GMAT® Official Guide 2019 Quantitative Review
written as (2m) + (2n + 1) = 2(m + n) + 1,
with m and n integers. It follows that x2 + j2
is not divisible by 2 and is therefore odd.
III. We know that one of x or y is even and the
other is odd. We can therefore see from the
discussion of statement II that x + y is odd,
and then also see, from the discussion of
statement II, that the product of x + y with
itself, (x + y)2, is odd.
The correct answer is D.
PS 00335
On Monday, the opening price of a certain stock was
$100 per share and its closing price was $110 per
share. On Tuesday the closing price of the stock was
10 percent less than its closing price on Monday, and
on Wednesday the closing price of the stock was 4
percent greater than its closing price on Tuesday. What
was the approximate percent change in the price of the
stock from its opening price on Monday to its closing
price on Wednesday?(A) A decrease of 6%
(B) A decrease of 4%
(C) A decrease of 1 %
(D) An increase of 3%
(E) An increase of 4%A rithmetic Percents
The closing share price on Tuesday was 10% less
than the closing price on Monday, $110. 10% of
$110 is equal to 0.1 x $110 = $11, so the closing
price on Tuesday was $110 - $11 = $99. The
closing price on Wednesday was 4% greater than
this: $99 + (0.04 x $99) = $99 + $3.96 = $102.96.
This value, $102.96, is 2.96% greater than $100,
the opening price on Monday. The percentage
change from the opening share price on Monday
is therefore an increase of approximately 3%,
which is the closest of the available answers to an
increase of 2.96%.The correct answer is D.38.yP(0,6)-- 0 ---Q(4,--0) -x
PS 05109
In the rectangular coordinate system shown above,
points 0, P,, and Q represent the sites of three proposed
housing developments. If a fire station can be built at
any point in the coordinate system, at which point would
it be equidistant from all three developments?(A) (3,1)
(B) (1,3)
(C) (3,2)
(D) (2,2)
(El (2,3)Geometr)r Coordinate geometry
Any point equidistant from the points (0,0) and (4,0)
must lie on the perpendicular bisector of the segment
with endpoints (0,0) and ( 4,0), which is the line
with equation x = 2. Any point equidistant from the
points (0,0) and (0,6) must lie on the perpendicular
bisector of the segment with endpoints (0,0) and
(0,6), which is the line with equation y = 3. Therefore,
the point that is equidistant from (0,0), ( 4,0), and
(0,6) must lie on both of the lines x = 2 and y = 3,
which is the point (2,3).Alternatively, let (x,y) be the point equidistant from
(0,0), (4,0), and (0,6). Since the distance between
(x,y) and (0,0) is equal to the distance between
(x,y) and (4,0), it follows from the distance formula
that ,J x^2 + y2 = ✓( x-4 )^2 + y^2 • Squaring both
sides gives x2 + j2 = (x - 4)^2 + j2. Subtracting
j2 from both sides of the last equation and then
expanding the right side gives x2 = x2-8x + 16,
or 0 = -8x + 16, or x = 2. Also, since the distance
between (x,y) and (0,0) is equal to the distance
between (.~:,y) and (0,6), it follows from thedistance formula that ,Jx^2 + y^2 = .Jx^2 +(y-6)2.
Squaring both sides of the last equation gives
x2 + j2 = x^2 + (y- 6)^2. Subtracting x2 from both
sides and then expanding the right side gives
j2 = j2 -12y + 36, or 0 = - 12y + 36, or y = 3.The correct answer is E.