If x 5 and y

Question

If x > 5 and y < −1, then which of the following statements is true? (A) (x + 4y) > 1 (B) x > −4y (C) −4x < 5y (D) -x > -y (E) None of these

chetan2u · Answer

If x > 5 and y < −1, then which of the following statements is true?

In such questions, you have to work on each choice. Although looking at x and y, we realize both can reach infinity on one of the sides-positive or negative. We can be sure of two cases only
1) If we subtract y from x, then we will get positive value.
2) If we subtract x from y, then we will get negative value.

(A) (x + 4y) > 1........Since we are looking at >1, make the x smaller and y greater.....x=6 and y = -10...x+4y=6+4*-10= -34<1

(B) x > −4y........this is again x+4y>0.., make the x smaller and y greater.....x=6 and y = -10...x+4y=6+4*-10= -34<0

(C) −4x < 5y....5y+4x>0...Again same as above...make the x smaller and y greater.....x=6 and y = -10...4x+5y=4*6+5*-10= -26<0

(D) -x > -y......y-x>0...y<0 and x>0...so y-x <0...

(E) None of these...Our answer

E

giuseppemvn · Answer

I drew a number line on paper to better visualise all the possible numbers for x and y, then found cases to prove wrong each answer choice.

A) x = 6 ; y = -2

===>  -2 > 1 ==> A is FALSE

B) x = 6 ; y = -2

===>  6 > 8 ==> B is FALSE

C) x = 6 ; y = -10

===>  -24 < -50 ==> C is FALSE

D) x = 6 ; y = -2

===>  -6 > 2 ==> D is FALSE

E) None of these

===>  Correct choice.

BraydinWalters · Answer

Should the question read as "must be true" and not "is true" or should E read as "cannot be determined"?

I set X as 6 and Y as -2.

for C: −4x < 5y

-4(6)<5(-2)
-24<-10.

Could be TRUE

Bunuel · Answer

"Is true" is the same as "must be true," and option E, "None of these," implies that none of the previous four answers is correct. This does not exclude the possibility that the correct answer is "cannot be determined."

If x > 5 and y < −1, then which of the following statements is true?

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