GMAT Official Guide Quantitative Review 2019_ Book

GMAT® Official Guide 2019 Quantitative Review

Arithmetic C ., .. ions on inteqers

Row

1st row

2nd row

3rd row

4th row

17th row

Number of parking spaces

20

21

21 + 1(2)

21 + 2(2)

21 + 15(2)

Then, letting S represent the total number of

parking spaces in the theater,

S = 20 + (16)(21) + (1 + 2 + 3 + ...

+ 15)(2)

=^20 +^336 + (l

(^5) )(l (^6) ) (2)
2
See note below
356 + 240
596
Note that ifs= 1 + 2 + 3 + ... + 15, then
2s = (1 + 2 + 3 + ... + 15) +
(15 + 14 + 13 + ... + 1), and so 2s = (1 + 15) +
(2 + 14) + (3 + 13) + ... + (15 + 1) = (15)(16).
Therefore, s = ---(15)(16).
2
The correct answer is C.
PS10810

89. Ada and Paul received their scores on three tests. On
    the first test, Ada's score was 10 points higher than
    Paul's score. On the second test, Ada's score was
    4 points higher than Paul's score. If Paul's average
    (arithmetic mean) score on the three tests was
    3 points higher than Ada's average score on the three
    tests, then Paul's score on the third test was how many
    points higher than Ada's score?

(A) 9

(B) 14

(C) 17

(D) 23

(E) 25

Algebra i i ics

Let a 1 , a 2 , and a 3 be Ada's scores on the first,

second, and third tests, respectively, and let pi,

p 2 , and p 3 be Paul's scores on the first, second,

and thirdl tests, respectively. Then, Ada's average

score is --=---"------"-a1 + a2 + a3 an d P a s ul' average score

3

is Pi + h + P^3. But, Paul's average score is

3

3 points higher than Ada's average score, so

Pi + Pi + h = a^1 + a^2 + a^3 + 3. Also it is given that

3 3 '

a 1 = p 1 + 10 and a 2 =Pi+ 4, so by substitution,

Pi+ Pi+ h = (Pi +lO)+(Pi +4)+ a3 + 3. Then,

3 3

Pi+ Pi+ h =(Pi +lO)+(Pi + 4)+ a 3 +9 and so

p 3 = a 3 + 23. On the third test, Paul's score was

23 points higher than Ada's score.

The correct answer is D.

PS06180

90. The price of a certain stock increased by 0.25 of
    1 percent on a certain day. By what fraction did the
    price of the stock increase that day?

(A)^1

2,500

(B)^1

400

(C)^1

40

(D)^1

25

(E)^1

4

Arithmetic er :ents

It is given that the price of a certain stock

increased by 0.25 of 1 percent on a certain day.

1 1

This is equivalent to an increase of - of-,

4 100

which is (!) (-

1

) , and (1-) (-

1

) =-

1

.

4 100 4 100 400

The correct answer is B.