A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
A. 0 and 13
B. 0 and 14
C. 1 and 10
D. 10 and 9
E. 2 and 8
Correct Answer: A
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You’ll find tons of practice questions, explanations for GMAT Official Guide questions, and strategies on our GMAT Question of the Day page.
Here are a few other extra challenging GMAT questions with in depth explanations:
Here’s a tough function question from the GMAT Prep tests 1 and 2:
For which of the following functions is f(a+b) = f(b) + f(a) for all positive numbers a and b?
And a very challenging word problem from the Official Guide. Almost no-one gets this one on the first try but there is a somewhat simple way through it:
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?
Tanya’s letters from the GMAT Prep tests. This one often gets GMAT tutoring students caught up in a tangled net. With combinatorics it’s important to stay practical. We’ll take a look at how to do that in the explanation:
Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
Here’s an exponents puzzle that comes up a lot in GMAT tutoring sessions:
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is
This is one of the most difficult questions in the GMAT universe. That said, there is a simple way to solve it that relies on a fundamental divisibility rule every GMAT studier should know:
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is?
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