August 30, 2014
GRE Question of the Day: Leah saves money every day for one year. She saves one penny on January 1, and then increases her contribution by one cent each day. For example, Day 1 she saves 1 cent, Dave 2 two cents, Day 3 three cents, Day 4 four cents, etc.). How much has she saved after 365 days?
Solution: The savings for the 365 days are as follows: .01 + .02 + .03 + .04 + ... + 3.62 + 3.63 + 3.64 + 3.65. Note that the savings from the first and last day add to $3.66, as are the savings from the second and second to last day, and from the third and third to last day. This will be the same sum for every pair. Since there are 365 days, there are 365/2 pairs, or 182.5 pairs. Multiply the number of pairs by the sum of each pair to get the total savings: $182.5*$3.66.
August 29, 2014
GRE Question of the Day: Textbooks cost between $90 and $180 at University A, and textbooks cost between $170 and $300 at University B. Alexa had to purchase 11 textbooks at University A and 12 textbooks at University B. At which University did she spend more money (or can it not be determined)?
Answer: University B
Solution: Since the highest possible cost of purchasing books at University A ($180*11=$1980) is still lower than the lowest possible cost of purchasing books at University B ($170*12=$2040), then Alexa must have spent more at University B.
August 28, 2014
GRE Question of the Day: What is the units digit of 89^38?
Solution: This number is too large to put into your calculator. It is also too large to calculate by hand. Therefore, it must be the case that a pattern is involved. First, consider that we are only being asked about the units digit. We can therefore focus on the units' digit alone, as there will be no numbers "carried over" that affect that place. So, consider this: when you raise 9^1, the units digit is 9; 9^2 has a units digit of 1; 9^3 has a units digit of 9; 9^4 has a units digit of 1. Every time you raise 9 to an odd number, the units digit is 9, and every time you raise 9 to an even number, the units digit is 1.
August 27, 2014
GRE Question of the Day: Wesley and Bryan went on a company retreat. Wesley drove due north from his home to the retreat, averaging 45 miles per hour for 5 hours. Bryan drove due south from his home to the retreat, averaging twice the speed in half the time. How far apart are their homes?
Answer: 450 miles
Solution: Wesley and Bryan are driving from opposite directions. Wesley drives 45 mph for 5 hours, or 225 miles. Bryan drives twice as fast (90 mph) for half the time (2.5 hours), which, multiplied together, is also 2225 miles. The total distance apart, then, is 450 miles.
August 26, 2014
From a jar of 300 marbles, Sam chose 30 green ones and 12 red ones. If he picks x additional marbles, half of which are red, what is the value of x if he ends up with a 2 to 1 ratio of green to red marbles?
Solution: The current ratio is 30:12 for green to red marbles. Sam chooses x additional marbles. Since these additional marbles are evenly split between green and red, the new ratio is (30 + 1/2x) : (12 + 1/2x)=2:1. If you cross multiply, you get (30+1/2x)=2(12+1/2x). This simplifies to 30+1/2x=24+x, or 1/2x=6, or x=12.
August 25, 2014
If five students take 2 hours to clean 4 classroooms, how long would it take 8 students to clean 12 classrooms?
Answer: 3.75 hours
Solution: Five students take 2 hours to clean 4 classrooms. If these 5 students were to clean 12 classrooms (three times as many) it would take 6 hours (three times as long). However, the number of students is increasing to 8/5 of what it was (new number/old number). The more students, the less time needed to complete the work. Therefore, this is an indirect relationship-- when one variable increases, the other decreases. As with any indirect relationship, if one input changes by a factor of x/y, then the output changes by the reciprocal, y/x. Thus, the time is 5/8 of 12 hours, which is 60/8 or 3.75 hours.