Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2601:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
19 May 2023, 06:30
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
47% (02:05) correct
53%
(02:04)
wrong
based on 34
sessions
History
Date
Time
Result
Not Attempted Yet
For positive integers m and n, is \(7+7^2+7^3+….+7^{mn}\) divisible by 14?
(1) \(n=even\)
(2) \(m = \frac{a}{b}\), where one of a and b is an odd and the other is an even
(1) \(n=even\)
(2) \(m = \frac{a}{b}\), where one of a and b is an odd and the other is an even
19 May 2023, 09:20
Kudos
Bookmarks
Bunuel
\(7+7^2+7^3+….+7^{mn}\)
\(7(1+7^1+7^2+….+7^{mn-1})\)
\(7(1+7^1+7^2+….+7^{mn-1})\) is a multiple of 7, hence \(7+7^2+7^3+….+7^{mn}\) is divisible by 14 if \((1+7^1+7^2+….+7^{mn-1})\) is even.
Hence, the question can be reframed as
Is \(1+7^1+7^2+….+7^{mn-1}\) even ?
Let's write a few terms to understand the pattern
\(1+7^1+7^2+7^3\)
= odd + odd + odd + odd = even
\(1+7^1+7^2+7^3+7^4+7^5\)
even+odd+odd = even
\(1+7^1+7^2+7^3+7^4+7^5+7^6+7^7\)
even+odd+odd = even
Inference:
- Whenever the value of the exponent of 7 is odd, the value of the sum is even.
- Whenever the value of the exponent of 7 is even, the value of the sum is odd.
Statement 1
(1) \(n=even\)
As n is even, mn-1 is odd.
Hence the sum \(1+7^1+7^2+….+7^{mn-1}\) will result in an even value.
Therefore, we can conclude that \(7+7^2+7^3+….+7^{mn}\) is divisible by 14.
The statement alone is sufficient. Eliminate B, C, and E.
Statement 2
(2) \(m = \frac{a}{b}\), where one of a and b is an odd and the other is an even
Very cleverly crafted statement
We are given that \(m = \frac{a}{b}\) and one of a and b is an odd and the other is an even
Therefore \(m = \frac{\text{odd}}{\text{even}}\) or \(m = \frac{\text{even}}{\text{odd}}\).
The question premise states that m is an integer. Hence, m cannot be of the form
\(m = \frac{\text{odd}}{\text{even}}\)
We can conclude that \(m = \frac{\text{even}}{\text{odd}}\). The result of this will always be even.
Hence, m = even.
If m = even, mn-1 is odd. Now the solution is similar to that of Statement 1.
From our previous work, we know that when mn-1 = odd, the sum \(1+7^1+7^2+….+7^{mn-1}\) will result in an even value and the sum \(7+7^2+7^3+….+7^{mn}\) is divisible by 14.
Statement 2 is also sufficient to answer the target question.
Option D
Moderators:
