
1.A prime number has two factors one and itself and definitely its greater than sqrt x
15 has one of its prime factors 5 > sqrt x and 3 < sqrt x. INSUFF as the condn holds true for both prime and composite nos

2.Only a prime no can have its prime factors (itself) > x/2. SUFF

IMO B.
Last edited by sam2304 on Thu Jan 12, 2012 7:20 pm, edited 2 times in total.
Getting defeated is just a temporary notion, giving it up is what makes it permanent.
https://gmatandbeyond.blogspot.in/
Top
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Thu Jan 12, 2012 7:10 pm
@sam, you made a mistake here, as the original question precisely specifies *all prime factors* and you account only for 5 in 15. What about 3?
sam2304 wrote:
user123321 wrote:
sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2
Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321
1.A prime number has two factors one and itself and definitely its greater than sqrt x
15 has one of its prime factors 5 > sqrt x. INSUFF as the condn holds true for both prime and composite nos

2.Only a prime no can have its prime factors (itself) > x/2. SUFF

IMO B.
Success doesn't come overnight!
Top
User avatar
Legendary Member
Posts: 1239
Joined: Tue Apr 26, 2011 6:25 am
Thanked: 233 times
Followed by:26 members
GMAT Score:680

by sam2304 » Thu Jan 12, 2012 7:22 pm
pemdas wrote:@sam, you made a mistake here, as the original question precisely specifies *all prime factors* and you account only for 5 in 15. What about 3?
sam2304 wrote:
user123321 wrote:
sud21 wrote:Integer x is greater than 0, is x a prime number?
1). All the prime factors of x are greater than root x
2). All the prime factors of x are greater than x/2
Hi

I think there is some issue in the problem.

a prime factor of x cannot be b/w root x and x.
please check once.

Regards,
user123321
1.A prime number has two factors one and itself and definitely its greater than sqrt x
15 has one of its prime factors 5 > sqrt x. INSUFF as the condn holds true for both prime and composite nos

2.Only a prime no can have its prime factors (itself) > x/2. SUFF

IMO B.
Edited it, missed it while typing. But then it breaks the condition right ? The statement is INSUFF.
Getting defeated is just a temporary notion, giving it up is what makes it permanent.
https://gmatandbeyond.blogspot.in/
Top
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Thu Jan 12, 2012 7:25 pm
no Sam, the condition is Sufficient

you are given precisely x>sqrt(x) for all prime factors, which is *true* only for primes

hence D
Success doesn't come overnight!
Top
User avatar
Legendary Member
Posts: 1239
Joined: Tue Apr 26, 2011 6:25 am
Thanked: 233 times
Followed by:26 members
GMAT Score:680

by sam2304 » Thu Jan 12, 2012 7:32 pm
pemdas wrote:no Sam, the condition is Sufficient

you are given precisely x>sqrt(x) for all prime factors, which is *true* only for primes

hence D
@pemdas: Yea. Got the point. We have to consider only nos which have prime factors > sqrt x, and disprove them if possible. I guess I took it in opposite sense. 15 cannot be considered. Thanks mate. Confusing traps :)
Getting defeated is just a temporary notion, giving it up is what makes it permanent.
https://gmatandbeyond.blogspot.in/
Top
Master | Next Rank: 500 Posts
Posts: 382
Joined: Thu Mar 31, 2011 5:47 pm
Thanked: 15 times

by ArunangsuSahu » Thu Jan 12, 2012 9:02 pm
Statement 1:
All the prime factors of x are greater than root x

Only satisfied by PRIME Numbers.

SUFFICIENT

Statement 2:
All the prime factors of x are greater than x/2

This is also only true for PRIME numbers
SUFFICIENT

else 8/2=4 but it's PRIME factor is 2
Top
Master | Next Rank: 500 Posts
Posts: 385
Joined: Fri Sep 23, 2011 9:02 pm
Thanked: 62 times
Followed by:6 members

by user123321 » Thu Jan 12, 2012 10:10 pm
Thanks all for correcting :0)

user123321
Just started my preparation :D
Want to do it right the first time.
Top
Post new topic Post Reply
• Page 1 of 1