GMAT Official Guide Quantitative Review 2019_ Book

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GMAT® Official Guide 2019 Quantitative Review


Arithmetic Sets
As shown in the table, the subsets of [ w, x, y, z}
can be organized into two columns, those
subsets of [ w, x, y, z} that do not contain w (left
column) and the corresponding subsets of [ w, x,
y, z} that contain w (right column), and each of
these collections has the same number of sets.
Therefore, there are 8 subsets of [ w, x,y, z} that
contain w.

/"subsets not containing w subsets containing w'
[ }
[x}
{y}
[z}
[x,y}
[x, z}
(y, z}

\.. [x,y, z}
The correct answer is D.
PS10309

[w}
[w,x}
[w,y}
[w, z}
[w, x,y}
[w, x, z}
[w,y, z}
[w,x,y,z}
~


  1. There are 5 cars to be displayed in 5 parking spaces,
    with all the cars facing the same direction. Of the
    5 cars, 3 are red, 1 is blue, and 1 is yellow. If the
    cars are identical except for color, how many different
    display arrangements of the 5 cars are possible?


(Al 20
(Bl
(Cl
(Dl

25
40
60
(El 125

Arithmetic El ll1 , .. -ry <. 1 > c
There are 5 parking spaces from which 3 must
be chosen to display the 3 identical red cars.

Thus, there are ( ~ ) = 3 ~~! = 10 different
arrangements of the 3 identical red cars in the
parking spaces. There are 2 spaces remaining for
displaying the single blue car and 1 space left for
displaying the single yellow car. Therefore, there
are (10)(2)(1) = 20 arrangements possible for
displaying the 5 cars in the 5 parking spaces.

The correct answer is A.

PSI 7461


  1. The number ✓63-36'13 can be expressed as x + yJ3
    for some integers x and y. What is the value of xy?


(Al -18
(Bl -6
(Cl 6
(Dl 18
(El 27

Algebra p r~tiOl'I<" on r=idir I e pressions

Squaring both sides of ../63-36J3 = x + y J3
gives 63 - 36J3 = x2 + 2xy .JS+ 3y2 =
(x2 + 3y2) + (2xy) J3, which implies that
-36 = 2xy, or xy = -18. Indeed, if-36 -:t-2xy, or
e~ivalently, if 36 + 2xy t:. 0, then we could write
✓ 3 as a quotient of the two integers 63 - x2 -3y2
and 36 + 2xy, which is not possible because J3 is
an irratio~al number. To be more explicit,
63 - 36 ✓ 3 = x2 + 2xy J3 + 3y2 implies
63 - x2 -3y2 = (36 + 2xy) ✓3, and if 36 + 2xy t:. 0,
then we could divide both sides of the equation
63 - x2-3y2 = (36 + 2xy) ✓ 3 by 36 + 2xy to get
63 - x

2


  • 3 y2 = J3.
    36+ 2xy
    The correct answer is A.
    PS0 1334



  1. There are 10 books on a shelf, of which 4 are
    paperbacks and 6 are hardbacks. How many possible
    selections of 5 books from the shelf contain at least
    one paperback and at least one hardback?


(Al 75
(Bl 120
(Cl 210
(Dl 246
(El 252

Arithmetic r na i(c
The number of selections of 5 books containing
at least one paperback and at least one hardback
is equal to T-N, where Tis the total number
of selections of 5 books and N is the number of
selections that do not contain both a paperback
and a hardback. The value of Tis

(

10) 10! (6)(7)(8)(9)(10)
5 - 5 !(10 - 5)! - (1)(2)( 3)( 4 )(5)
= (7)(2)(9)(2) = 252.
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