If x 2y and y

Question

If x > 2y and y < −5, which of the following must be true? A. x/y > 2 B. x > y C. x/2 < y D. x/y < 2 E. 2y + x < 0

IanStewart · Accepted Answer

We know y is negative here, so when we divide by y on both sides of the inequality below, we need to reverse the inequality:

x > 2y
x/y < 2

which is D.

B is not right -- notice that If y is negative, then 2y < y. When we know x > 2y, we can't be sure if x > y; we could have:

2y < x < y
2y < y < x

It's maybe easier to see just picking numbers: if, say, y = -10, then when we know x > 2y, we know x > -20. But x could be -15, which is less than y, or x could be 100, which is greater than y.

Luckisnoexcuse · Answer

Second attempt

if x> 2y then for every value of y (y<-5) 
x/y<2
D

mohshu · Answer

divide the first equation by y.. 
the equation becomes x/y <2..

ans D

ScottTargetTestPrep · Answer

We can let y = -6 and x = -6, we see B is false. Since x/y = 1, A is also false. Since x/2 = -3, C is also false. This leaves us with choices D and E, which are each true when x = y = -6. However, if y = -6 and x = 18, we see that x/y = -3 and 2y + x = 6, which only makes D true. Thus, the correct answer is D. Alternate Solution: We observe that answer choices A and D are x/y > 2 and x/y < 2. The only way both of these statements can be false is if x/y = 2 or in other words, x = 2y; but that is impossible since x > 2y. Thus, either A or D must be correct; so we can eliminate all the other answer choices and just focus on comparing x/y and 2. Note that from the second inequality y < -5, we know that y is a negative number. If we divide each side of the inequality x > 2y by the negative number y, we obtain x/y < 2. Answer: D

Arushit · Answer

Can someone explain why option E is wrong?

eega · Answer

Given x<2y ..........(i)
and y<-5 .........(ii)
This shows y is a negative number
Hence when (i) is divided by y the sign of equality changes
x/y > 2  Option D

If x > 2y and y < −5, which of the following must be true?

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