If X>1 and Y>1, is X<Y?

Question

If X>1 and Y>1, is X<Y?

(1) X^2/(XY+X)<1

(2) XY/Y^2-Y<1

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

d) EACH statement ALONE is sufficient

e) Statements (1) and (2) TOGETHER are NOT sufficient

Answer 1

no.

x can be 10, y can be 5.  Both are greater than 1, but 10 is not less than 5.

Answer 2

Statement (1):

X^2 / (XY+X) &lt; 1 :multiply both sides by XY+X, which is &gt; 0

X^2 &lt; (XY+X) :divide both sides by X, which is &gt; 0

X &lt; Y + 1 ==&gt; not sufficient. If X=Y=3, then 3 &lt; 3+1

Statement (2):

XY / Y^2 - Y &lt; 1 :multiply both sides by Y^2-Y, which is &gt; 0

XY &lt; Y^2 - Y :divide both sides by Y, which is &gt; 0

X &lt; Y - 1 : but Y - 1 &lt; Y, so

X &lt; Y-1 &lt; Y

X &lt; Y

ANSWER: b) Statement (2) ALONE is sufficient,...

P.S. When dealing with inequalities, it&#039;s very important to know if you are multiplying and dividing by positive or negative values, because if you multiply/divide by a negative, you must change the direction of the inequality, e.g.

3 &lt; 5

3*(-2) &gt; 5*(-2) ---- multiply by -2, change from &lt; to &gt;

-6 &gt; -10

Answer 3

e) Statements (1) and (2) TOGETHER are NOT sufficient