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), (-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
_________________
I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, Indiahttps://www.instagram.com/prepster_education/