GRE Prep 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.
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
x - y > 38 and y - 3x > 12 where, x and y are integers
[#permalink]
25 Aug 2021, 04:11
25 Aug 2021, 04:11
2
5
Bookmarks
00:00
Question Stats:
21% (03:13) correct
78% (01:57) wrong based on 23 sessions
Hide Show timer Statistics
\(x - y > 38\) and \(y - 3x > 12\)
where, \(x\) and \(y\) are integers
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
where, \(x\) and \(y\) are integers
Quantity A |
Quantity B |
Least possible value of \(xy\) |
1664 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: x - y > 38 and y - 3x > 12 where, x and y are integers
[#permalink]
26 Aug 2021, 20:51
26 Aug 2021, 20:51
1
1
Bookmarks
KarunMendiratta wrote:
\(x - y > 38\) and \(y - 3x > 12\)
where, \(x\) and \(y\) are integers
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
where, \(x\) and \(y\) are integers
Quantity A |
Quantity B |
Least possible value of \(xy\) |
1664 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
\(x - y > 38\)
\(y - 3x > 12\)
Since the sign of ineqialities are same, we can add both;
\(-2x > 50\)
\(\frac{-2x}{(-2)} < \frac{50}{(-2)}\)
\(x < -25\)
i.e. \(x\) could be -26, -27, -28, ......
\(3(x - y > 38)\)
\(y - 3x > 12\)
\(3x - 3y > 114)\)
\(y - 3x > 12\)
Since the sign of ineqialities are same, we can again add both;
\(-2y > 126\)
\(\frac{-2y}{(-2)} < \frac{126}{(-2)}\)
\(y < -63\)
i.e. \(y\) could be -64, -65, -66, ......
So, \(xy\) could be (-26)(-64), (-26)(-65), (-27)(-64), ....
But, (-26) and (-64) does not satisfy the above 2 inequalities.
So, we need to take -26 and -65
Col. A: (-26)(-65) = 1690
Col. B: 1664
Hence, option A
NOTE: Whenever we divide or multiply the inequality with a -ve number, the sign flips
General Discussion
Re: x - y > 38 and y - 3x > 12 where, x and y are integers
[#permalink]
27 Aug 2021, 05:53
27 Aug 2021, 05:53
KarunMendiratta wrote:
KarunMendiratta wrote:
\(x - y > 38\) and \(y - 3x > 12\)
where, \(x\) and \(y\) are integers
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
where, \(x\) and \(y\) are integers
Quantity A |
Quantity B |
Least possible value of \(xy\) |
1664 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
\(x - y > 38\)
\(y - 3x > 12\)
Since the sign of ineqialities are same, we can add both;
\(-2x > 50\)
\(\frac{-2x}{(-2)} < \frac{50}{(-2)}\)
\(x < -25\)
i.e. \(x\) could be -26, -27, -28, ......
\(3(x - y > 38)\)
\(y - 3x > 12\)
\(3x - 3y > 114)\)
\(y - 3x > 12\)
Since the sign of ineqialities are same, we can again add both;
\(-2y > 126\)
\(\frac{-2y}{(-2)} < \frac{126}{(-2)}\)
\(y < -63\)
i.e. \(y\) could be -64, -65, -66, ......
So, \(xy\) could be (-26)(-64), (-27)(-65), (-28)(-66), ....
Col. A: (-26)(-64) = 1664
Col. B: 1664
Hence, option C
NOTE: Whenever we divide or multiply the inequality with a -ve number, the sign flips
KarunMendiratta,
Hi sir,
Thank you for the answer.
I have a small doubt in your solution. If x = -26 and y = -64 are the minimum values, are they not supposed to satisfy the first inequality, i.e., x - y > 38? Using these values we get 38 > 38.
Thanks in advance!
