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 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.
04 Nov 2021, 02:15
Kudos
Bookmarks
B
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:
61% (03:13) correct
39%
(02:54)
wrong
based on 199
sessions
History
Date
Time
Result
Not Attempted Yet
Out of all the points on line 3x + 2y = 6, where x & y are integers and |y| < 12. What is the probability |x| = |y|?
A. \(\frac{1}{3}\)
B. \(\frac{1}{7}\)
C. \(\frac{2}{7}\)
D. \(\frac{1}{2}\)
E. \(\frac{2}{3}\)
A. \(\frac{1}{3}\)
B. \(\frac{1}{7}\)
C. \(\frac{2}{7}\)
D. \(\frac{1}{2}\)
E. \(\frac{2}{3}\)
04 Nov 2021, 10:21
Kudos
Bookmarks
IMO ans is 1/7
reasoning :
X and Y are integers. Therefore -11<Y<11
X = (6-2Y)/3
For X to be integer, Y needs to be divisible by 3
Therefore the possibilities for Y are -9,-6,-3,-0,3,6,9
substituting each, it can be found that |X| = |Y| only when Y = -6
therefore probability is 1/7
reasoning :
X and Y are integers. Therefore -11<Y<11
X = (6-2Y)/3
For X to be integer, Y needs to be divisible by 3
Therefore the possibilities for Y are -9,-6,-3,-0,3,6,9
substituting each, it can be found that |X| = |Y| only when Y = -6
therefore probability is 1/7
04 Nov 2021, 11:40
Kudos
Bookmarks
(1st) if the absolute value of [y] < 12 for integer solutions of the Line given by
3x + 2y = 6
Since the coefficients in front of the x variable and y variable are BOTH evenly divisible into 6, the X Intercept and Y Intercept will both be Integer Coordinates
When x = 0 ———-> Y = 3
When Y = 0 ———-> X = 2
Points:
(0 , 3)
(2 , 0)
(2nd) to maintain Integer Coordinates that satisfy the equation of the line (I.e., fall on the line), we can move the exact number of spaces given by the Slope in its most simplified form
As we move 2 units to the right on the X Axis from point (0 , 3) ——-> to point (2 , 0)
The line DESCENDS by 3 units
Therefore, we have a slope of: -3 / 2
To find the other integer coordinates that fall on the line and satisfy the constraint of -12 < y < +12
From (2 , 0)
Move 3 units down, and 2 to the right: (4 , -3)
Same movement from this new point: (6 , -6)
Same movement again: (8 , -9)
The next integer point will violate the condition: (10 , -12)
And then from (0 , 3) we can do the moves in REVERSE to maintain the downward sloping line
2 units to the LEFT And 3 units UP: (-2 , 6)
same move: (-4 , 9)
The next integer point will violate the condition: (-6 , 12)
(3rd) calculate the probability
We have 7 total points that satisfy the condition
(-4 , 9)
(-2 , 6)
(0 , 3)
(2 , 0)
(4 , -3)
(6 , -6)
(8 , -9)
This is 7 Total Possible Outcomes
Out of these 7 possible outcomes, only one Integral Coordinate Point is a favorable outcome in which [X] = [Y] ———> point (6 , -6)
The probability therefore is:
1/7
Posted from my mobile device
3x + 2y = 6
Since the coefficients in front of the x variable and y variable are BOTH evenly divisible into 6, the X Intercept and Y Intercept will both be Integer Coordinates
When x = 0 ———-> Y = 3
When Y = 0 ———-> X = 2
Points:
(0 , 3)
(2 , 0)
(2nd) to maintain Integer Coordinates that satisfy the equation of the line (I.e., fall on the line), we can move the exact number of spaces given by the Slope in its most simplified form
As we move 2 units to the right on the X Axis from point (0 , 3) ——-> to point (2 , 0)
The line DESCENDS by 3 units
Therefore, we have a slope of: -3 / 2
To find the other integer coordinates that fall on the line and satisfy the constraint of -12 < y < +12
From (2 , 0)
Move 3 units down, and 2 to the right: (4 , -3)
Same movement from this new point: (6 , -6)
Same movement again: (8 , -9)
The next integer point will violate the condition: (10 , -12)
And then from (0 , 3) we can do the moves in REVERSE to maintain the downward sloping line
2 units to the LEFT And 3 units UP: (-2 , 6)
same move: (-4 , 9)
The next integer point will violate the condition: (-6 , 12)
(3rd) calculate the probability
We have 7 total points that satisfy the condition
(-4 , 9)
(-2 , 6)
(0 , 3)
(2 , 0)
(4 , -3)
(6 , -6)
(8 , -9)
This is 7 Total Possible Outcomes
Out of these 7 possible outcomes, only one Integral Coordinate Point is a favorable outcome in which [X] = [Y] ———> point (6 , -6)
The probability therefore is:
1/7
Posted from my mobile device
