GMAT Official Guide Quantitative Review 2019_ Book

4.5 l'1 { I , Answer Explanations

To find the value of N, first note that no selection

of 5 books can contain all paperbacks, since there

are only 4 paperback books. Thus, the value of N

is equal to the number of selections of 5 books

that contain all hardbacks, which is equal to 6

since there are 6 ways that a single hardback can

be left out when choosing the 5 hardback books.

It follows that the number of selections of 5

books containing at least one paperback and at

least one hardback is T- N = 252 -6 = 246.

Th e correct answer 1s D.

PS03774

158. 
     

     If xis to be chosen at random from the set (1, 2, 3, (^4) )
     and y is to be chosen at random from the set (5, 6,^7 ),
     what is the probab山tythat xy will be even?
     (Al
     (Bl
     (Cl
     (Dl
     (E)
     l-61-31_22-35-6
     Arithmetic; Algebra beth 11t'✓ C ,,r. p+
     By the principle of multiplication, since there are
     4 elements in the first set and 3 elements in the
     second set, there are (4)(3) = 12 possible products
     of xy, where x is chosen from the first set and y is
     chosen from the second set. These products will
     be even EXCEPT when both x and y are odd.
     Since there are 2 odd numbers in the first set and
     2 odd numbers in the second set, there are (2)(2) =
     4 products of x and y that are odd. This means
     that the remaining 12 -4 = 8 products are even.
     Thus, the probability that xy is even is -^8 =—^2.
     12 3
     Th e correct answer 1s D.
     PS04254

     
     


159. 
     

     The function f is defined for each positive three-dig代
     integer n by ffn) = 2 x 3Y 51 , where x, y, and z are the
     hundreds, tens, and units digits of n, respectively. If m
     and v are three-digit positive integers such that
     ffm) = 9 的，thenm-V=

     
     

(A)

(Bl

(Cl

(D)

(E)

89800

12

8

Algebra

Let the hundreds, tens, and units digits of

m be A, B, and C, respectively; and let the

hundreds, tens, and units digits of v be a, b,

and c, respectively. From八m)=�凡）it follows

that 2A 3 B5c = 9(2竺灶sc)= 3^2 (2a 3 妇于）= 2a 3 b+^25 c_

Therefore,A = a, B = b + 2, and C = c. Now

calculate m - v.

m-v=

＝

＝

＝

'··-

(100A + 10B + C)

-(100a + 10b + c)

(100a + lO(b + 2) + c)

• (100a + 10b + c)
  lO(b + 2) -10b

10b + 20-lOb

20

place value

property

obtained above

combine like

terms

distributive

property

combine like

terms

Th e correct answer 1s D.

PS06312

160. If 1050 - 74 1s written as an integer in base 10
     notation, what is the sum of the digits in that integer?

(A)

(B)

(C)

(D)

(E)

424

433

440

449

467