|
|
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.
22 May 2020, 03:27
Kudos
Bookmarks
D
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:
36% (02:55) correct
64%
(02:55)
wrong
based on 242
sessions
History
Date
Time
Result
Not Attempted Yet
If \(|x| < 100\) and \(|y| < 100\), then what is the number of ordered pairs of integers (x, y) satisfying the equation \(4x + 7y = 3\) ?
A. 26
B. 27
C. 28
D. 29
E. 30
Are You Up For the Challenge: 700 Level Questions
A. 26
B. 27
C. 28
D. 29
E. 30
Are You Up For the Challenge: 700 Level Questions
22 May 2020, 04:01
Kudos
Bookmarks
Bunuel
\(|x| < 100\)
i.e. -100 < x < 100
\(|y| < 100\)
i.e. -100 < y < 100
\(4x + 7y = 3\)
Let's find first solution using simple trial and error
y = 3 and x = 6
RULE:
In such linear equation in two variables, the value of x changes by coefficient of y (7 in this case) and value of y changes by coefficient of x (4 in this case)
In such linear equation in two variables, the value of x changes by coefficient of y (7 in this case) and value of y changes by coefficient of x (4 in this case)
Now, x changes by 7 and y changes by 4
Since x has larger variation (7) in comparison to variation of y (4) so number of solutions will as many as possible values of x in given range
because there will be less possible values of x in the given range -100 to 100 than the values of y
among 200 numbers (-100 to +100) the values of x
RULE:
nth term of an Arithmetic progression, T_n = a+(n-1)*d where a is teh first term and d is the common differece i.e. 2nd term.- 1st term or 3rd term - 2nd term
nth term of an Arithmetic progression, T_n = a+(n-1)*d where a is teh first term and d is the common differece i.e. 2nd term.- 1st term or 3rd term - 2nd term
Positive values of x = {6, 13, 20....}
nth term, 6+(n-1)*7 < 100
i.e. n-1 < 13.4
i.e. n = 14
Values of x less than 6 = {-1, -8, -15}
nth term, -1+(n-1)*(-7) > -100
i.e. (n-1) < 99/7
i.e. (n) < 15.5
i.e. n = 15
So total possible values of x = 14+15 = 29
Answer: Option D
Bunuel: The question must mention that x and y are integers. You might want to mention it.
22 May 2020, 22:41
Kudos
Bookmarks
See the attachment
Attachments
1.PNG [ 23.79 KiB | Viewed 10264 times ]
