If a, b, c, and d are integers, is ab - bd - ac + cd < 0?
1. b < c
2. d < a
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ab - bd - ac + cdtonebeeze wrote:If a, b, c, and d are integers, is ab - bd - ac + cd < 0?
1. b < c
2. d < a
= b(a-d) - c(a-d)
= (a-d)(b-c)
Question rephrased: Is (a-d)(b-c) < 0?
Statement 1: b<c.
Thus, (b-c) = smaller - larger = negative.
No information about (a-d).
Insufficient.
Statement 2: d<a.
Thus, (a-d) = larger - smaller = positive.
No information about (b-c).
Insufficient.
Statements 1 and 2 combined:
(a-d)(b-c) = positive * negative = negative.
Sufficient.
The correct answer is C.
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clock60
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hi
i solved this way
is ab-bd-ac+cd<0
a(b-c)-d(b-c)<0
(b-c)(a-d)<0
possible in two cases
1) b-c>0, b>c, and a-d<0, a<d or
2) b-c<0, b<c, and a-d>0 a>d
to the statements
(1)b<c insuff as we don`t know any relations between a and d
(2) a>d also insuff, as no info about b and c
both
c>b, and a>d it coincides with 2 case
my answer is C
i solved this way
is ab-bd-ac+cd<0
a(b-c)-d(b-c)<0
(b-c)(a-d)<0
possible in two cases
1) b-c>0, b>c, and a-d<0, a<d or
2) b-c<0, b<c, and a-d>0 a>d
to the statements
(1)b<c insuff as we don`t know any relations between a and d
(2) a>d also insuff, as no info about b and c
both
c>b, and a>d it coincides with 2 case
my answer is C
