k
to represent Kendra’s age, and the problem states that
k
>
5 (this is important only because Quantity B requires you to consider
Kendra’s age five years ago, and if she were younger than 5 years old, that
would create an impossible negative age!).
Quantity A = 2
k
– 5
Quantity B = 2(
k
– 5) = 2
k
– 10
Since 2
k
is common to both quantities it can be subtracted from both without
affecting their relative values.
Quantity A = –5
Quantity B = –10
Quantity A is less negative, so it is greater.
10.
$50.
Since Profit = Revenue – Expenses, and $12 for a car wash
multiplied by 20 car washes = $240:
190 = 240 –
E
–50 = –
E
$50 =
E
11.
(A).
Since Profit = Revenue – Expenses, and revenue = $720:
P
= 720 –
E
Expenses are equal to $22 per hour times 8 hours, plus a fixed $160, or 22(8)
+ 160 = $336. Thus:
P
= 720 – 336
P
= $384
12.
(B).
12 gallons of regular gas are needed to go 300 miles (300 divided by
25 miles per gallon), costing $36 (12 gallons × $3 per gallon). 10 gallons of
premium would be needed to go 300 miles (300 divided by 30 miles per
gallon), costing $40 (10 gallons × $4 per gallon). The question asks for the
difference, which is $40 – $36 = $4.
13.
(D).
For problems that ask for percents and use no real numbers, it is
almost always possible to use 100 as a starting number. Suppose the retailer
buys each toy for $100, and thus sells it for a regular price of $125. A
reduction of this regular selling price by 80% drops the price to $25. The loss
on each toy sold as a percent of the retailer’s cost is:
14.
(D).
The most straightforward approach is to determine the total weight of
all 20 students and divide that total by 20:
12 boys × 80 pounds per boy = 960 pounds
8 girls × 70 pounds per girl = 560 pounds
Total = 1,520 pounds
= 76
Alternatively, many or even most GRE multiple-choice weighted average
problems have the same five answers:
Much closer to the lesser value
A little closer to the lesser value
The unweighted average of the two values
A little closer to the greater value
Much closer to the greater value
Any of these five choices
could
be correct, but the correct answer is usually
“a little closer to the lesser value” or “a little closer to the greater value.” In
this case, because there are a few more boys than girls, the average for the
whole class will be a little closer to the boys’ average weight than to the girls’.
15.
(C).
The question asks how many bicycles the factory must sell to make a
profit. One way of phrasing that is to say the profit must be greater than 0.
Since Profit = Revenue – Cost, you can rewrite the equation to say:
Revenue – Cost > 0
Let
b
equal the number of bicycles sold. Each bike sells for $700, so the total
revenue is 700
b
. The cost is equal to $11,000 plus $300 for every bicycle
sold.
(700
b
) – (11,000 + 300
b
) > 0
Isolate
b
on one side of the inequality:
700
b
– 11,000 + 300
b
> 0
400
b
– 11,000 > 0
400
b
> 11,000
b
> 27.5
If
b
must be greater than 27.5, then the factory needs to sell at least 28
bicycles to make a profit.
16.
(B).
The typical way to do this problem would be to assign variables and
set up equations, using
x
to represent the number of classes Randolf took, 12
x
to represent the amount he paid, and 45
x
to represent the number of minutes
he spent.
A quicker way might be to notice that with every class Randolf takes, the
difference between the number of minutes he spends and the amount he pays
increases by 33. If Randolf takes 1 class, then the number of minutes he
spends is 33
greater than the number of dollars he pays. If he takes 2 classes, the number
of minutes is 66 greater than the number of dollars, and so on. Since 132 = 4
× 33, Randolf must have taken 4 classes.
17.
(B).
Profit is equal to Revenue – Expenses. First, calculate revenue:
Now, calculate expenses. How many total bottles of wine were sold? 12 cases
× 12 bottles, plus 60 individual bottles = 204 bottles. Note that the bottles sold
individually versus those sold in cases have the same purchase cost ($10), but
different shipping costs. Thus:
Profit = Revenue – Expenses
Profit = $3,840 – $2,820
Profit = $1,020
18.
(D).
This is a maximization question. To solve maximization questions,
you often have to minimize something else. In order to find the maximum
number of donors, minimize the donation per person. In this case, everyone
could pay exactly $14:
= 16.92
Rounding up to 17 is not right, because it is not possible that 17 people
donated $14 each (the total contributions would be $238, which is greater
than $237). The answer is (D), or 16.
19.
(B).
If 1 sack of rice is worth
of a bushel of tomatoes, buying the
whole bushel would require 3 sacks of rice. Quantity B is equal to 3. The
math is a bit tougher in Quantity A, but no calculation is really required—if a
sack trades for 2.5 pounds of beans, a single pound of beans is worth less than
a sack of rice. Quantity A is less than 1.
20.
(D).
If Francisco’s MP3 player is three-quarters full, the current content
equals
× 64 GB = 48 GB. He then deleted 25%, or 12 GB, of that data,
reducing the amount of data saved to 48 – 12 = 36 GB. After saving 20 GB of
new data to the device, it holds 36 + 20 = 56 GB. This is
=
87.5% of the total capacity.
21.
(E).
Assign the variable
s
for the number of subscribers last year:
Last year:
$50 per subscription
s
subscribers
This year:
$60 per subscription
s
– 4 subscribers
The question states that the magazine “could” lose 4 subscribers and that the
magazine would then collect the same revenue as last year—don’t let the
“could” throw you off. Calculate using this hypothetical situation:
50
s
= 60(
s
– 4)
50
s
= 60
s
– 240
–10
s
= –240
s
= 24
22.
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