GMAT® Official Guide 2019 Quantitative Review
segments) or from a pair of solid segments taped
together ( there are^10 = 5 such pairs of solid
2
segments), and the solid has 8 faces because there
are 8 small triangles in the given figure. Therefore,
the sum of the number of edges and the number
of faces of the solid is 12 + 8 = 20.The correct answer is C.PS033562x+ y = 12
iY1 ~12- For how many ordered pairs (x,yl that are solutions of
the system above are x and y both integers?
(Al 7
(Bl 10
(Cl 12
(D) 13
(El 14Algebra
From I y I ~ 12, if y must be an integer, then y
must be in the set
S = {± 12, ±11, ±10, ... , ±3, ±2, ± 1, 0}.
12-y
Since 2x + y = 12, then x = ---. If x must be
2
an integer, then 12 - y must be divisible by 2; that
is, 12 - y must be even. Since 12 is even, 12 - y
is even if and only if y is even. This eliminates
all odd integers from S, leaving only the even
integers ±12, ±10, ±8, ±6, ±4, ±2, and 0. Thus,
there are 13 possible integer y -values, each with
a corresponding integer x-value and, therefore,
there are 13 ordered pairs (x,y), where x and y are
both integers, that solve the system.The correct answer is D.PS08859- The points R, T, and U lie on a circle that has radius 4.
If the length of arc RTU is^4 n what is the length of line
3
segment RV?
(Al(Bl4
3
8
3
(Cl 3
(Dl 4
(El 6Geometr~f(
In the figure above, 0 is the center of the circle
that contains R, T, and U and x is the degree
measure of LROU. Since the circumference of
the circle is 2n(4) = 8n and there are 360° in the
circle, the ratio of the length of arc RTU to the
circumference of the circle is the same as the
4n
ratio of x to 360. Therefore, _^3 _ = ___l£__.1hen
-(360)^4 n 8n^360
x = 3 =^43 on = 60. This means
8n 8n
that l:).ROU is an isosceles triangle with side
lengths OR = OU= 4 and vertex angle measuring
60°. The base angles of l:).ROU must have equal
measures and the sum of their measures must be
180° - 60° = 120°. Therefore, each base angle
measures 60°, l:).ROU is equilateral, and RU= 4.The corred answer is D.