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29 Dec 2014, 16:51
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:41) correct
34%
(01:56)
wrong
based on 483
sessions
History
Date
Time
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Not Attempted Yet
If p is a positive integer and p^2 is divisible by 12, then the largest positive integer that must divide p ^3 is
(A) 2^3
(B) 2^6
(C) 3^3
(D) 6^3
(E) 12^2
(A) 2^3
(B) 2^6
(C) 3^3
(D) 6^3
(E) 12^2
30 Dec 2014, 21:28
Kudos
Bookmarks
Hi sunita123,
This question is essentially about prime factorization and how exponents "work."
When a question uses an exponent, you have to remember what the exponent implies:
Here, we have P^2, which means (P)(P)
For example, if P is a positive integer and P^2 = 100, then P = 10
This can be written in a variety of ways:
P^2 = 100
P^2 = 10^2
P^2 = (10)(10)
P^2 = [2x5][2x5]
The point of all of this is that each "P" has to be made up of the same "pieces" - in this example, P is made up of one "2" and one "5."
Here, we're told that P is a positive integer and P^2 is DIVISIBLE by 12. This causes a bit of extra work for us because 12 = (2)(2)(3). P CANNOT = 12 though because there aren't enough "pieces" to make both Ps the same. We can put a "2" into each "P" but we can't split up the 3....
P^2 = (P)(P) = (2 x something)(2 x something) ....but the 3 has to go in there somewhere....
If we had ANOTHER 3 though, then we'd have P^2 = (2)(2)(3)(3) and then we can put one "2" and one "3" into each P...
P^2 = (2x3)(2x3) = 36
P = 6
Having that extra 3 is the simplest/smallest value for P that fits this question. From here, P^3 = 6^3.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question is essentially about prime factorization and how exponents "work."
When a question uses an exponent, you have to remember what the exponent implies:
Here, we have P^2, which means (P)(P)
For example, if P is a positive integer and P^2 = 100, then P = 10
This can be written in a variety of ways:
P^2 = 100
P^2 = 10^2
P^2 = (10)(10)
P^2 = [2x5][2x5]
The point of all of this is that each "P" has to be made up of the same "pieces" - in this example, P is made up of one "2" and one "5."
Here, we're told that P is a positive integer and P^2 is DIVISIBLE by 12. This causes a bit of extra work for us because 12 = (2)(2)(3). P CANNOT = 12 though because there aren't enough "pieces" to make both Ps the same. We can put a "2" into each "P" but we can't split up the 3....
P^2 = (P)(P) = (2 x something)(2 x something) ....but the 3 has to go in there somewhere....
If we had ANOTHER 3 though, then we'd have P^2 = (2)(2)(3)(3) and then we can put one "2" and one "3" into each P...
P^2 = (2x3)(2x3) = 36
P = 6
Having that extra 3 is the simplest/smallest value for P that fits this question. From here, P^3 = 6^3.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
29 Dec 2014, 19:56
Kudos
Bookmarks
Since p is an integer so p cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making p^2 as a multiple of 12))
p^2 is divisible by 12 (12 = 2*2*3), So, p should have at least one 2 and one 3 so that p^2 has a 2^2 and two 3
So, p will have a 2 and a 3. Or p will be a multiple of 6
So, largest possible integer than should divide p^3 is 6^3
So, Answer will be D
Hope it helps!
p^2 is divisible by 12 (12 = 2*2*3), So, p should have at least one 2 and one 3 so that p^2 has a 2^2 and two 3
So, p will have a 2 and a 3. Or p will be a multiple of 6
So, largest possible integer than should divide p^3 is 6^3
So, Answer will be D
Hope it helps!
sunita123
If p is a positive integer and p^2 is divisible by 12, then the largest positive integer that must divide p ^3 is
(A) 2^3
(B) 2^6
(C) 3^3
(D) 6^3
(E) 12^2
(A) 2^3
(B) 2^6
(C) 3^3
(D) 6^3
(E) 12^2
