A group of burglars is trying to decide whether to target the houses in a particular neighborhood in which there are 100 households. x of the households own a high-definition television, y of the households own a valuable piece of artwork, z of the households own a luxury car, and all of the households own at least one of these items. The burglars will target the houses in the neighborhood unless the probability of any given household owning all three items exceeds 50%, as this is correlated with tighter security. If z < y < x, do the burglars target the houses in the neighborhood?
x = households with HDTV
y = households with Artwork
z = households with a luxury car
Let d = number of households with all three items
If d ≤ 50% then burglars will target, if d > 50% then no.
(1) x+y=120
Nothing about z is given so.
INSUFFICIENT.
(2) z=55
Nothing about x and y.
INSUFFICIENT.
Together 1 and 2
Refer snapshot.
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X + Y + Z + a + b + c + d = 100 --> Eqn. 1
X + Y + a + b + c + d = 120 --> Eqn. 2
Z + b + d + c = 55 --> Eqn. 3
Adding Eqn. 2 and Eqn. 3
X + Y + a + b + c + d + Z + b + d + c = 120 + 55
(X + Y + Z + a + b + c + d) + b + d + c = 175 [from Eqn. 1]
100 + b + d + c = 175
b + d + c = 75
So,
d ≤ 50 OR d > 50
INSUFFICIENT.
Answer E.
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