The converse of
If A, then B is
If B, then A.
The converse of an
if-then statement is not necessarily true.
Consider the following case:
If John is in San Francisco, then John is in the United States.
The
if-then statement above is true.
Converse:
If John is in the United States, then John is in San Francisco.
The converse in red is not necessarily true.
Mo2men wrote:Max@Math Revolution wrote:[GMAT math practice question]
$$If\ \ 0<2x+3y<10\ and\ -10<3x+2y<0$$ , then which of the following must be true?
I. x<0
II. y<0
III. x < y
A. I only
B . II only
C. I & II
D.I & III
E. I, II, &III
Can we sum up the 2 inequalities? it will be as follows:
-10 < 5x + 5y < 10...........
-2 < x + y < 2
In that case,
x could be 1 & y could be 0 or vice versa
so I & II are invalid.
Where did I go wrong?
Thanks
Your algebra is correct.
The inequality in blue implies the following
if-then statement:
If x and y satisfy the two inequalities, then x and y have a sum between -2 and 2.
The
if-then statement above is true.
Converse:
If x and y have a sum between -2 and 2, then x and y satisfy the two inequalities.
The converse in red is not necessarily true.
Thus, we cannot conclude that ANY x-y combination with a sum between -2 and 2 will satisfy the two original inequalities.
Neither of your cases in red satisfies -10 < 3x+2y < 0.
An analogous example:
If we add together x>0 and y>0, we get x+y > 0.
Implied
if-then statement:
If x>0 and y>0, then x+y > 0.
The
if-then statement above is true.
Converse:
If x+y > 0, then x>0 and y>0.
The converse in red is not necessarily true:
If x=-1 and y=2, then x+y > 0 but x<0.
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