Last visit was: 05 Nov 2024, 17:57 It is currently 05 Nov 2024, 17:57

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3209 [7]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Most Helpful Community Reply
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3209 [2]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
General Discussion
Intern
Intern
Joined: 10 Apr 2021
Posts: 16
Own Kudos [?]: 11 [0]
Given Kudos: 155
Send PM
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3209 [1]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Re: x - y > 38 and y - 3x > 12 where, x and y are integers [#permalink]
1
godxyz wrote:
KarunMendiratta wrote:
KarunMendiratta wrote:
\(x - y > 38\) and \(y - 3x > 12\)
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!


godxyz
Absolutely correct
Kudos

The value of x must be \(-26\) and y must be \(-65\)
So, \(xy = 1690\)
Prep Club for GRE Bot
Re: x - y > 38 and y - 3x > 12 where, x and y are integers [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne