Problem
Solving Answers & Explanations
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. The 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 minimize the prices of these 14
products, we would want to price each at $1,000. That means that,
out of the $30,000 total that 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 cheapest items. The greatest selling
price of the most expensive item can thus be calculated 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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