GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Feb 2019, 17:43

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 in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     February 17, 2019

     February 17, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Free GMAT Strategy Webinar

     February 16, 2019

     February 16, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

(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

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52902
(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, 00:23
12
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (02:14) correct 40% (02:22) wrong based on 137 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

_________________

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

Current Student
User avatar
P
Joined: 18 Aug 2016
Posts: 623
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
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, 00:44
1
1
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


Thanks
Luckisnoexcuse

Manager
Manager
avatar
S
Joined: 30 Mar 2017
Posts: 66
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, 00:56
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
Intern
Intern
avatar
B
Joined: 18 May 2017
Posts: 48
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, 11:13
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.
Senior Manager
Senior Manager
avatar
G
Joined: 02 Apr 2014
Posts: 476
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
(s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso  [#permalink]

Show Tags

New post 11 Jan 2018, 05:47
Given: v is an integer => \(\sqrt{s^3 * t^3}\) => must be an integer

but given s and t are prime numbers, then \(\sqrt{s^3 * t^3}\) cannot be an integer, unless and until both the primes are same.

for v to be an integer, s = t , \(v^2 = s^3 * s^3 = s^6\)
=> \(v = s^3\)
=> number of factors of v = (3 + 1) = 4
=> Number of factors of v greater than 1 = (4 - 1) = 3
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4915
Location: United States (CA)
Re: (s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso  [#permalink]

Show Tags

New post 18 Jan 2018, 07:41
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


In order for the equation (s^3)(t^3) = v^2 to hold, we see that s and t must be equal;, thus, we can say:

(s^3)(s^3) = v^2

s^6 = v^2

s^3 = v

To determine the total number of factors of v, we can add 1 to the exponent of 3, and thus v has 3 + 1 = 4 total factors. Since one of those factors is “1”, v has 3 factors other than 1.

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 933
Location: India
Re: (s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso  [#permalink]

Show Tags

New post 09 Feb 2019, 22:08
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


I preferred plug in here,

(s^3)(t^3) = v^2 If s and t are both primes

s & t can be same => 2^6 = 8^2

8 has 3 divisors 2,4,8

Before marking the question, lets check another case

3^3 2^3 = 216 ! = a perfect square

5^3 * 2^3 = 1000 ! = a perfect square

3^6 = 9^2, this will again work

B
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

GMAT Club Bot
Re: (s^3)(t^3) = v^2 If s and t are both primes, how many positive diviso   [#permalink] 09 Feb 2019, 22:08
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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.