1. B
We need to realize that each time the stock changes its price
by a percentage of different wholes. For instance, in July the
original price increases by 10%. When it declines in August, it
declines by 20% of the new price. So the net change after August
will not be 10%-20% or -10%; it's not that easy. The best way to
work with percent change is to pick a number. Usually 100 is the
easiest number to start with for percents — it's easy to take a
percent of 100.
So say the original July price is $100. It increases by 10% or
$10, up to $110. In August, it declines by 20% of $110, or 1/5 x
$110 = $22. So now it's down to $110-$22 or $88. Then it goes up
by 10% or $88 or 1/10 x $88 = $8.80; this brings the price up to
$96.80, only $3.20 less that it started. The percent change
equals the amount of change divided by the original whole (100 in
this case), or 3.2/100 x 100% = 3.2%.
2. D
The catch here is that it's not which of the following is 850
percent of 8 x 103, it's which of the following
is 850 percent greater than 8 x 103. Well,
what's bigger, 850 percent of 1 or a number that's 850 percent
greater than 1? 850 percent of 1 is 8.5 x 1 or 8 1/5. But a
number that's 850 percent greater than 1 is 1 + 850 percent of 1,
it's 1 + 8.5 or 9.5. So the number we want is 9.5 x 8 x
103. 9.5 x 8 = 76, so the answer is 76 x
103, or 7.6 x 104 in scientific
notation.
3. B
Since the vending machine dispenses gumballs in a regular
cycle of ten colors, there are exactly nine other gumballs
dispensed between each pair of gumballs of the same color. For
example, gumballs one and eleven must be the same color, as must
gumballs two and twelve, forty-two and fifty-two, etc. To get
three gumballs all of the same color, we get one of the chosen
color, then nine of another color before another of the chosen
color, then nine of another color before the third of the chosen
color. That's a total of 1 + 9 + 1 + 9 + 1 = 21 gumballs to get
three matching ones. Since each quarter buys three gumballs, and
we need twenty-one gumballs in all, we have to spend 21 / 3 = 7
quarters to get three matching gumballs, 7 x 25 cents =
$1.75.
4. A
Method I:
Find the cost of the stereo to the dealer, then subtract 40% of
this to find the price it was sold for. The selling price equals
the dealer's cost plus the profit. The dealer would have made a
20% profit if he had sold the stereo for $600; therefore, letting
x represent the cost to the dealer,
600 = x + 20% of x
600 = 120% of x
600 = 6/5x
x = 5/6 x 600
x = 500
Instead, the dealer sold the stereo at a loss of 40%. Since 40%
or 2/5 of 500 is 200, he sold the stereo for $500 - $200 =
$300.
Method II:
Let x represent the dealer's cost. Then we're told that
$600 represents x + 20% of x, or 120% of x.
We want the value of x - (40% of x) or 60% of
x. Since 60% of x is one-half the value of 120% of
x, the sale price must have been one-half of $600, or
$300.
5. D
Calculate separately the amount of usable beef, and the price
at which he must sell all the beef to make a 25% profit, then
divide the total price by the number of kilograms of usable
beef.
Usable beef: he buys 240 kilograms, but 20% of this is
unusable. This means the remainder, 80% of the beef, is usable.
80% = 4/5, so 4/5 x 240 = 4 x 48, or 192. So he can sell 192
kilograms.
Total price: he wants a 25% profit. Since he paid $380 for the
beef, he must sell it for 25% more than $380, or 125% of $380.
125% = 5/4, so he has to sell it for 5/4 x $380 = $475.
Price per kilogram: divide the total price ($475) by the
number of kilograms (192). The approximate price is $2.47 a
pound.
Other PracticeQs:
