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 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2212:30 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 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 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.
11 Jun 2022, 03:45
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
33% (02:55) correct
67%
(02:58)
wrong
based on 67
sessions
History
Date
Time
Result
Not Attempted Yet
A function f is defined recursively by \(f(1) = f(2) = 1\) and \(f(n) = f(n-1) - f(n-2) + n\) for all integers \(n \geq 3\). What is f(2018) ?
A. 2016
B. 2017
C. 2018
D. 2019
E. 2020
A. 2016
B. 2017
C. 2018
D. 2019
E. 2020
16 Jun 2022, 07:36
Kudos
Bookmarks
Solving for each value of \(f(n)\) until a pattern is seen:
\(f(1) = 1\)
\(f(2) = 1\)
\(f(3) = 3\)
\(f(4) = 6\)
\(f(5) = 8\)
\(f(6) = 8\)
\(f(7) = 7\)
\(f(8) = 7\)
\(f(9) = 9\)
\(f(10) = 12\)
\(f(11) = 14\)
\(f(12) = 14\)
\(f(13) = 13\)
\(f(14) = 13\)
\(f(15) = 15\)
If one excludes the first 3 functions, one notices that there is a pattern of 6 which occurs: single value, then two identical numbers, two different identical numbers and then a single value. Each of which correlate to their respective functions, however one doesn't need to focus on them as of yet.
\(\frac{(2018 - 3)}{6} = 335\) with a remainder of \(5\). In other words we complete 335 cycles of the pattern, and now need to focus on what happens to the fifth function of the cycle to solve for \(f(2018)\)
.
As we are excluding the first 3 functions, the first 5th function we see is \(f(8) = 7\), and then \(f(14) = 13\). In both cases the value of the function is one less than the function itself. This means that \(f(2018) = 2017\)
Answer B
\(f(1) = 1\)
\(f(2) = 1\)
\(f(3) = 3\)
\(f(4) = 6\)
\(f(5) = 8\)
\(f(6) = 8\)
\(f(7) = 7\)
\(f(8) = 7\)
\(f(9) = 9\)
\(f(10) = 12\)
\(f(11) = 14\)
\(f(12) = 14\)
\(f(13) = 13\)
\(f(14) = 13\)
\(f(15) = 15\)
If one excludes the first 3 functions, one notices that there is a pattern of 6 which occurs: single value, then two identical numbers, two different identical numbers and then a single value. Each of which correlate to their respective functions, however one doesn't need to focus on them as of yet.
\(\frac{(2018 - 3)}{6} = 335\) with a remainder of \(5\). In other words we complete 335 cycles of the pattern, and now need to focus on what happens to the fifth function of the cycle to solve for \(f(2018)\)
.
As we are excluding the first 3 functions, the first 5th function we see is \(f(8) = 7\), and then \(f(14) = 13\). In both cases the value of the function is one less than the function itself. This means that \(f(2018) = 2017\)
Answer B
02 Sep 2022, 23:09
Kudos
Bookmarks
Given that \(f(1) = f(2) = 1\) and \(f(n) = f(n-1) - f(n-2) + n\) for all integers \(n \geq 3\) and we need to find the value of f(2018)
In these type of problems its always advised to find a pattern and then try to conclude the answer based on the pattern you identify.
Let's start by finding f(3)
To find f(3) we need to compare what is inside the bracket in f(3) and f(n)
=> We need to substitute n with 3 in f(n) = f(n-1) - f(n-2) + n to get the value of f(3)
=> f(3) = f(3-1) - f(3-2) + 3 = f(2) - f(1) + 3 = 1-1 + 3 = 3
Similarly, f(4) = f(4-1) - f(4-2) + 4 = f(3) - f(2) + 4 = 3-1 + 4 = 2 + 4 = 6
f(5) = f(4) - f(3) + 5 = 6 - 3 + 5 = 3 + 5 = 8
f(6) = f(5) - f(4) + 6 = 8 - 6 + 6 = 2 + 6 = 8
f(7) = f(6) - f(5) + 7 = 8 - 8 + 7 = 7
f(8) = f(7) - f(6) + 8 = 7 - 8 + 8 = 7
f(9) = f(8) - f(7) + 9 = 7 - 7 + 9 = 9
f(10) = f(9) - f(8) + 10 = 9 - 7 + 10 = 12
f(11) = f(10) - f(9) + 11 = 12 - 9 + 11 = 14
f(12) = f(11) - f(10) + 12 = 14 - 12 + 12 = 14
f(13) = f(12) - f(11) + 13 = 14 - 14 + 13 = 13
f(14) = f(13) - f(12) + 14 = 13 - 14 + 14 = 13
f(15) = f(14) - f(13) + 15 = 13 - 13 + 15 = 15
f(16) = f(15) - f(14) + 16 = 15 - 13 + 16 = 18
f(1) = 1
f(2) = 1
f(3) = 3
f(4) = 6
f(5) = 8
f(6) = 8
f(7) = 7
f(8) = 7 = 8-1
f(9) = 9
f(10) = 12
f(11) = 14
f(12) = 14
f(13) = 13
f(14) = 13 = 14-1
f(15) = 15
f(16) = 18
Leaving the first two value of f(1) and f(2) we notice that Every Odd Multiple of 3 has the same value as the number inside the function and we can calculate the values before after using the pattern given above
Ex: f(3) = 3, f(9)=9 and f(15) = 15
Now, 2018 = 2019-1 and 2019= 3*673 => odd multiple of 3
=> f(2019) = 2019
=> f(2018) = 2018-1 = 2017 ( as f(8) = 8-1 and f(14) = 14-1
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
In these type of problems its always advised to find a pattern and then try to conclude the answer based on the pattern you identify.
Let's start by finding f(3)
To find f(3) we need to compare what is inside the bracket in f(3) and f(n)
=> We need to substitute n with 3 in f(n) = f(n-1) - f(n-2) + n to get the value of f(3)
=> f(3) = f(3-1) - f(3-2) + 3 = f(2) - f(1) + 3 = 1-1 + 3 = 3
Similarly, f(4) = f(4-1) - f(4-2) + 4 = f(3) - f(2) + 4 = 3-1 + 4 = 2 + 4 = 6
f(5) = f(4) - f(3) + 5 = 6 - 3 + 5 = 3 + 5 = 8
f(6) = f(5) - f(4) + 6 = 8 - 6 + 6 = 2 + 6 = 8
f(7) = f(6) - f(5) + 7 = 8 - 8 + 7 = 7
f(8) = f(7) - f(6) + 8 = 7 - 8 + 8 = 7
f(9) = f(8) - f(7) + 9 = 7 - 7 + 9 = 9
f(10) = f(9) - f(8) + 10 = 9 - 7 + 10 = 12
f(11) = f(10) - f(9) + 11 = 12 - 9 + 11 = 14
f(12) = f(11) - f(10) + 12 = 14 - 12 + 12 = 14
f(13) = f(12) - f(11) + 13 = 14 - 14 + 13 = 13
f(14) = f(13) - f(12) + 14 = 13 - 14 + 14 = 13
f(15) = f(14) - f(13) + 15 = 13 - 13 + 15 = 15
f(16) = f(15) - f(14) + 16 = 15 - 13 + 16 = 18
f(1) = 1
f(2) = 1
f(3) = 3
f(4) = 6
f(5) = 8
f(6) = 8
f(7) = 7
f(8) = 7 = 8-1
f(9) = 9
f(10) = 12
f(11) = 14
f(12) = 14
f(13) = 13
f(14) = 13 = 14-1
f(15) = 15
f(16) = 18
Leaving the first two value of f(1) and f(2) we notice that Every Odd Multiple of 3 has the same value as the number inside the function and we can calculate the values before after using the pattern given above
Ex: f(3) = 3, f(9)=9 and f(15) = 15
Now, 2018 = 2019-1 and 2019= 3*673 => odd multiple of 3
=> f(2019) = 2019
=> f(2018) = 2018-1 = 2017 ( as f(8) = 8-1 and f(14) = 14-1
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
