GMAT® Official Guide 2019 Quantitative Review
Arithmeticr10^2 -74 = 100-74 = (^26) "
103 - (^74) = 1,000-74 = 926
104 - (^74) = 10,000- (^74) = 9,926
105 -74 = 100,000- (^74) = 99,926
106 -74 = 1,000,000 -^74 = 999,926
'- ~
From the table above it is clear that 1050 - 7 4 in
base 10 notation will be 48 digits of 9 followed by
the digits 2 and 6. Therefore, the sum of the digits
of 1050 - 7 4 is equal to 48(9) + 2 + 6 = 440.
The correct answer is C.
PS09056
- A certain company that sells only cars and trucks
reported that revenues from car sales in 1997 were
down 11 percent from 1996 and revenues from truck
sales in 1997 were up 7 percent from 1996. If total
revenues from car sales and truck sales in 1997 were
up 1 percent from 1996 , what is the ratio of revenue
from car sales in 1996 to revenue from truck sales
in 1996?
(Al 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3Algebra; ArithmeticLet C 96 and C 97 represent revenues from car sales
in 1996 and 1997 , respectively, and let T 96 and T97
represent revenues from truck sales in 1996 and
1997, respectively. A decrease of 11 percent in
revenue from car sales from 1996 to 1997 can be
represented as (1 -0.11)C 96 = C 97 , and a 7 percent
increase in revenue from truck sales from 1996 to
1997 can be represented as (1 + 0.07)T96 = T97.
An overall increase of 1 percent in revenue from car
and truck sales from 1996 to 1997 can be
represented as C97 + T97 = (1 + 0.01)( C96 + T96)·
Then, by substitution of expressions for
C97 and T97 that were derived above,
(1 -0.11)C 96 + (1 + 0.07)T 96 = (1 + 0.01)(C 96 + T 96 )
and so 0.89C96 + 1.07T96 =
1.01(C96 + T96) or 0.89C96 + 1.07T96 =
1.01 C 96 + 1.01 T 96. Then, combining like terms
gives (1.07 - 1.01)T96 = (1.01 - 0.89)C96 or0.06T96 = 0.12C96· Thus~: = ~:~~=½.The ratio
of revenue from car sales in 1996 to revenue from
truck sales in 1996 is 1:2.The corre:ct answer is A.
PSl4267- Becky rented a power tool from a rental shop. The rent
for the tool was $12 for the first hour and $3 for each
additional hour. If Becky paid a total of $27, excluding
sales tax, to rent the tool, for how many hours did she
rent it?
(A) 5
(Bl 6
(C) 9
(D) 10
(E) 12Arithmetic
Becky paid a total of $27 to rent the power
tool. She paid $12 to rent the tool for the first
hour and $27 - $12 = $15 to rent the tool
for the additional hours at the rate of $3 per
additional hour. It follows that she rented the
tool for^15 = 5 additional hours and a total of
3
1 + 5 = 6 hours.The correct answer is B.
PS06959
163. If 4 <^7 ; X., which of the following must be true?I. 5<X
II. lx+31>2
Ill. -(x + 5) is positive.
(A) II only
(B) Ill only
(Cl I and II only
(D) II and Ill only
(E) I, II, and Ill