The given question is a challenging GMAT hard quant problem solving question testing concepts in number properties - Product of factors of cubes and squares of numbers.

Question 38: What is the product of all the factors of the cube of a positive integer 'n' if the product of all the factors of square of n is n^{3}?

- n
^{4} - n
^{6} - n
^{9} - n
^{5} - Cannot be determined

@ INR

'n' is a positive integer.

Product of the factors of n^{2} is n^{3}.

If the product of the factors of n^{2} = n^{3}, the only factors of n^{2} are 1, n, and n^{2}.

So, we can infer that n does not have any factor other than 1 and itself.

Therefore, n is a prime number.

Factors of n^{3} if n is a prime number are 1, n, n^{2} and n^{3}.

So, the product of the factors of n^{3} = 1 × n × n^{2} × n^{3} = n^{6}

Try it free!

Register in 2 easy steps and

Start learning in 5 minutes!

31. GMAT 650 Level Sample Question | Arithmetic DS | Number Properties

32. GMAT Hard Math Arithmetic - Counting Methods | GMAT Problem Solving

33. GMAT Challenging Question | Geometry DS | Coordinate Geometry & Quadratic Equations

34. GMAT Hard Math | Geoemtry Right Triangles | GMAT 750 Level Data Sufficiency

35. GMAT Challenging Math Question | Arithmetic | Number Properties - Remainders

36. GMAT Data Sufficiency | Number Properties

37. GMAT DS Sample Question | Arithmetic - Statistics | Mean, Median, and Range

38. GMAT Number Properties Practice | 650 Level Question | Factors Problem Solving

39. GMAT Arithmetic Question | Numbers Counting Methods Problem Solving

40. GMAT Algebra Practice Question | Equations & Numbers PS

Copyrights © 2016 - 21 All Rights Reserved by Wizako.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

GMAT^{®} is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.

GRE^{®} is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.

SAT^{®} is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.

Wizako - GMAT, GRE, SAT Prep

An Ascent Education Initiative

48/1 Ramagiri Nagar

Velachery Taramani Link Road.,

Velachery, Chennai 600 042. India

**Phone:** (91) 44 4500 8484

**Mobile:** (91) 95000 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@wizako.com

Leave A Message