Challenge Problem Showdown – July 23rd, 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:
X is a three-digit positive integer in which each digit is either 1 or 2. Y has the same digits as X, but in reverse order. What is the remainder when X is divided by 3?
(1) The hundreds digit of XY is 6.
(2) The tens digit of XY is 4.
Challenge Problem Showdown – July 16th, 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:
A decade is defined as a complete set of consecutive nonnegative integers that have identical digits in identical places, except for their units digits, with the first decade consisting of the smallest integers that meet the criteria, the second decade consisting of the next smallest integers, etc. A decade in which the prime numbers contain the same set of units digits as do the prime numbers in the second decade is the
Decoding the Prime Disguise
How can the GMAT disguise a prime number (or any other) problem? I asked this question a couple of years ago at the start of a very important article entitled Disguising “ and Decoding “ Quant Problems. Go read that article right now, if you haven’t already. I’ll wait.
Towards the end of that article, I referenced two Official Guide problems. I was very excited today to see that one of these problems is part of the free practice problem set that now comes with the new GMATPrep 2.0 software “ so I can actually reproduce it here and we can try it out!
Disclaimer: this is a seriously challenging problem. Set your timer for 2 minutes, but practice your 1 minute timing here. If you don’t have a pretty good idea of what’s going on by the halfway mark, try to figure out how to make a guess. Pick an answer by the 2 minute mark (all right, I’ll let you go to 2 minutes 30 seconds if necessary “ but that’s all!).
Does the integer k have a factor p such that 1 < p < k?
(1) k > 4!
(2) 13! + 2 < k < 13! + 13
Challenge Problem Showdown – July 9th, 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:
If a, b, and c are nonzero integers and z = bc, is az negative?
(1) abc is an odd positive number.
(2) | b + c | < | b | + | c |
Challenge Problem Showdown – July 2nd, 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:
Ax(y) is an operation that adds 1 to y and then multiplies the result by x. If x = 2/3, then Ax(Ax(Ax(Ax(Ax(x))))) is between
Recognizing Relative Numbers On The GMAT
Given the statement, the ratio of men to women in the room is 3 to 5, how many men are in the room?
You probably recognize pretty quickly that it is not possible to answer the question above. Just given a ratio, it is not possible to identify the actual number of men in the room. At this point we know the number of men in the room must be a multiple of 3, but the actual number could be 3 or 3,000 (although I am not sure I have been in a room that large).
Along with ratios in their traditional form (3 to 5 or 3:5), there are other types of numbers that are ratios, slightly disguised
a) Fractions: The container is 2/3 full.
This statement is expressing that there are 2 full parts for every 3 total parts of the container (a ratio of 2 to 3).
b) Percentages: 33% of company employees have Master’s degrees.
This statement is expressing for every 33 employees with Master’s degrees there are 100 total employees (a ratio of 33 to 100).
c) Percentage or fractional increase: The company’s profits increased 25% (or ¼) from 2010 to 2011.
Challenge Problem Showdown – June 25th, 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 x-y coordinate plane, what is the minimum distance between a point on line L and a point on line M?
Challenge Problem Showdown – June 18th, 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 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick from each of 3 different complete bags of Pick-Up Sticks, what is the probability that Tommy CANNOT form a triangle from the 3 sticks?
GMATPrep Quant Question: What is this?
I don’t have a great title for you because I don’t have a really clean category for this question “ and that’s exactly why it caught my attention and why I’m sharing it with you today.
Try out this GMATPrep problem:
Did one of the 3 members of a certain team sell at least 2 raffle tickets yesterday?
(1) The 3 members sold a total of 6 raffle tickets yesterday.
(2) No 2 of the members sold the same number of raffle tickets yesterday.
This really does not look like a tough question does it? It looks easy! We can’t know for sure exactly how this question was rated, but consider this. I received this as the 15th question in my GMATPrep quant section. Up until that point, I had missed 2 questions, #6 and #14.
By the way, I took the test on a plane without scrap paper and the two I missed were both geometry questions for which I really needed to draw something out. Don’t try that at home! Write everything down. (After #14, I got a napkin from the flight attendant and started using that!)
So, yes, I’d missed the question right before (#14), but I had also gotten 12 of 14 questions right so far. In other words, the above question is at the upper end of the range.
So, the question is harder than it looks. Let’s talk about why. = )
How To Turn Algebra Into Arithmetic
I have never met anyone who is better at algebra than he or she is at arithmetic. As good as a person may be with algebra, that person’s going to be even better with real numbers (arithmetic). How can we use that to our advantage on the test?
Algebra and arithmetic are very similar, but algebra uses variables where arithmetic would use real numbers. On certain GMAT problems, we can taken a problem in which we were given variables and use real numbers instead “ we’re turning algebra into arithmetic!
Note: a lot of my students will complain that this method takes too much time. Of course it does when you first start studying it. You’ve been doing algebra for years, but most of you are just learning how to turn algebra into arithmetic. Think how slow you were when you first started learning algebra. Put in the practice and you’ll pick up the speed!