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.
May 1212:00 PM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
05 Apr 2022, 04:00
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:
24% (02:39) correct
76%
(02:27)
wrong
based on 322
sessions
History
Date
Time
Result
Not Attempted Yet
If \(f(x) = |3x - 20| + |11 - x | + |2x - 17|\), for how many integers n is \(f(n) = f(n + 1\)) ?
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Are You Up For the Challenge: 700 Level Questions
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Are You Up For the Challenge: 700 Level Questions
19 Jun 2022, 05:32
Kudos
Bookmarks
If f(x)=|3x−20|+|11−x|+|2x−17|f(x)=|3x−20|+|11−x|+|2x−17|, for how many integers n is f(n)=f(n+1f(n)=f(n+1) ?
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Here is a way to solve this problem..
Hope it assists..
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Here is a way to solve this problem..
Hope it assists..
Attachments
PS-3.jpg [ 1.92 MiB | Viewed 6878 times ]
29 May 2022, 01:37
Kudos
Bookmarks
f(n) = |3n - 20| + |11 - n | + |2n - 17|
f(n+1) = |3n + 3 - 20| + |11 - n -1 | + |2n + 2 - 17| = |3n - 17| + |10 - n | + |2n - 15|
Now since both are expressions in modulus, we know by property of modulus that it means absolute value implying that anything inside a modulus can be positive or negative so we can say that:
f(n) {on simplification using all modulus as themselves} = 4n - 26 or f(n) {all modulus negative} = -4n + 26
f(n+1) = 4n - 22 or f(n+1) = -4n + 22
Question asks us for how many integers is f(n) = f(n+1):
Now here we can have 4 different situations:
1. Both positive: 4n - 26 = 4n - 22; both variables get cancelled so not possible
2. Both negative: Same as above both variables will get cancelled so not possible
3. f(n) positive and f(n+1) negative: 4n - 26 = -4n + 22; we can solve for n
4. f(n) negative and f(n+1) positive: Similar expression and same value for n
So, there is just 1 integer that satisfied f(n) = f(n+1) hence answer B
f(n+1) = |3n + 3 - 20| + |11 - n -1 | + |2n + 2 - 17| = |3n - 17| + |10 - n | + |2n - 15|
Now since both are expressions in modulus, we know by property of modulus that it means absolute value implying that anything inside a modulus can be positive or negative so we can say that:
f(n) {on simplification using all modulus as themselves} = 4n - 26 or f(n) {all modulus negative} = -4n + 26
f(n+1) = 4n - 22 or f(n+1) = -4n + 22
Question asks us for how many integers is f(n) = f(n+1):
Now here we can have 4 different situations:
1. Both positive: 4n - 26 = 4n - 22; both variables get cancelled so not possible
2. Both negative: Same as above both variables will get cancelled so not possible
3. f(n) positive and f(n+1) negative: 4n - 26 = -4n + 22; we can solve for n
4. f(n) negative and f(n+1) positive: Similar expression and same value for n
So, there is just 1 integer that satisfied f(n) = f(n+1) hence answer B
