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

Redeem

Another Factor Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Fri Oct 23, 2009 12:49 pm

Another Factor Problem

by panda8989 » Sat Oct 24, 2009 11:48 am
If x is even, and 90 <= x <= 100, what is the value of x?

(1) x and x/2 have the same distinct prime factors.
(2) x/2 has two prime factors

ANS C

My approach...

x can be
90 92 94 96 98 100
and x/2 can be
45 46 47 48 49 50

(1) satisfies 92, 96, and 100
(2) satisfies 90, 92, 96 and 100

so... even when the arguments are combined, both 92, 96 and 100 can be an answer... So I chose (E).. Where did I go wrong?

Prime Factors
90 2, 3, 5
45 3, 5

92 2, 23
46 2, 23

94 2, 47
47 47

96 2, 3
48 2, 3

98 2, 7
49 7

100 2, 5
50 2, 5
Top
Source: — Data Sufficiency |
Master | Next Rank: 500 Posts
Posts: 124
Joined: Thu Jun 18, 2009 5:33 am
Thanked: 35 times

by NikolayZ » Sat Oct 24, 2009 1:55 pm
Hey!
I think you misread or misunderstood the problem.
Think about (2) i think that problem meant that x/2 has ONLY 2 prime factors. Check 92=2*46, 46=2*23 - only 2 primes.
So 1+2 is sufficient.
Top
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Fri Oct 23, 2009 12:49 pm

by panda8989 » Sat Oct 24, 2009 2:34 pm
Thanks for the reply, NikolayZ.

I am still unclear on "only two prime factors"

I guess you meant that every factor for x/2 is a prime?

In that sense...Since factor of 46 is 1, 2, 23, 46... It has 4 factors, of which 2 are prime and 2 are non-prime. Thus (2) cannot be satisfied.. In fact, all numbers have 1 as a factor, so (2) can never be satisfied with such logic.

I must seriously be misunderstanding something here, since OA mentions 92 as only # that satisfies both (1) and (2). I'd really appreciate if you could clarify it for me!
Top
Master | Next Rank: 500 Posts
Posts: 124
Joined: Thu Jun 18, 2009 5:33 am
Thanked: 35 times

by NikolayZ » Sat Oct 24, 2009 3:56 pm
Look
Statement 2 says that there are 2 PRIME factors of the x/2. Let's see:
as x we have

100 98 96 94 92 90

respectively x/2:

50 49 48 47 46 45

let's prime factorize them

50(2,5,5)- three prime factors overall
49(3,13) - two prime factors overall
48(2,2,2,2,3) - 5 primes
47 (47) - 1 prime
46(2,23) -2 primes
45(5,3,3) - 3 primes

So, statement two tells us that only 49 and 46 can be x/2. Insufficient.
But statement 1 tells us that x has exactly the same primes as x/2 has.

let's look
49*2=98=2*49=2*3*13, BUT 49 doesn't have 2 as a prime factor. So 98 clearly out.

46*2=92=2*46=2*2*23. Both 46 and 92 have 2's and 13 as primes. So 92 is our choice.
Hope it is clear now ;)
Top
Senior | Next Rank: 100 Posts
Posts: 43
Joined: Fri Aug 28, 2009 9:15 am

by geemat » Sun Oct 25, 2009 12:07 am
IMO E, both 92 and 100 satisfy both the conditions, do u have OE with you?
Top
Master | Next Rank: 500 Posts
Posts: 124
Joined: Thu Jun 18, 2009 5:33 am
Thanked: 35 times

by NikolayZ » Sun Oct 25, 2009 4:25 am
I believe that 100 does not satisfy the condition.
100/2=50=2*5*5 = 3 prime factors overall. Stmt 2 says that x/2 has only 2 prime numbers in its prime factorization.
Top
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Fri Oct 23, 2009 12:49 pm

by panda8989 » Sun Oct 25, 2009 6:59 am
Here's the explanation of the answer from the book.
Plug in. From the question, x can be 90, 92, 94, 96, 98, or 100.

For statement (1), list the distinct prime factors for each value of x and x/2. The distinct prime factors of both 92 and 92/5 = 46 are 2 and 23. So x could be 92. But the distinct prime factors for both 100 and 50 are 2 and 5, so statement (1) is not sufficient because x could be 92 or 100. Eliminate choices (b), (c), and (e).

Statement (2) says x/2 has two prime factors. So x could be 92, because the prime factors of 46 are 2 and 23. But x could also be 98, because the prime factors of 98/2 = 49 are 7 and 7. Statement (2) is not sufficient, so eliminate choice (b)

Combine the statements. Only 92 makes both statements true, so x must be 92. The answer is choice (c).
I guess the keyword is "distinct". I do see the logic, but I am not sure if it's correct to say 49 has two prime factors because 7 * 7 = 49... The way I thought was 49 has 3 factors - 1, 7, 49, one of which is a prime factor.
Top
Post new topic Post Reply
• Page 1 of 1