Is xy <= 6 ? (1) 1 <= x <= 2 and 4 <= y <= 6 (2) x + y = 7

Is \(xy \leq 6\)? If x and y are opposite signs, then xy is ≤ 6; If they are the same sign, then we must solve for x and y.

(1) \(1 \leq x \leq 2\) and \(4 \leq y \leq 6\). If we multiply both inequalities we have: \(4 \leq xy \leq 12\), then xy could be ≥ 6 or xy ≤ 6, insufficient.

(2) \(x + y = 7\). If x = 3 and y = 4, xy = 12, condition is false. If x = 1 and y = 6, xy = 6, condition is true. Both cases, x and y could be opposite signs or not.. insufficient.

(3) Combining both: (1) x and y are the same signs (positive) bound by the inequality, and (2) their sum has to be equal to 7.

So if x = 1 y = 6, x + y = 7 and xy = 6 ≤ 6. But if x = 2 y = 5, x + y = 7 then xy = 10 ≥ 6. We have more than one possibility, insufficient.

(E) is the answer.

Hi exc4libur

highlighted portion is not correct. if x=3 & y =-4 then x+y=-1 which is not possible here.

Hi niks, thanks!! I got distracted, but its correct now. regds.

Hi,

Based on what you have provided, the answer should be E.

x =1 & y = 6.........xy ≤ 6.............Answer is Yes

x =2 & y = 5.........xy ≤ 10.............Answer is NO

Also small comment. The highlighted is not correct. You assumed that x and y are integers but x could be 1.9 & y could be 5.1. Nothing in the questions says that those are integers.

The question is, Is xy<= 6? Hence, (1)(6) = 6 is a YES and (2)(5) = 10 is a NO. Answer should be E.

Done, thank you Mo