It is currently 19 Sep 2017, 05:09

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

(s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41598

Kudos [?]: 123967 [0], given: 12070

(s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso [#permalink]

Show Tags

New post 01 Aug 2017, 01:23
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (01:33) correct 31% (01:47) wrong based on 55 sessions

HideShow timer Statistics

(s^3)(t^3) = v^2 If s and t are both primes, how many positive divisors of v are greater than 1, if v is an integer?

(A) two

(B) three

(C) five

(D) six

(E) eight
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 123967 [0], given: 12070

Director
Director
User avatar
G
Joined: 18 Aug 2016
Posts: 502

Kudos [?]: 125 [0], given: 120

GMAT 1: 630 Q47 V29
GMAT ToolKit User Premium Member Reviews Badge
Re: (s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso [#permalink]

Show Tags

New post 01 Aug 2017, 01:44
1
This post was
BOOKMARKED
Bunuel wrote:
(s^3)(t^3) = v^2 If s and t are both primes, how many positive divisors of v are greater than 1, if v is an integer?

(A) two

(B) three

(C) five

(D) six

(E) eight


Let s & t be 2

2^6 = v^2
v = 2^3
v will have 4 divisors including 1
excluding 1 it will have 3

B
_________________

We must try to achieve the best within us

(Please like the below page on FB)

https://www.facebook.com/DeclutterCamp

Kudos [?]: 125 [0], given: 120

Manager
Manager
avatar
B
Joined: 30 Mar 2017
Posts: 61

Kudos [?]: 13 [0], given: 10

Re: (s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso [#permalink]

Show Tags

New post 01 Aug 2017, 01:56
S and T will be equal for v to be an integer.
So V=S^3. And number of divisors will be 3+1=4
Since we are not counting 1 so answer will be B (three)

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app

Kudos [?]: 13 [0], given: 10

Manager
Manager
avatar
B
Joined: 18 May 2017
Posts: 54

Kudos [?]: 4 [0], given: 125

Re: (s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso [#permalink]

Show Tags

New post 01 Aug 2017, 12:13
The easiest way in my opinion is to plug numbers and pick the right answer. Here is another way - more logical - to solve the question: As V^2 is a perfect square it has even number of each of his prime factors. As S and T are both prime numbers the multiplication of S^3 x T^3 has 3 S's and 3 T's. The only way for the aforementioned multiplication to has even numbers of primes is when S equal to T (3+3=6). Therefore we can write T^6=V^2 ----> T^3=V. As T is a prime number it has a total of 4 factors (3+1). We ask for the factors of V which are greater than 1, so we should exclude the case of T in a power of 0 (T=1). So the answer is 4-1=3.

Kudos [?]: 4 [0], given: 125

Re: (s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso   [#permalink] 01 Aug 2017, 12:13
    Similar topics Author Replies Last post
Similar
Topics:
8 EXPERTS_POSTS_IN_THIS_TOPIC How many positive integers less than 28 are prime numbers damham17 10 12 Mar 2017, 03:42
5 How many positive three-digit integers have an odd digit in both the SW4 2 10 Oct 2016, 14:37
51 EXPERTS_POSTS_IN_THIS_TOPIC How many positive three-digit integers are divisible by both alex1233 11 01 Jul 2017, 04:10
56 EXPERTS_POSTS_IN_THIS_TOPIC How many positive integers between 200 and 300 (both inclusi sdrandom1 27 25 Aug 2013, 06:17
1 If a and b are both odd prime numbers and a < b, then how many differe AbdurRakib 6 17 Oct 2016, 18:59
Display posts from previous: Sort by

(s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.