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1. B
The family pays $800 per year for the plan, plus (100 percent
minus 80 percent) or 20 percent of the first $1,000 in medical
expenses, while the insurance company pays 80 percent of the
first $1,000, or $800. It must pay an additional $200 to match
what the family pays out. Since the $200 comes after the first
$1,000 in expenses, it must represent 100 percent of additional
expenses. Therefore, there must have been $1,000 plus $200
or $1,200 in medical expenses altogether.
2. D
We're told that cheese, bologna, and peanut butter sandwiches
are made in the ratio of 5 to 7 to 8. Every time they make
5 cheese sandwiches, they also have to make 7 bologna and
8 peanut butter. So there must be 5x cheese sandwiches (and
we don't know what x is at this point), 7x bologna sandwiches,
and 8x peanut butter. How many bologna sandwiches were made?
Well, the number of bologna sandwiches must be a multiple
of 7. But only choice D is a multiple of 7.
In other words: 5x + 7x = 8x = 120
20x = 120
x = 6
7(6) = 42
3. E
The key to solving this one is to focus on the quantity of
water drained away, which we will call x. We're told that
x liters of water are drained away, and x - 6 liters are left.
So x (liters taken away) plus x - 6 (liters left) equals 12
(total liters in the sink). Therefore 2x - 6 = 12, and x =
9.
4. D
Since 25 products sell at an average of $1,200, to buy one
of each we'd have to spend 25 x $1,200 = $30,000. We want
to find the greatest possible selling price of the most expensive
product. They way to maximize this price is to minimize the
prices of the other 24 products. Ten of these products sell
for less than $1,000, but all sell for at least $420. This
means that we can have 10 sell at $420. That leaves 14 more
that sell for $1,000 or more. So, in order to keep minimizing,
we'll price these at $1,000. That means that, out of the $30,000
we know it will take to purchase one of each item, only 10($420)
+ 14($1,000) = $18,200 is needed in order to purchase the
24 cheap items. The final most expensive item can thus cost
as much as $30,000 - $18,200 = $11,800.
5. B
The quickest solution is to pick numbers for n and m. Since
n = 1 and m = 1 would amount to 7 points, and since we want
to minimize the difference between n and m, and since 50/7
is just a bit more than 7, we'll start with values near 7.
The key is to discover what values for n, when multiplied
by 2 points, will leave a muliple of 5 as the remaining points.
The solution turns out to be 5 for n (10 points), which allows
for 8 for m (40 points). That's a total of 50 points, and
the positive difference between the two values is only 3.
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