Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!
The tens digit of
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Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!
A circle is inscribed in an equilateral triangle, such that the two figures touch at exactly 3 points, one on each side of the triangle. Which of the following is closest to the percent of the area of the triangle that lies within the circle?
There are two types of interest problems on the GMAT, and they include simple interest and compound interest. Simple interest is the most basic and is a function of P, the principle amount of money invested, the interest rate earned on the principle, i, and the amount of time the money is invested, t (this is usually stated in periods, such as years or months). The resulting equation is:
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!
Skier Lindsey Vonn completes a straight 300-meter downhill run in t seconds and at an average speed of (x + 10) meters per second. She then rides a chairlift back up the mountain the same distance at an average speed of (x – 8 ) meters per second. If the ride up the mountain took 135 seconds longer than her run down the mountain, what was her average speed, in meters per second, during her downhill run?
Prime Factorization: My single favorite topic on the GMAT. Hands down.
My passionate (some would say evangelical!) advocacy of prime factorization results not only from my finding prime numbers so intrinsically fascinating in and of themselves, but also from the plain and simple truth that prime factorization proves surprisingly useful on questions on which prime numbers aren’t even mentioned.
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!
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Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!
Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?
Probability is a perennially dreaded GMAT topic by students of all scoring levels. It’s hard enough to master concepts that you haven’t seen since high school, such as triangles and exponents, but probability is a topic that many test takers have never seen before, unless you did a little research before your last trip to the casino (in which case you may have decided to stay home instead!).
There are three tenets of probability theory that underlie every probability question on the GMAT, each of which follows from the last. You’ll still have to put some practice in on your own to really get the concepts down, but these are a good start:
On the most advanced GMAT content, you will see complicated geometric figures. While these questions are often the most daunting questions, you (as the prepared and confident test taker) will realize that the GMAT is only testing a couple concepts.
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!
If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12) + 11 is
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!
Two different primes may be said to “rhyme” around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
In this excerpt from a Kaplan Lesson on Demand, Adi Hanash covers an advanced geometry question.
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!
The consumer price index in Zeropia in 2009 relative to the year 2000 was 1.75, meaning that for every Zeropian dollar spent on consumer goods in 2000, $1.75 on average had to be spent in 2009. In Zeropian dollars, what was the increase in the price of Brand Z running shoes from 2000 to 2009, if these shoes’ price increased precisely according to the consumer price index?
(1) The price of Brand Z running shoes was $91 in 2009.
(2) The ratio of the dollar increase in the price of Brand Z running shoes to the price of the shoes in 2009 was 3:7.
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!
What is the 18th digit to the right of the decimal point in the decimal expansion of 1/37?
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!
If 1/(x – 2) = 1/(x + 2) + 1/(x – 1), which of the following is a possible value of x?
