Latest Accenture Aptitude Question SOLUTION: A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily

• Placement Papers
• /
• Accenture
• /
• Numerical Ability
• /
• Algebra

Accenture Question Papers: Accenture Interview Experience(7) ACCENTURE Company Profile

(#M40003698) ACCENTURE Numerical Ability question Keep an EYE

A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
a) 8p b) pq c) pq + 27 d) -p e) (p - q)6

Asked In Accenture (12 years ago)

Unsolved Read Solution (3)

Is this Puzzle helpful?   (4)   (6) Submit Your Solution Algebra

Read Solution (3) :

Dr.Dipin Singh  (12 years ago)

c) pq + 27
e) (p - q)6

These two terms may not be perfect cubes.
If last term is (p-q)^6 , then only [ pq + 27] is such term.

Is this solution Helpfull? Yes (5) | No (9)  

kavya rastogi  (8 years ago)

A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5

Consider the answer choices in turn.

8 is the cube of 2, and p is a cube, and so the product will also be a cube.

pq will also be a cube as shown above.

pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube.

-p will be a cube.

Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).

Is this solution Helpfull? Yes (2) | No   

Shreyas P  (9 years ago)

perfect cube multiplied or divided by another perfect cube yields a perfect cube. Therefore,

(c) and (e) are not NECESSARILY perfect cubes.

Is this solution Helpfull? Yes (1) | No (1)  

Please Login to Read Solution.