|
|
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.
25 Aug 2021, 08:00
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:
37% (02:27) correct
63%
(02:42)
wrong
based on 248
sessions
History
Date
Time
Result
Not Attempted Yet
In the xy-coordinate plane, does region bounded by x > 0, y < 0, and -y + 2x < 4 contain point (a, b), where a and b are integers ?
(1) ab = -4
(2) a + 4b = 0
(1) ab = -4
(2) a + 4b = 0
|
Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
24 Sep 2021, 03:03
Kudos
Bookmarks
Bunuel
Official Solution:
In the xy-coordinate plane, does region bounded by \(x > 0\), \(y < 0\), and \(-y + 2x < 4\) contain point \((a, \ b)\), where a and b are integers ?
Let's check which set(s) of integers \((a, \ b)\), where \(a > 0\) and \(b < 0\), satisfy \(-b + 2a < 4\). Notice that since \(b\) must be negative, then \(-b\) will be positive, so \(-b + 2a =(positive \ integer) + (even \ positive \ integer)\), which is at least 3. \(-b + 2a\) is 3, when \(b=-1\) and \(a=1\). For all other values, \(-b + 2a\) will be \( \geq 4\), not \(< 4\). So, the question basically asks whether \(a=1\) and \(b=-1\). (In other words, point \((1, \ -1)\) is the ONLY point which satisfies \(a > 0\), \(b < 0\), and \(-b + 2a < 4\).)
(1) \(ab = -4\). Since \(a=1\) and \(b=-1\) is not a solution of this equation, then point \((a, \ b)\) is not in the region. Sufficient.
(2) \(a + 4b = 0\). Since \(a=1\) and \(b=-1\) is not a solution of this equation, then point \((a, \ b)\) is not in the region. Sufficient.
For better understanding check the image below:
The question asks whether point \((a, \ b)\) is in the yellow region. As you can see the only point in this region which has integer coordinates is point (-1, 1), so the question aks whether \(a=1\) and \(b=-1\)
Answer: D
General Discussion
25 Aug 2021, 08:39
Kudos
Bookmarks
On solving the equation -y + 2x - 4 = 0 we get the coordinates of this line as (0,-4) and (2,0)
Therefore, for the inequality to be valid, the integer points should be less than these two points and should also satisfy x > 0 and y > 0.
Statement 1: ab = -4
1) a = 1, b= -4 => Not in the region
2) a = -1, b= 4 => Not in the region
3) a = 4, b= -1 => Not in the region
4) a = -4, b= 1 => Not in the region
5) a = 2, b= -2 => Not in the region
6) a = -2, b= 2 => Not in the region
Hence we get a definite answer and Statement 1 is sufficient.
Statement 2: a = -4b
1) a = 0, b= 0 => Not in the region
2) a = -4, b= 1 => Not in the region
3) a = 4, b= -1 => Not in the region
4) a = 8, b= -2 => Not in the region
5) a = -8, b= 2 => Not in the region
The rest of the values of a and b will lie outside the bounded region.
Hence we get a definite answer and Statement 2 is sufficient.
Hence the answer is D.
Therefore, for the inequality to be valid, the integer points should be less than these two points and should also satisfy x > 0 and y > 0.
Statement 1: ab = -4
1) a = 1, b= -4 => Not in the region
2) a = -1, b= 4 => Not in the region
3) a = 4, b= -1 => Not in the region
4) a = -4, b= 1 => Not in the region
5) a = 2, b= -2 => Not in the region
6) a = -2, b= 2 => Not in the region
Hence we get a definite answer and Statement 1 is sufficient.
Statement 2: a = -4b
1) a = 0, b= 0 => Not in the region
2) a = -4, b= 1 => Not in the region
3) a = 4, b= -1 => Not in the region
4) a = 8, b= -2 => Not in the region
5) a = -8, b= 2 => Not in the region
The rest of the values of a and b will lie outside the bounded region.
Hence we get a definite answer and Statement 2 is sufficient.
Hence the answer is D.
