Last visit was: 21 Jul 2024, 01:13 It is currently 21 Jul 2024, 01:13
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94433
Own Kudos [?]: 642636 [4]
Given Kudos: 86715
Send PM
Senior Manager
Senior Manager
Joined: 10 Mar 2015
Posts: 252
Own Kudos [?]: 236 [2]
Given Kudos: 175
Location: India
Concentration: Strategy, Marketing
GPA: 3.5
WE:Advertising (Advertising and PR)
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5318
Own Kudos [?]: 4239 [2]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Intern
Intern
Joined: 17 Jan 2023
Posts: 12
Own Kudos [?]: 14 [1]
Given Kudos: 493
Location: India
GMAT Focus 1:
695 Q85 V84 DI84
GMAT 1: 700 Q49 V35
GMAT 2: 710 Q49 V36
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
Bunuel wrote:
If \(3^{(-\frac{k}{2})} > \frac{1}{81}\), what is the value of k ?


(1) \(k\) is the square of a prime number.

(2) \(\frac{k}{2}\) is a prime number.


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 




We know that 1/81 = 1/3^4 = 3^-4
Expressing both sides in terms of power of 3:

-k/2 > -4
k/2 < 4
k < 8

From (1),
If k is the square of a prime number, k = 2^2, 3^2, 5^2, .... = 4, 9, 25, .....

But from the given statement, k < 8, hence k = 4 is the only possible solution. (1) is sufficient

From (2),
k/2 is a prime number. So k = 4, 6, 10, .... so that k/2 = 2, 3, 5, .... (primes)

Not sufficient

Ans. (1)
Manager
Manager
Joined: 07 May 2023
Posts: 201
Own Kudos [?]: 243 [1]
Given Kudos: 47
Location: India
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
Bunuel wrote:
If \(3^{(-\frac{k}{2})} > \frac{1}{81}\), what is the value of k ?


(1) \(k\) is the square of a prime number.

(2) \(\frac{k}{2}\) is a prime number.


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 



\(3^{(-\frac{k}{2})} > \frac{1}{81}\)

\(3^{(-\frac{k}{2})} > 3^{-4}\)

\(-\frac{k}{2} < -4\)

\(- k > -8\)

\(k < 8\)

1) Only possible value of k = 4

The statement is sufficient.

2) k can be 4 or 6 as 4/2 = 6 and 6/2 = 3

The statement is not sufficient.

IMO A
Intern
Intern
Joined: 22 Dec 2022
Posts: 30
Own Kudos [?]: 70 [1]
Given Kudos: 166
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
\(3^{(-\frac{k}{2})} > \frac{1}{81}\)

\(\frac{1}{3^\frac{k}{2}} > \frac{1}{3^4}\)

As we are dealing with fractions, for the left hand side to be a bigger we need the denominator to be smaller. Therefore with dropping the base of 3: \(\frac{k}{2}<4\)
\(k<8\)

(1) k is the square of a prime number.

Given the parameters of k, the only possible answer for k is 2. \(2^2 = 4\) works. \(3^2 = 9\) exceeds the inequality \(k<8\)

SUFFICIENT

(2) k/2 is a prime number.

If k is 6: \(\frac{6}{2}= 3\)
If k is 4: \(\frac{4}{2}= 2\)

One cannot come to a single value for k.

INSUFFICIENT

Answer A
Manager
Manager
Joined: 23 Mar 2021
Status:Trying to push it higher!
Posts: 57
Own Kudos [?]: 61 [1]
Given Kudos: 748
Location: India
Concentration: Strategy, General Management
GPA: 3.5
WE:Analyst (Computer Software)
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
Given:
If 3^(−k/2)>1/81, what is the value of k ?
(1) k is the square of a prime number.
(2) k/2 is a prime number.

Let's evaluate:
=> 3^(-k/2) > 1/(3^4)
=> 3^(-k/2) > 3 (-4)

Therefore, we can write:
=> - k/2 = -4
=> -k > -8
=> k < 8

Statement 1: k is the square of a prime number.
2^2 = 4
3^2 = 9
So, here, we can definitely say that k is 4. (k<8)
Also, we should remember that square of any number is a positive number.

(Sufficient)

Statement 2:
k/2 is a prime number.

Plug in a few values:
k = 4 => 4/2 = 2 (prime)
k = 6 => 6/2 = 3 (prime)
So we don't have a single answer.
(Not sufficient.)

So that means, Statement 1 alone is sufficient.
I will go with option A.
Intern
Intern
Joined: 12 Jun 2023
Posts: 9
Own Kudos [?]: 13 [1]
Given Kudos: 8
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
3^ (−k/2)> 1/81
3^ (−k/2)> 3^(-4)
(−k/2)> (-4)
k/2 < 4
k < 8

(1) k is the square of a prime number.
2^2 = 4

(2) k / 2 is a prime number.
6/2 = 3
4/2 = 2

So, 1 alone is sufficient, but 2 alone is not
Ans : A
Intern
Intern
Joined: 14 Dec 2020
Posts: 24
Own Kudos [?]: 35 [1]
Given Kudos: 24
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
So here is my ans:

When we solve the equation we get k< 8

a) k is square of prime number

sqre of 2 = 4
sqre of 3 = 9

so we know that there can be only one option which is k=4

b) k/2 is prime number
so that means k is a even number
so k can be 4,6
when k = 4 =>4/2=2 prime number
when k = 6 =>6/2=3 prime number
so both the answers are possible.

Hence only a is sufficient
Intern
Intern
Joined: 17 Nov 2022
Posts: 19
Own Kudos [?]: 6 [1]
Given Kudos: 26
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
If 3^(-k/2) > 1/81. Then K=?

We can rewrite Question as:-

3^(-k/2) > 1/3^4
3^(-k/2 + 4) > 1
so for 3^x to be greater than 1. x should be greater than 0.

-k/2 + 4 > 0
k < 8
Question :- if K<8 what is k?

Statement 1: k is the square of a prime number.

i.e. K can take the values -> 2^2 , 3^2 , 5^2....... -> 4,9,25...
As K<8 only possible value is 4 so S1: SUFFICIENT

Statement 2: k/2 is a prime number.

i.e. K can take the values -> 2*2 , 3*2 , 5*2....... -> 4,6,10...
As K<8 k can take 4 and 6 so S2: INSUFFICIENT

IMO A
Intern
Intern
Joined: 11 Dec 2022
Posts: 37
Own Kudos [?]: 68 [1]
Given Kudos: 10
GMAT 1: 650 Q49 V29
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
We can write 3^(-k/2) = 1/(3^(k/2))

Hence, 1/(3^(k/2)) > 1/81.

We can cross multiple the denominators for simplification and this wont change the sign between them, since "81" is positive and "3^(k/2)" is also positive (independent whether "k" is positive or negative)

Therefore:- 3^(k/2) < 81
So, (k/2) < 4, hence k < 8

(1) k is square of a prime number:-
Square of prime numbers are 4, 9, 25,.... and only "4" satisfies our condition of k < 8.

Hence statement (1) alone is sufficient.

(2) k/2 is a prime number:-
Using this condition, the possible values of "k" are 4, 6, 10, 14,....
Here "4" and "6" both satisfies the condition of k < 8. So using statement (2) we still cannot uniquely find the value of "k".

Hence statement (2) alone is NOT sufficient.
Manager
Manager
Joined: 11 May 2023
Posts: 90
Own Kudos [?]: 115 [1]
Given Kudos: 47
Location: India
Concentration: General Management, Strategy
GMAT Focus 1:
675 Q88 V81 DI82
GPA: 76%
WE:Engineering (Non-Profit and Government)
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
Bunuel wrote:
If \(3^{(-\frac{k}{2})} > \frac{1}{81}\), what is the value of k ?


(1) \(k\) is the square of a prime number.

(2) \(\frac{k}{2}\) is a prime number.


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 



Q:- \(3^{(-\frac{k}{2})} > 3^{(-4)}\)
-k/2 > -4
k/2 < 4
k < 8

s1 :- k = square of a prime number
prime number less than \sqrt{8} = 2
So, k = 2
Therefore, statement 1 is sufficient.

s2:- k/2 = prime number

prime numbers valid for above cases = 2 , 3
Therefore, s2 is not sufficient.

Hence, A is correct answer.
DI Forum Moderator
Joined: 05 May 2019
Status:GMAT Club Team member
Affiliations: GMAT Club
Posts: 998
Own Kudos [?]: 739 [1]
Given Kudos: 1003
Location: India
GMAT Focus 1:
645 Q82 V81 DI82
GMAT 1: 430 Q31 V19
GMAT 2: 570 Q44 V25
GMAT 3: 660 Q48 V33
GPA: 3.26
WE:Engineering (Manufacturing)
Send PM
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
1
Kudos
Bunuel wrote:
If \(3^{(-\frac{k}{2})} > \frac{1}{81}\), what is the value of k ?


\(3^{(-\frac{k}{2})} > \frac{1}{81}\)
=> \(3^{(-\frac{k}{2})}\) > \(3^(-4)\)

=> \(-(\frac{k}{2})\) > -4
=> \(\frac{k}{2 }\)< 4
=> k < 8

Quote:
(1) \(k\) is the square of a prime number.


From Statement 1, we get
Squares of prime numbers are \(2^2\), \(3^2\), \(5^2\) , and so on
But k < 8 , this implies that k = 4.

Statement 1 is sufficient

Quote:
(2) \(\frac{k}{2}\) is a prime number.


From Statement 2, we get

\(\frac{k}{2}\) = Prime number = n
=> k = 2 * n
Since k < 8
=> 2*n < 8
=> n < 4
Therefore, n could be 2 or 3.
Statement 2 is not sufficient.

IMO OA should be A.
GMAT Club Bot
Re: Around the World in 80 Questions (Day 2): If 3^(-k/2) > 1/81 [#permalink]
Moderator:
Math Expert
94433 posts