[email protected] wrote:If a, b, c are integers such that b > a, is b + c > a?
(1) c > a
(2) abc > c
STATEMENT 1: c > a
Be sure to satisfy the constraint in the question stem: b>a.
If a=1, b=2 and c=2, then b+c > a.
If a=-2, b=-1, and c=-1, then b+c = a.
INSUFFICIENT.
STATEMENT 2: abc > c
abc - c > 0
c(ab-1) > 0.
For this inequality to hold true, c and (ab-1) must be the SAME SIGN.
Be sure to satisfy the constraint in the question stem: b>a.
Case 1: c>0 and ab-1>0, implying that ab>1.
Here, it's possible that c=2, a=1, and b=2.
In this case, b+c>a.
Case 2: c<0 and ab-1<0, implying that ab≤0.
Here, it's possible that c=-10, a=-1, and b=0.
In this case, b+c<a.
INSUFFICIENT.
STATEMENTS COMBINED:
To see the relationships more clearly, PLOT THE VALUES ON A NUMBER LINE.
Case 1:
From statement 2: c>0 and ab>1.
From the question stem: b>a
From statement 1: c>a
Here, there are the following options:
0.....a....b....c
0.....a....c....b
0.....a....b=c.....
In all of these options, b+c > a.
Case 2:
From statement 2: c<0 and ab≤0.
From the question stem: b>a
From statement 1: c>a
Here, there are the following options:
a....c....0.....b
a....c....b=0
In both options, b+c > a.
Thus, when the statements are combined, b+c > a.
SUFFICIENT.
The correct answer is
C.
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