GMAT® Official Guide 2019 Quantitative Review
Note: Figure not drawn to scale.
DS18386
21 7. The figure above shows Line L, Circle 1 with center at
C 1 , and Circle 2 with center at C 2. Line L intersects
Circle 1 at points A and B, Line L intersects Circle 2 at
points D and E, and points C 1 and C 2 are equidistant
from line L. Is the area of .6ABC 1 less than the area of
.6DEC2?
(1) The radius of Circle 1 is less than the radius of
Circle 2.
(2) The length of chord AB is less than the length of
chord DE.Geometry
We are given various elements of information
that apply regardless of whether we assume
that statements 1, 2, or both are true, and asked
whether it is possible, when considering one or
both of these statements, to determine if the
area of triangle MBC 1 is less than the area of
!J..DEC 2.(1) Given the condition that the radius of
Circle 1 is less than the radius of Circle 2,
it may be useful to consider the following
diagrams of the triangles, in which they
have been rotated so as to have the sides AB
and DE represented as horizontal and on
the bottom. The diagrams are not drawn to
scale.Note that the radius of the Circle 1 is equal
to (the length) C 1 B (= C 1 A) and that the
radius of Circle 2 is equal to C 2 D (= C 2 E).
Furthermore, because line L is equidistant
from points C 1 and C 2 , we know that the
respective heights of the triangles (distances
from C 1 and C 2 to the respective bases BA and
DE) are the same. However, because (with
statement 1) the radius of Circle 1 is less than
the radius of Circle 2, we know that C 1 B and
C 1 A' are less than C2D and C2E, Because the
triangles have the same height, triangle MBC 1
must be less "wide" than !J..DEC 2 and must
thus have a lesser base (length). And because
the area of a triangle is always 1 X base X
2
height, we can irlfer that the area of MBC 1 is
less than the area of !J..DEC 2 ; SUFFICIENT.(2) Given that AB is less than DE, we can
infer that the area of MBC 1 is less than
the area of !J..DEC 2. After all, we know that
the heights of the two triangles are the
same (because, as discussed in connection
with statement 1, line Lis equidistant from
C 1 and C 2 ). The formula for the area of atriangle, 1 X base X height, thus allows us to
2
make our inference; SUFFICIENT.
The correct answer is D;
each statement alone is sufficient.
DSI5938- Yesterday between 9:00 a.m. and 6:00 p.m. at
Airport X, all flights to Atlanta departed at equally
spaced times and all flights to New York City departed
at equally spaced times. A flight to Atlanta and a
flight to New York City both departed from Airport X
at 1 :00 p.m. yesterday. Between 1 :00 p.m. and
3:00 p.m. yesterday, did another pair of flights to
these 2 cities depart from Airport X at the same time?
(1) Yesterday at Airport X, a flight to Atlanta and a
flight to New York City both departed at 10:00 a.m.
(2) Yesterday at Airport X, flights to New York City
departed every 15 minutes between 9:00 a.m.
and 6:00 p.m.