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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

50% (01:00) correct
50% (01:07) wrong based on 56 sessions

HideShow timer Statistics

[GMAT math practice question]

\(i, j\), and \(k\) are non-negative integers such that \(i+j+k=3\). If \(p, q\), and \(r\) are three fixed, but different, prime numbers, how many different values of \(p^iq^jr^k\) are possible?

\(i, j\), and \(k\) are non-negative integers such that \(i+j+k=3\). If \(p, q\), and \(r\) are three fixed, but different, prime numbers, how many different values of \(p^iq^jr^k\) are possible?

A. 8 B. 9 C. 10 D. 11 E. 12

Hi...

Since I,j,k have a sum of 3, we have to find ways it is possible.. 1) all three are 1..... One way 2) 0,1,2.....…............. 3! Ways=6 ways 3) 0,0,3….……….......... 3!/2!=3 ways

i, j, and k are non-negative integers such that i+j+k=3. If p, q, and [#permalink]

Show Tags

22 Nov 2017, 03:58

The question basically asks how many whole number solution is possible here the answer is 5c2 = 10 ways therefore the answer must be 10 DIRECT FORMULA : (n+r-1) C (r-1) here n= 3 and r=3

The number of possible values of \(p^iq^jr^k\) is equal to the number of solutions of the equation \(i + j + k = 3\). The solution set of the equation \(i + j + k = 3\) includes all permutations of \((3,0,0), (2,1,0), and (1,1,1)\). The number of permutations of \((3,0,0)\) is \(\frac{3!}{2!} = 3\). The number of permutations of \((2,1,0)\) is \(3! = 6.\) The number of permutations of \((1,1,1)\) is \(1\).

Therefore, the number of solutions of the equation \(i+j+k=3\) is \(3 + 6 + 1 = 10\).

\(i, j\), and \(k\) are non-negative integers such that \(i+j+k=3\). If \(p, q\), and \(r\) are three fixed, but different, prime numbers, how many different values of \(p^iq^jr^k\) are possible?

A. 8 B. 9 C. 10 D. 11 E. 12

Let’s first determine the number of non-negative integer triples (i, j, k) we can have: