Sample GRE Multiple Choice Math Problem – Mean Means

The human race will tremble before my unstoppable math problem.

On every GRE Math section, the test makers try to come up with a few extremely difficult problems that will leave even the cleverest students scratching their heads. The really evil part, though, is that even these problems can be solved in under a minute without a calculator – if you know what to do. This means that once you “figure out the trick,” these difficult problems become easy. So, while those test makers are busy cackling with sadistic glee, let’s see if we can’t beat them at their own game.

Consider the following problem:

If the average (arithmetic mean) of four different positive integers is 5, then the least possible product of the four integers is:

A) 20

B) 84

C) 104

D) 480

E) 504

This one might seem like a hard nut to crack. After all, there are many possible sets of four distinct positive integers that have an average of 5. We could not possibly test them all one by one given the time constraints of the GRE. So how are we going to figure out which four integers are the ones that yield the smallest possible product?

Well, if we want the smallest product, then we want as many of the integers to be as small as possible. If the smallest of the three integers were equal to 1, then that would be great, since multiplying by one simply produces the same number and would thus not increase the product of the three numbers. Since the four integers must be distinct, we can make the second integer 2 so that it is also as small as possible, and by the same logic the third integer would be 3. All that remains is to determine the fourth integer, which we can find using algebra:

The fourth integer is 14, and the product is:

Logically, the answer must be 84, or choice B. If you are still feeling unsure, you could try a few other sets of four integers to see if their products are less than 84. What happens, for instance, when we increase the 3 to 4 and decrease the 14 to 13?

No, Magneto! We have to educate humanity, not destroy it!

No, Magneto! We have to educate humanity, not destroy it!

Already, the product begins to increase. Try any other set and you will see that its product is greater than 84. It doesn’t matter that we decreased 14 to 13, because what controls the outcome in this problem is how small we can make the smallest numbers in the set. Thus, our original reasoning was correct.

If you know what to do, it takes only about 30 seconds to solve this problem. So you see, with practice, even the hardest problems on the GRE become easy. Check back here each week for more extra hard problems and the tricks you need to solve them! Also, remember that you can find out all the tricks from experts like me with a Test Masters course or private tutoring. Until  then, keep up the good work and happy studying!

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Can I Apply to Graduate School Without Letters of Recommendation?

Need a letter of a recommendation? We have some tips to help you out!

Need a letter of a recommendation? We have some tips to help you out!

Today’s topic is one we see asked fairly often, so we wanted to address this multi-faceted problem and offer a few ways you can potentially skirt around grad schools’ requirements for letters of recommendation. It’s important to note, however, that this advice is primarily geared towards non-traditional students (i.e. those who have been out of school for a number of years and wouldn’t necessarily have the same resources as a current undergraduate or recent grad). If you are currently an undergraduate student or have graduated within the last 2 years or so, you absolutely must get those letters of recommendation! While non-trads may have a good excuse for not having LoRs, since they’ve been out of school for 5-10 years, admissions committees will be much more curious about a recent graduate who cannot muster up these documents.

That being said, here’s a few things you can do for those letters of recommendation

  • Take some time and do research: Whether as a research assistant or lab tech, doing paid research, even if only at minimum wage, allows you to form strong bonds with a professor who can then write you a letter of recommendation. Many professors are looking for a minimum 2-year commitment to research before taking anyone on, so this might not be the fastest route, but it’s certainly a surefire way to acquire a letter of recommendation when you might not have one, especially if you’re currently an undergrad scrambling to get letters.
  • Talk to old professors who may still remember you: This is probably the least desirable option, in terms of awkwardness and strength of the letter, but if worst comes to worst, you can try going back to your undergraduate institution to talk to an old professor. If you explain your situation, that you finally decided on applying to graduate school after some time away from academia, you may find some sympathy and have some assistance there.
  • Use your current employer: Some graduate programs do not specify who the letters of recommendation should come from, and if that is the case, you may be able to use a current employer as a reference. The catch is that this may not be as useful if you are not currently in a field related to your graduate program of interest. If you’re baking cakes, your head chef’s recommendation may not be useful for applying to a physics program, though of course it can still help in demonstrating your dedication and perseverance! If you’re working as an oilfield chemist, your supervisor’s recommendation may carry more weight for a chemistry Ph.D. program.
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How Many Graduate Programs Should You Apply To?

You don't need a calculator to figure out how many graduate programs to apply to.

You don’t need a calculator to figure out how many graduate programs to apply to.

With admissions season quickly approaching, we wanted to answer a question we see fairly often: “How many graduate programs should I apply to?” The answer to this depends on each individual student, but a good rule of thumb is to try and apply to no more than 10 schools.

There’s a few reasons for this somewhat arbitrary cutoff:

  • You don’t want to overwhelm your letter writers: Each letter writer will have to tailor his/her letter to each school, and even if it is just slightly tweaking each letter for a specific school, that’s still a lot of work! Many letter writers we’ve talked to said they would not tweak more than 10 letters unless there was a very strong and compelling reason for them to. These advisors and professors are doing you a favor! Don’t make more work than is usually expected
  • You don’t want to spread yourself too thin: Submitting 6-10 strong, tailored applications is far more advantageous than submitting 10-15 less well-written applications. You want to ensure your applications reflect your high achievement and positive qualities, so you don’t want to overwhelm yourself with more applications than you can successfully complete. It’s completely understandable to want to spread your risk out and apply to more schools in the hopes of getting in to at least one, but this may backfire if you submit many low quality applications rather than few high quality applications.
  • You don’t want to apply to schools you don’t want to attend: Worst case scenario, you are only accepted to a single graduate program. Would you be willing to attend this institution? Don’t apply to schools you wouldn’t be willing to spend 4+ years of your life at! Don’t apply to programs where you wouldn’t be happy grueling in lab for hours on end. You don’t want to end up in a situation where you’re stuck in a program you despise, just because you were more afraid of not getting in at all! Make sure you would be 100% happy and content with attending each program you apply to.
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Does Undergrad Prestige Matter for Graduate School Admissions?

Didn't attend an Ivy League school for undergrad? Don't worry! You still have a shot at attending a prestigious graduate program!

Didn’t attend an Ivy League school for undergrad? Don’t worry! You still have a shot at attending a prestigious graduate program!

We get this question fairly often: “I went to a relatively low-ranked school. Do I have a shot at attending an Ivy League graduate program?” The short answer to this is yes, you do have a shot! The full answer is a little bit more complicated than that, so read on for more information!

How Much Does Undergrad Prestige Actually Matter?

Graduating from a prestigious undergraduate institution will not in and of itself grant you admissions into an Ivy League or similarly top graduate institution. What it will do for you, however, is give you a leg up on similarly qualified applicants. If you graduate with a 3.9 GPA from Duke University, and your competitor graduated from Greendale Community College with a 3.9, you’re definitely going to have an advantage there. Admissions officers will view your application in its context; a somewhat lower (~0.2 points, roughly) GPA from a highly regarded institution will likely be viewed more favorably than a somewhat higher GPA from a less well-known institution. Similarly, a letter of recommendation from a well-known researcher in the field will hold more weight than a letter of recommendation from a researcher who hasn’t published as much.

Well, What Can I Do About This?

Plenty! Not graduating from a “top” undergrad school doesn’t mean you don’t have a shot! Plenty of students from relatively unknown schools matriculate in top graduate programs, but you really have to prove yourself to do so.

  • Publish, publish, publish: For STEM fields especially, publications are key to success in graduate programs. Even getting last author on a paper is impressive as an undergrad, as it shows that you’re capable of finding and completing research, which is essentially the entirety of academia nowadays.
  • Find an advisor or professor who you can really get to know: You want a STRONG letter of recommendation going into your file, not a mediocre one. You want a professor who has known you for a while and who can speak to your strengths and character. This is usually only achieved through knowing an advisor for several years or by completing an intensive research project with him/her. Get working on that!
  • Maintain a high GPA: This is a no brainer, but you want to have as close to a 4.0 GPA as you can possibly manage. A 3.9 from an unknown school looks infinitely better than a 3.3 from a prestigious institution. You need to ensure that your GPA is high enough to hopefully counteract any bias the admissions council might have against your institution
  • Destroy the GRE: The GRE, as are all standardized tests, is the great equalizer in terms of admissions. It’s an objective standard by which all students are measured — no bias in terms of institution or curriculum here. Make sure to prepare well and absolutely dominate the exam so  you can show admissions officers how rigorous your curriculum was and how much you’ve learned!
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Best of the Blog: GRE Subject Tests: To Take, or Not To Take

Wait. There are subject tests, too?!

Wait. There are subject tests, too?!

Today we’ll be reposting one of our favorite blog articles, which was originally published by James. Enjoy!

Remember when you took the SAT for the first time? You were so anxious because it was the SAT AND IT WAS THE BIGGEST TEST YOU WERE EVER GOING TO TAKE! And just as you got up to the front of the line to check-in, they asked you if you were taking an SAT II. A WHAT?!

And, indeed, it turned out that on top of the SAT reasoning tests there were other subject tests that were “optional.” Perhaps if you’re a strange Martian who is immune to the horrors of standardized testing, you were excited for another chance to show what you know, but more likely, your heart sank with the realization that “subject tests” meant that more future Saturdays would begin with your stomach in knots at 8 AM in a cold testing center.

You may have thought applying to graduate school would be more straightforward, but if you’re taking the GRE, you’re likely to find yourself at the same crossroads. Yes, luckily for you, if you’re applying to graduate school in the field of Biology, Biochemistry, Chemistry, Literature (in English), Mathematics, Physics, or Psychology, you have the option to take a GRE Subject Test to support your graduate school application. The tests are administered in April, September, and October and scored on a scale of 200-990 in ten point increments. The Biochemistry, Cell and Molecular Biology; Biology; and Psychology Tests all have subsections scored on a scale of 20-99 in one point increments. The question is, do you need to give up $150 and a weekend?

If you turn to Google for an answer, you’ll immediately find about 394 different opinions, and, if you’re lucky, two will be helpful. Of course the ETS (Educational Testing Service), the company in charge of administering the GRE, makes it sound like coughing  up an additional registration fee to them is the best idea you ever had, while bitter graduate students who were burned by their own scores argue vehemently against the oppressive institution of standardized testing. Ultimately, you’re the only one who has all of the information to make an informed decision about whether or not  you need to take the GRE Subject test for your field. With that in mind, here are some things to consider:

  • Did you check all the programs you’re applying to? Some programs require the GRE Subject tests as part of their application. Figure out if any of your programs require the test NOW! You’ll need to plan ahead if you’re going to study for a subject test while you’re preparing for the standard GRE.
    • “What if the program says the Subject Test is ‘Recommended’”? Here’s where thing get hazy. I mean, if it isn’t “required,” how recommended is “recommended”? Well, for one, how competitive is the program? If you’re applying to one of the top ten programs in your field, “recommended” probably might as well say “required.” But, again, reading through experiences on any graduate school/GRE forum will turn up examples of students who didn’t submit the “recommended” test scores and were unconditionally accepted by their programs as well as students who feel that their submission of said “recommended” scores is the only thing that got them an interview. Really, “recommended” means just that, “recommended;” yes, you can get into the program without submitting scores, but are you really putting your best foot forward if you deny information the program politely asked for?
  • What was your undergraduate program like? If you graduated with honors from the top undergraduate program in your field, you can probably save the $150. However, if you went to a small liberal arts school, you may be just as competitive an applicant, but, if they’ve never had an applicant from your school before, how will your dream program know you’re a star? It may not be the most glamorous option, but showing up at a testing center in sweatpants one extra Saturday may be the best way to show what you know.
  • What was your undergraduate career like? If you have a resume full of REUs, internships, and extracurriculars as well as glowing recommendation letters and a 4.0, you’re probably safe. However, if maybe your GPA could have been better, or you spent your summers working, or you majored in something else altogether in undergrad, a good GRE Subject Test score may help set you apart as a competitive applicant, especially among students who didn’t bother to send in a score.
  • How important is that $150? Students applying to graduate programs come from all different backgrounds. If you’re still completing undergraduate school, the time and money spent preparing for and taking yet another standardized test may simply be out of the question, and that’s OK. However, if you’ve set aside time to and resources to prepare for grad school, there’s no real reason not to take the test. GRE Score Select is available for the subject tests, so if you aren’t happy with your scores, no one has to see them!
  • How will the graduate program use your score? Some programs use the subject tests (particularly those with subsections) for placement purposes. Keep in mind, this could be one reason a program recommends but does not require scores. If you’re confident that your score will help place you out of some coursework, you could end up saving money in the long run; however, if this is the only reason you’re taking the subject test, you should try to figure out if any of the programs you’re applying to actually do use the test for placement purposes.

Important take away? Don’t stress over the GRE Subject Test! Yes, some programs require scores, but even so, your score will just be one number on a multifaceted application—probably the least important one! Remember, the nice thing about the subject tests is that they’re in your field; a little practice and preparation is really all you need.

 

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4 Ways to Improve Your Grad School Odds With a Bad GPA

Afraid your GPA is going to sink  your application! Fear not! There are ways you can make up for a low GPA.

Afraid your GPA is going to sink your application! Fear not! There are ways you can make up for a low GPA.

We often get asked “I have a low GPA. Can I still get into a graduate program?” The answer to this is while a bad GPA does hinder your application, there are steps you can take to mitigate the overall effect the GPA has.

  1. Crush the GRE. This is an absolute must if you have a subpar GPA. If you’re looking at competitive programs, your GRE score is one of the most surefire ways to pull up your entire application. If you have <3.0, in general you want to shoot for a 95th percentile or higher overall to show programs that your academic ability is more than your GPA suggests. Look at GRE test prep services  and practice, practice, practice! There’s no way around it– you must absolutely destroy this exam if you want a good shot at having top programs forgive your GPA.
  2. Publish! A lot! Most, if not all, top programs are research-heavy, so if you have an extensive publishing history, professors will see that you’re both hardworking and well-acquainted with the ins and outs of publishing. If you don’t have any research experience, it’s absolutely imperative you acquire some, either through an internship or post-undergrad research job. Publishing is key to being accepted to graduate school, especially for the natural sciences, and the more publications you have under your belt, the more impressive.
  3. Make Connections. As hand-wavy as the word “networking” may seem, it is an important part of any application. If your advisers know professors in the programs you’re applying to and could make calls around, your chances improve significantly! This alone won’t save your application, but it can be the difference between reviewers immediately discarding your application and taking a second look.
  4. Take Additional Classes. If you have the opportunity, take more classes to pull your GPA up, and if at all possible, look to take the advanced versions of the classes you did poorly in. If you can show that your low GPA was due to freshman year woes and that you succeeded in the more difficult classes, you will be in much better shape!
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Sample GRE Multiple Choice Math Problem – Fun with Fractions!

What about their math scores? They don't need them, do they?

What about their math scores? They don’t need them, do they?

On every GRE Math section, the test makers try to come up with a few extremely difficult problems that will leave even the cleverest students scratching their heads. The really evil part, though, is that even these problems can be solved in under a minute without a calculator – if you know what to do. This means that once you “figure out the trick,” these difficult problems become easy. So, while those test makers are busy cackling with sadistic glee, let’s see if we can’t beat them at their own game.

Consider the following problem:

If Aragorn can dispatch 5 orcs every 11 seconds and Legolas can dispatch 3 orcs every 9 seconds, then together, how many orcs they can dispatch in how many seconds?

A) 2 orcs every 5 seconds

B) 8 orcs every 20 seconds

C) 26 orcs every 33 seconds

D) half an orc every second

E) genocide

To solve this problem, all you need to realize is that the rates at which Aragorn and Legolas slaughter orcs can be represented as fractions and then combined to give their combined rate:

5 orcs every 11 seconds = 5/11

3 orcs every 9 seconds = 3/9 = 1/3

You will notice that we simplified 3/9 to 1/3. It’s always a good idea to simplify fractions whenever possible, as this will save time later. Next, we need to give the fractions like denominators so that we can add them together:

Mass slaughter of orcs doesn't count as genocide, does it?

Mass slaughter of orcs doesn’t count as genocide, does it?

Thus, together they can kill 26 orcs every 33 seconds, and the answer is choice C. If you know what to do, it takes only about 30 seconds to solve this problem. So you see, with practice, even the hardest problems on the GRE become easy. Check back here each week for more extra hard problems and the tricks you need to solve them! Also, remember that you can find out all the tricks from experts like me with a Test Masters course or private tutoring. Until  then, keep up the good work and happy studying!

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What Graduate Programs Should I Apply To?

As you're narrowing down which graduate programs to apply to and attend, take a look at our quick tips!

As you’re narrowing down which graduate programs to apply to and attend, take a look at our quick tips!

As summer begins, and the search for graduate schools ramps up, many of you may be asking “What graduate programs should I apply to? How do I know which ones are the best? We’ll be answering all that and more today!

  • Undergrad prestige doesn’t necessarily translate into graduate program prestige: As wee high schoolers, we’ve all dreamed Ivy League dreams, and while the Ivy League and Company are the top undergraduate institutions, this may not be true for graduate programs. If you take a look at our recent post on The Most Funded Schools, you’ll note that many aren’t even Ivy League schools! The University of Michigan and the University of California, San Francisco dominate NIH funding, and the NSF supports the University of Illionois and the University of California, Berkeley. Gunning for an Ivy League may sound good, but when looking for professorships, an Ivy League program may not hold more weight than another school!
  • It’s the department that matters: Though a school as a whole may be prestigious, the individual departments may have differing levels of excellence. As the law of averages dictates, every school will have above-average departments/programs, and every school will have below-average departments/programs. In general, a school that is prestigious as a whole will have solid departments all around, but there are exceptions to this, so don’t be caught unawares!
  • Talk to your advisors and professors: Only those in a field truly know which programs are well-regarded and which ones are not. Ask around and see what programs your advisor holds in high esteem, and go from there! Academia is all about reputation, and there’s no better compliment than a recommendation from an unaffiliated source. In the end, it’s not national rankings or blogs that can tell you the best programs in the nation — it’s your professors. Listen to their recommendations and go from there!
  • Look at grant funding and publications: If all else fails, take a look at overall grant funding allocations and the frequency of publications in a certain field. Check out which schools are frequently represented in Nature or Science, and check the authors! If an author is highly published in numerous high-impact journals, that’s a good sign for the department and program as a whole!
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