Last visit was: 13 Aug 2024, 20:59 It is currently 13 Aug 2024, 20:59
Toolkit
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

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.

# What is the value of r?

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 05 Dec 2016
Posts: 194
Own Kudos [?]: 89 [3]
Given Kudos: 49
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Retired Moderator
Joined: 25 Feb 2013
Posts: 893
Own Kudos [?]: 1563 [2]
Given Kudos: 54
Location: India
GPA: 3.82
Retired Moderator
Joined: 25 Feb 2013
Posts: 893
Own Kudos [?]: 1563 [1]
Given Kudos: 54
Location: India
GPA: 3.82
Intern
Joined: 29 Dec 2016
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 1
Re: What is the value of r? [#permalink]
Will this be considered 750+ level?
Manager
Joined: 05 Dec 2016
Posts: 194
Own Kudos [?]: 89 [0]
Given Kudos: 49
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
What is the value of r? [#permalink]
lavya07
I'm not sure whether it can be ranked as 750+, but % of correct responses shows that it is definitely not an easy one
I think if I had encountered such a question on real GMAT I'd have spent more than 2 min to solve it...
Manager
Joined: 05 Dec 2015
Posts: 82
Own Kudos [?]: 16 [0]
Given Kudos: 982
Re: What is the value of r? [#permalink]
How did you know 128 was a possible outcome too? I follow you until m=2 and from there thought q=2, k=4 and therefore i could solve. Didn't realize k could = 8 as well

niks18 wrote:
Alexey1989x wrote:
The sum of $$q$$ and $$m$$ equals to some positive odd number, where $$q$$ and $$m$$ are prime numbers.
When $$30$$ is divided by $$q^k$$ it leaves the remainder $$r$$, where $$k$$ is a positive integer. What is the value of $$r$$ ?
(1) $$15 < q^k < 40$$
(2) $$q < m$$ and $$q^k$$ leaves $$2$$ as a remainder when divided by $$7$$

Analyzing question stem we can see that either q or m is 2 because q and m are prime numbers and their sum is odd. Since E+O = O and except 2 all other prime numbers are odd.
Now 30 = q^k*(Quotient) +r. this implies that q^k<30 because if q^k>=30 then either there will be no remainder (if q^k=30) or the remainder will be 30 itself.

Statement 1: if q=2 then from this statement q^k could be 16 or 32 i.e. powers of 2 but if q is not equal to 2 then it could be 27, 25. Hence the statement is not sufficient

Statement 2: As q<m this means q has to be 2 and m could be any prime no greater than 2. Also from this statement we get to know that q^k = 7n+2 (where "n" is the quotient). so we have 2^k = 7n+2

if n = 2; q^k = 16 and if n = 18; q^k = 128. Hence this statement is not sufficient.

Combining Statement 1 & 2 we get q^k = 16.
So option C
Re: What is the value of r? [#permalink]
Moderator:
Math Expert
94927 posts