a, b, c, d are positive integers such that exactly one of the following inequalities is false. Which inequality is false?  Choose the correct choice from the following answers:	A) a<b	B) c<d	C) a+c<b+c	D) a+c<b+d	E) a<b+c+d
Essentially, we need to find the statement thatcouldbe false if all the other statements are true.   The first thing that jumps out to me is statements A and C:   (A) a &lt; b   (C) a+c &lt; b+c   Regardless of the value of c, these statement are either both false or both true. Since only statement CAN be false, we can eliminate these two.   (E) a &lt; b+c+d   Since c and d are both positive integers, and we have determined that statement A is true, statement E must be true as well. This leaves us with:   (B) c &lt; d   (D) a+c &lt; b+d   Since we know statement A (a &lt; b) to be true, if statement B is true, statement D MUST be true. However, if statement D is true, as long as c-d &lt; b-a, statement B does NOT have to be true.   Therefore, the answer isB: c &lt; d. Good question, +1.
<result>B</result>
a, b, c, d are positive integers such that exactly one of the following inequalities is false. Which inequality is false?