GMAT Official Guide Quantitative Review 2019_ Book

4.5 .j-， s Answer Explanations

Algebra

Given the expression x^2 - 10x + 16, a table

of values can be created for the corresponding

function八x) = x^2 — 10x + 16 and the graph

in the standard (x,y) coordinate plane can be

sketched by plotting selected points:

X J(x)

— 4 72

• 3 55


• 2 40


• 1 27
  。 16
  1 7
  2 。
  3 - 5
  4 - 8
  5 -^9
  6 - 8
  7 - 5
  8 。
  9 7
  y

30.

31.

x=—一b ，and so the vertex of the graph of

2a

归＝灶- lOx + 16 is at

x=—（奇）= (^5).
Because a = l and 1 is positive, this parabola
opens upward and values of x^2 - lOx + 16
ecrease as x increases from -4 to 4. Therefore,
the greatest value of x^2 - lOx + 16 for all values
of x between—4 and 4, inclusive, is at x =—4.
Th e correct answer 1s A.
PS15994 5 1
If x = -- and y =--,what is the value of the
8 2
expression -2x - y^2?
(A)
(8)
(Cl
(D)
(El
3-2l
l
3-27_4
Algebra ct1or
If x = --5 1 and y = --, then
8 2

• 2x子=-2门
  ）－门）

(^2) 5 1 4
=---= —=l.
4 4 4
Th e correct answer ts C.
PS13686
If x - y = R and xy = S, then (x - 2)(y + 2) =
尤＇

• 4

(5,-9)

It is clear from both the table of values and

the sketch of the graph that as the value of x

increases from -4 to 4, the values of

灶- 10x + 16 decrease. Therefore, the value of

x^2 -10x + 16 is greatest when x = -4.

Alternatively, the given expression, x^2 - 10x + 16,
has the form ax^2 +bx+ c, where a = 1, b = -10,
and c = 16. The graph in the standard (x,y)
coordinate plane of the corresponding function
卢） =a灶+ bx+ c is a parabola with vertex at

(A)

(Bl

(C)

(D)

(El

R+ S-4

R+ 2S-4

2R-S-^4

2R+ S-4

2R+ S

Algebra nplifym

; .......

(x -2)(y + 2) = xy + 2x -2y -4 multiply binomials

= xy + 2(x - y) - 4 distributive principle

= S + 2R -4

=2R+ S-4

alqrbrdic f,J(prl <;'>1on ,

substitution

commutative principle

The correct answer is D.