what does oa mean? the first post says, "check the oa". does it mean original answer?
in the gmat og 12, diagnostic
If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?
I. 8
II. 12
III. 18
A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
i sorta understand the solution, but taking 4 and 6 and it's prime factors, why cant the product xy be 12? my reasoning is that the prime factors of 4 are 2 and 2, and the prime factors of 6 are 2 and 3.
i would've thought the unique primes are 2 * 2 * 3, since one 2 is shared between 4 and 6. therefore the answer i arrived at was A
or i guess my question is, when do i use all the primes for a product and when do i remember not to double count?
thanks
easy ps - factors/multiple problem
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- krusta80
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CORRECTION!!dhlee922 wrote:what does oa mean? the first post says, "check the oa". does it mean original answer?
in the gmat og 12, diagnostic
If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?
I. 8
II. 12
III. 18
A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
i sorta understand the solution, but taking 4 and 6 and it's prime factors, why cant the product xy be 12? my reasoning is that the prime factors of 4 are 2 and 2, and the prime factors of 6 are 2 and 3.
i would've thought the unique primes are 2 * 2 * 3, since one 2 is shared between 4 and 6. therefore the answer i arrived at was A
or i guess my question is, when do i use all the primes for a product and when do i remember not to double count?
thanks
The following is to be used when determining the LEAST COMMON FACTOR for an integer that is divisible by 4 and by 6, HOWEVER that is not what this question is asking for!!
Step 1: Break up all numbers that are factors of the product into the product of prime factors.
4 = 2*2
6 = 2*3
Step 2: Pool together 1 instance of every listed prime number that is shared by all factors
Shared factor -> 2
Step 3: Pool together all non-repeated prime factors
Non-shared -> 2,3
Step 4: Multiply together all factors from both groups
2*2*3 = 12
===============================
In this question, they are giving us the product xy, which MUST be a multiple of 24. Therefore, any choice that is a factor of 24 will also be a factor of xy.
Answer is B
Last edited by krusta80 on Tue Feb 28, 2012 8:24 pm, edited 1 time in total.
- krusta80
- Master | Next Rank: 500 Posts
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Sorry for my sloppy initial response...I'm a bit rusty.dhlee922 wrote:i'm sorry krusta80, but that answer is wrong. it's the same logic i applied. i didnt write out the answer b/c i didnt want to confuse people and wanted to get ideas on why my method was incorrect
I've edited my response now to adjust to the specifics of the problem.
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- Brent@GMATPrepNow
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A lot of integer property questions can be solved using prime factorization.dhlee922 wrote:what does oa mean? the first post says, "check the oa". does it mean original answer?
in the gmat og 12, diagnostic
If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?
I. 8
II. 12
III. 18
A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N
Consider these examples:
24 is divisible by 3 because 24 = (2)(2)(2)(3)
Likewise, 70 is divisible by 5 because 70 = (2)(5)(7)
And 112 is divisible by 8 because 112 = (2)(2)(2)(2)(7)
And 630 is divisible by 15 because 630 = (2)(3)(3)(5)(7)
-----------ONTO THE QUESTION-------------------------------
positive integer x is a multiple of 4
In other words, x is divisible by 4, which means 4 is hiding in the prime factorization of x
So, we can write: x = (2)(2)(?)(?)(?)(?).... [ASIDE: The ?'s represents other primes that COULD be in the prime factorization. However, the only part of the prime factorization that we are certain of is the two 2's]
positive integer y is a multiple of 6
In other words, y is divisible by 6, which means 6 is hiding in the prime factorization of y
So, we can write: y = (2)(3)(?)(?)(?)(?)....
This means xy = (2)(2)(2)(3)(?)(?)(?)(?)....
This tells us that xy is divisible by all products formed by any combination of (2)(2)(2)(3)
So, xy must be divisible by 2, 3, 4, 6, 8, 12, 24
Answer: B
Cheers,
Brent