Challenge Problem Showdown – August 27th, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
Harold plays a game in which he starts with $2. Each game has 2 rounds; in each round, the amount of money he starts the round with is randomly either added to or multiplied by a number, which is randomly either 1 or 0. The choice of arithmetic operation and of number are independent of each other and from round to round. If Harold plays the two-round game repeatedly, the long-run average amount of money he is left with at the end of the game, per game, is between
Challenge Problem Showdown – August 20, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
The symbol $ is defined by the formula a$b = a2 + b2. If 35$x = 372 and ((3$4)½$x)½$n = 852, then |n| =
How to Analyze a GMAT Integrated Reasoning Two-Part Question
This is the latest in a series of How To Analyze articles that began with the general How To Analyze A Practice Problem article (click on the link to read the original article). This week, we’re going to analyze a specific IR question from the Two-Part prompt category. First, give yourself up to 2.5 minutes to try the below GMATPrep problem.
An architect is planning to incorporate several stone spheres of different sizes into the landscaping of a public park, and workers who will be applying a finish to the exterior of the spheres need to know the surface area of each sphere. The finishing process costs $92 per square meter. The surface area of a sphere is equal to 4Ï€r2, where r is the radius of the sphere.
In the table, select the value that is closest to the cost of finishing a sphere with a 5.50-meter circumference as well as the cost of finishing a sphere with a 7.85-meter circumference. Make only two selections, one in each column.
Circumference 5.50 m Circumference 7.85 m Finishing cost $900 $1,200 $1,800 $2,800 $3,200 $4,500
After trying the problem, checking the answer, and reading the given solution (if any), I then try to answer the questions listed below. First, I’ll give you what I’ll call the standard solution (that is, one we might see in an Official Guide book if this were an official guide problem “ a correct solution but not necessarily one that shows us the easiest way to do the problem). Then we’ll get into the analysis.
Standard solution: The formula for circumference is C = 2Ï€r. We can use this to calculate the radii of the two spheres (note that the problem asks us to find the closest values, so we can estimate):
Challenge Problem Showdown – August 13, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
Rounded to four decimal places, the square root of the square root of 0.9984 is approximately…
Ryan Gosling’s Paycheck: Weighted Average on the GMAT
If you’ve read my previous post you know I got married very recently. When I asked my new wife the other day to name her favorite celebrity, she said Ryan Gosling; unfortunately I look nothing like him “ so I’m not quite sure where that leaves me. As a form of revenge I’ve decided to use Mr. Gosling to demonstrate some key insights in the commonly misunderstood topic of Weighted Average. Ryan will never forgive me!
For the purpose of this blog post let’s assume that Ryan Gosling made $10M per movie in 80% of his movies and $20M per movie in 20% of his movies. His average paycheck would have been $15M if his salary were distributed evenly between $10M and $20M “ but an 80-20 distribution means we’ll have to put a little more thought into the situation. If we want to know how much Mr. Gosling made on average per movie, we have no choice but to calculate the weighted average.
Some math lovers might use an algebraic formula to calculate the weighted average, but I believe using a visual approach for this calculation will drive a deeper level of understanding for us regular folks.
Use your intuition and try a visual approach
If I asked you for a range of the weighted average of Ryan Gosling’s paychecks, your intuition would probably suggest between $10M and $20M. You might even propose that the weighted average be closer to $10M than to $20M (since $10M has a heavier weight “ 80% vs. 20%). You would be absolutely correct!
An Olympics-Inspired GMAT Data Sufficiency Question
In honor of Gabby Douglas’ gold medal win, as well as the U.S. women’s gymnastics team’s all-around gold medal win, here is an Olympics-inspired Data Sufficiency problem.
A particular gymnastics tournament awards a gold, a silver, and a bronze medal in each of four events: Floor, Beam, Bars, and Vault. A platinum Best All-Around medal is awarded to the competitor who gains the most points from winning the other medals: 3 points for gold, 2 points for silver, 1 point for bronze. If McKenzie won the Best All-Around medal, and no one can win more than one medal in any of the four events, did she win at least one gold medal?
- All of the gold, silver, and bronze medals were won by fewer than six competitors, including McKenzie
- Another competitor in the tournament has 8 points.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Choose your answer before proceeding!
First, you may ask, How could someone win the All-Around without winning a single gold medal?
Easy “ just imagine that McKenzie won ALL of the silver medals (8 points), and that no one else won more than one medal (the other medals are won by 8 separate people), so each person who has a gold has just 3 points, and each person who has a bronze has just 1 point.
Challenge Problem Showdown – August 6, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?
(1) 56 < N < 63 (2) N is a multiple of 3.
Part to Part and Part to Whole Ratios
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Take a look at the following problems.
Data Sufficiency: What was Company X’s percentage profit in 2011?
1) The ratio of costs to profits for Company X was 3 to 1 in 2011.
2) Company X’s costs in 2011 were $360,000.
A recipe for punch calls for 4 parts seltzer to one part juice. If John wants to make 5 gallons of punch, how many 8 ounce cans of juice does he need (1 gallon = 128 ounces)?
A) 32
B) 20
C) 16
D) 10
E) 8
4 Common Types of Data Sufficiency Traps
If the GMAT were a sport, it would definitely be baseball, and not just because it’s three and a half hours long. In baseball, you might dominate the minor league by hitting fastballs, but once you reach the show you’ll have to hit some change-ups and curveballs too. Not only is the GMAT going to throw you some hard problems, but once you start to do well, the GMAT will throw you something different. That’s why learning the types of trap answers can help you from falling for them. Here’s four types of curveballs that you want to be mindful of on test day.
If you test it, they will come.
Challenge Problem Showdown – July 30th, 2012
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
In the country of Celebria, the Q-score of a politician is computed from the following formula:
Q = 41ab2c3/d2, in which the variables a, b, c, and d represent various perceived attributes of the politician, all of which are measured with positive numbers. Mayor Flower’s Q-score is 150% higher than that of Councilor Plant; moreover, the values of a, b, and c are 60% higher, 40% higher, and 20% lower, respectively, for Mayor Flower than for Councilor Plant. By approximately what percent higher or lower than the value of d for Councilor Plant is the corresponding value for Mayor Flower?