If y - 3x 12 and x - y 38, which of the following are possible val

Question

If x and y are integers,  y - 3x > 12  and  x - y > 38 , which of the following is the least value of xy?

A. 0
B. 1536
C. 1575
D. 1664
E. 1690

nick1816 · Answer

y - 3x > 12.....(1) x - y > 38......(2) From (1) and (2) x<-25 y<-63 For the least value of xy, x=-26 and y=-64 xy= 1664

LeoN88 · Answer

The entire sum is based on one crucial concept: If x > -a, multiplying -1 to both sides the inequality will change. => -x < a y-3x>12 x-y>38...Adding -2x> 50, * -1 on both sides 2x < -50 x < -25 y-3x>12 x-y>38...Multiplying 3 y-3x>12 3x-3y> 114...Adding -2y > 126 * -1 on both sides 2y < -126 y< -63. xy should be an integer (I*I=I) and their product can't be -ve or zero. Least value= (-64) * (-26) = Lowest +ve value possible = D. 1664

ScottTargetTestPrep · Answer

Adding the inequalities together, we have: -2x > 50 x < -25 Next, we can multiply the second inequality by 3, and we have: 3x - 3y > 114 Adding the above inequality to y - 3x > 12, we have: -2y > 126 y < -63 Since x and y are integers, we see that x is no larger than -26 and y is no larger than -64. Therefore, the least value of xy is (-26)(-64) = 1664. Answer: D

BrushMyQuant · Answer

Given that x and y are integers, y - 3x > 12 and x - y > 38 and we need to find which of the following is the least value of xy? Finding Value of x y - 3x > 12 x - y > 38 Adding both of them we get ( we can add both the inequalities as they have the same sign ">") y - 3x + x - y > 12 + 38 => -2x > 50 => x < \frac{-50}{2} => x < -25 => x = -26, -27,.... Finding Value of y x - y > 38 => 3*(x-y) > 3*38 => 3x - 3y > 114 y - 3x > 12 Adding both of them we get 3x - 3y + y - 3x > 114 + 12 => -2y > 126 => y < \frac{-126}{2} => y < -63 => y = -64, -65, ... Since both x and y are negative => xy will be comes positive => we need to take the greatest value of x and y (As they are negative) and multiply them to get the least value of xy => Min(xy) = -26*-64 = 1664 So, Answer will be D Hope it helps! Watch the following video to learn the Basics of Inequalities https://www.youtube.com/watch?v=1THrnWJtOqc

Paras96 · Answer

If x and y are integers, y−3x>12 and x−y>38 which of the following is the least value of xy?

y−3x>12 and x−y>38

Adding both we will get

-2x>50
x<-25
or -x>25

adding x−y>38 and -x>25

-y>63
y<-63

Now x<-25 and y<-63

Since x and y both are negative, the product xy will always be positive
Therefore, for minimum xy, x = -26 and y = -64

xy=1664

Hence D

If y - 3x > 12 and x - y > 38, which of the following are possible val

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