Is p^2 divisible by 24? p is an integer. 1) p is divisible by 6 2) p^3

Question

Is  p^2  divisible by 24? p is an integer.

(1)  p  is divisible by 6
(2)  p^3  is divisible by 24

chetan2u · Answer

Is  p^2  divisible by 24? p is an integer.
1)  p  is divisible by 6
So  p^2  will be divisible by  6^2  or 36..
But 36 is not a multiple of 24, so we cannot say anything about 24.
Insufficient

2)  p^3  is divisible by 24
So  p^3=24a=2^3*3*a .
Thus p will surely be divisible by 2*3 or 6..
But we cannot say anything about 24 as 6 is not a multiple of 24.
If a number is divisible by 24, it is surely divisible by its factors 1,3,4,6,12 etc but the vice versa need not be true.
Insufficient

Combined
Both the choices tell us that p is divisible by 6, but nothing about 24.
Insufficient

E

miquelperezn · Answer

I do not understand why statement 1) and 2) combined are insufficient... could any expert help here?

Thanks!

Bunuel · Answer

Is  p^2  divisible by 24? p is an integer.

Since p is an integer, for  p^2  to be divisible by 24 = 2^3*3, p must be divisible by 2^23.

(1)  p  is divisible by 6

This implies that p is divisible by 2*3. Not sufficient.

(2)  p^3  is divisible by 24

This implies the same as above: that p is divisible by 2*3. Not sufficient.

(1)+(2) Both statements give us the same information: p is divisible by 2*3. If p = 6, then the answer is NO:  p^2 = 36  is NOT divisible by 24. However, if  p = 2^2*3 = 12 , then  p^2 = 144  IS divisible by 24. Not sufficient.

Answer: E.

P.S. Worth noting though that such type of pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:
 
 Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won't encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

Hope it helps.

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Is p^2 divisible by 24? p is an integer. 1) p is divisible by 6 2) p^3

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Is p^2 divisible by 24? p is an integer. 1) p is divisible by 6 2) p^3

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