GMAT® Official Guide 2019 Quantitative Review
BCD$03989- In the figure shown, quadrilateral ABCD is inscribed in a
circle of radius 5. What is the perimeter of quadrilateral
ABCD?
(1) The length of AB is 6 and the length of CD is 8.
(2) AC is a diameter of the circle.GeometryDetermine the perimeter of quadrilateral ABCD,
which is given by AB+ BC+ CD+ DA.(1) This indicates that AB= 6 and CD= 8, but
gives no information about BC or DA.For example, the perimeter of ABC 1 D 1 is
clearly different than the perimeter of ABC 2 D 2
and CD could be positioned where C 1 D 1 is on
the diagram or it could be positioned where
C 2 D 2 is on the diagram; NOT sufficient.
(2) This indicates that AC= 2(5) = 10 since AC
is a diameter of the circle and the radius of
the circle is 5. It also indicates that LABC
and LADC are right angles since each is
inscribed in a semicircle. However, there
is no information about AB, BC, CD, or
DA. For example, if AB= CD= 6, then
BC= DA= ,J10^2 -6^2 = 164 = 8 and
the perimeter of ABCD is 2(6 + 8) = 28.
However, if AB = DA= 2, then BC= CD =
,J10^2 - 22 = J% and the perimeter of
ABCD = 2(2 + J%); NOT sufficient.Taking (l) and (2) together, MBC is a
right triangle with AC= 10 and AB= 6. It
follows from the Pythagorean theorem that
BC= ,J10^2 - 62 = 164 = 8. Likewise, MDC
is a right triangle with AC= 10 and CD= 8.
It follows from the Pythagorean theorem that
DA= ,J10^2 - 82 = ✓' 36 = 6. Thus, the perimeter
of quadrilateral ABCD can be determined.The corrc!ct answer is C;
both statements together are sufficient.
DS05766- How many members of a certain legislature voted
against the measure to raise their salaries?
(1) ¾ of the members of the legislature did not vote
on the measure.
(2) If 5 additional members of the legislature had
voted against the measure, then the fraction of
members of the legislature voting against the
measure would have been .!.
3
Arithmetic
The task in this question is to determine whether,
on the basis of statements 1 and 2, it is possible
to calculate the number of members of the
legislature who voted against a certain measure.(1) This statement, that¼ of the members of
the legislature did not vote on the measure,
is compatible with any number of members
of the legislature voting against the measure.
3
After all, any number among the
4of
the remaining members could have voted
against the measure. Furthermore, based on
statement 1, we do not know the number
of members of the legislature (although we
do know, based on this statement, that the
number of members of the legislature is
divisible by 4); NOT sufficient.
(2) This statement describes a scenario, of
5 additional members of the legislature
voting against the measure, and stipulatesthat ½ of the members of the legislature
would have voted against the measure
in the scenario. Given this condition, we
know that the number of members of the
legislature was divisible by 3, and that the