Return of the Hardest Easy Math Problem in the World
The last blog post I wrote showed how modifiers can fool people on quant problems “ here’s the link.
Several of my students who got the baseball problem from that post correct dismissed the issue entirely and scoffed at me for showing them such an easy problem, then inevitably missed a variant of the problem I’m about to show you. Try it for yourself, and watch out for the modifiers!
The town of Malmo, Sweden has only two late-night food options: Pizza and Kebab. All sellers of late-night food have either a street permit or a permanent store permit. 60% of all the late-night food sellers in Malmo are street vendors that serve Kebab; 20% of all the late-night food sellers who have a permanent store serve Pizza. If Malmo’s ratio of total street permits to total permanent store permits is exactly 7 to 3, what percentage of all late-night food sellers in Malmo serve pizza?
(A) 10%
(B) 16%
(C) 24%
(D) 30%
(E) 70%
(If you’re not sure how to approach this problem, try brushing up on overlapping sets, covered in the Manhattan GMAT Word Problems strategy guide. Then come back and give it a shot.)
Challenge Problem Showdown – January 7, 2013
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 x3 = 25, y4 = 64, and z5 = 216, and xy > 0, which of the following is true?
5 Simple Math Tricks for Faster Computations
Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.
For every five hours of studying combinatorics-type questions, the average GMAT student increases their chances of being able to correctly answer a question type that is found only on the very difficult end of the GMAT spectrum. Meanwhile, the same student will have to compute hundreds of basic computations without the aid of a calculator. For students who know how to quickly do these computations, they are rewarded with extra minutes that can be spent double-checking their work and critically thinking about whether their answers make sense. As BenGMAT Franklin might say, a second saved is a second earned on the GMAT, but it doesn’t matter if those extra seconds come from being faster at doing combinatorics questions or quicker at computations. So check out these five math tricks, learn the ones that you like, and practice them daily to give yourself some extra time to finish off that 37th and final Quant question.
Note: like everything else on the GMAT, being able to do something and being able to do something QUICKLY are two different tasks. If you like any of the following math tricks, make sure you know it inside and out before you try using it during your test. Read more
Challenge Problem Showdown – December 17, 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:
How many distinct positive factors does 30,030 have?
This Fraction Problem Is Harder Than It Looks
I’ve spoken with multiple students lately who received a disappointing (lower than they were expecting) score on the Quant section and who all said that the Quant felt relatively easy or straightforward. How is that possible?
First of all, thinking that a test like the GMAT is easy is actually a warning sign: things probably are not going very well. If the test was going very well, then you’d be seeing some seriously hard—next to impossible—problems.
Second, the test writers are phenomenal at writing questions that don’t seem all that complicated but are in fact your worst nightmare. My worst nightmare is not an impossible question—I know I can’t do it, so I just pick and move on. My worst nightmare is a question that I think I can do, and I spend a decent chunk of time doing it, and then I get it wrong anyway—even though I’m sure I got it right! Read more
Challenge Problem Showdown – December 10, 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:
For how many different pairs of perfect squares is the difference of the squares equal to 105?
Challenge Problem Showdown – December 3, 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:
Operation F means take the square root, operation G means multiply by constant c, and operation H means take the reciprocal. For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?
Challenge Problem Showdown – November 26, 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:
For a particular company, the profit P generated by selling Q units of a certain product is given by the formula P = 128 + (“Q2/4 + 4Q “ 16)z, where z > 0. The maximum profit is achieved when Q =
Challenge Problem Showdown – November 19, 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 n is a prime number greater than 2, is 1/x > 1?
(1) xn < x < x(1/n)
(2) x(n“1) > x(2n“2)
Challenge Problem Showdown – November 12, 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:
5/6 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is