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One reason GMAT math problems can be hard is that the test
writers try to trick you. After writing a question and choosing
one answer choice to be the correct answer, test writers
have four answer choices left to fill. One of the questions
they ask at this point is whether there are any numbers
that would make good trap answers. GMAT test-takers as a
whole are predictable (so are most groups of people as a
whole) and it’s not hard for the test writers to come
up with some answers that will be very tempting. Part of
your job in preparing for the GMAT is to become less predictable
and less subject to these temptations. Let’s tackle
a few examples.
| The price of a jacket is reduced
by 25%. During a special sale the price of the jacket
is reduced another 10%. By approximately what percent
must the price of the jacket now be increased in order
to restore it to its original amount?
A) 32.5
B) 35
C) 48
D) 65
E) 67.5
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So what’s the answer here? If 35 looks like a good
option to you, you’re in good company. It seems that
a 25% discount followed by a 10% discount should total a
35% discount. But if the question were really that easy
it wouldn’t be on the GMAT. This is where test-taking
savvy has to kick in. You aren’t going to spend your
time on the GMAT adding together two numbers that appear
in the problem and getting the correct answer. That’s
way too easy. 35 is a trap answer, and you need to train
yourself to spot trap answers. So what’s the real
answer if it’s not 35?
Let’s make this more concrete and give the jacket
a price. For simplicity, call it a $100 jacket. A 25% discount
will be $25, so now we have a $75 jacket. Next, another
10% is taken off. 10% of 75 is 7.5, so the new price is
75 - 7.5 = 67.5. After the two discounts the jacket costs
$67.50. (Now you can see why 35% is incorrect. The two discounts
can’t simply be added, because the second one is being
taken from a different base number (75) than the first one
(100) is.) To get back to $100 we have to raise the price
$32.50. Now we need to use the percent change formula: Percent
change = {difference/original}*100. In a percent increase
problem, the “original” number will be the smaller
one, so our formula is {32.5/67.5}*100. We don’t need
to do the full calculation because 32.5/67.5 is a little
less than one half, and the only answer that’s in
the ballpark is 48% in Answer C. As you can see, there are
a lot of steps to this problem, and anyone who blithely
picks 35 and moves on is missing all the important stuff.
Let’s look at another example.
| Vivian drives to her sister’s
house and back. She takes the exact same route both
ways. On the trip out she drives an average speed
of 50 miles per hour. On the trip back she drives
an average speed of 70 miles per hour. What is her
approximate average speed for the round trip in miles
per hour?
A) 50
B) 58.3
C) 60
D) 61.7
E) 70
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Does anything look tempting here? Something that seems
logical, but is perhaps too good to be true? The trap answer,
of course, is 60. It seems to make perfect sense —
half way between 50 and 70 — but it’s just too
easy. No matter how much you want to pick it, you have to
tell yourself that if the problem could be solved that easily
it wouldn’t be on the GMAT. So 60 is out. What else
can we eliminate?
Common sense should tell you that answer can’t be
50 or 70. You can’t drive there at 50, come back at
70, and average 50 for the whole trip, for example. That
makes no sense. It has to be somewhere between those numbers.
Let’s look at our remaining answers, 58.3 and 61.7.
One of these is closer to 50 and one is closer to 70. So
apparently one of these trips — either the 50mph trip
or the 70mph trip — has had a greater effect and is
“pulling” the average speed closer to itself.
Which one? When dealing with problems about rates, there
are three parts to consider: rate, distance, and time. We
know the rates here. The distance is the same for each trip.
The determining factor, therefore, is time. It takes longer
to make the trip at 50mph than at 70 mph, so Vivian spends
more time at that speed. This means the average will be
closer to 50 than 70, and the answer is B.
Another way to solve this problem is to plug a distance
into the problem. Because the trip is the same distance
each way it doesn’t matter what you choose —
the answer will be the same no matter what. Mathematically,
however, it will be much easier if you pick a number that
is divisible by 50 and 70. So let’s make this a 350
mile trip. That means it will take Vivian 350 ÷ 50
= 7 hours to drive there, and 350 ÷ 70 = 5 hours
to drive back. That’s a total of 12 hours to drive
700 miles. Thus, her average speed for the round trip is
700 ÷ 12 = 58.3.
Keep an eye out for answer choices that are too simple.
If you remember that the GMAT is going to make you work
for answers, you’ll avoid falling for the traps that
ensnare so many test-takers. |
