Quantitative Comparison Questions for GRE Preparation

Strategies when the numbers are huge Let us try a tricky quantitative comparison question. Let’s see if you can get it in less than one minutes!

Quantity-A	Quantity-B
10^7	7^10

One way of solving this problem is to do the tedious calculations. However, doing so is a time-consuming, error-prone process, and though it may work, the GRE is not testing your ability to do laborious mathematics. Rather, it is testing the way you think, your logical approach to a complex problem. One useful approach is to approximate. For instance if we take 7^² we get 49. Notice 49 is very close to 50. So let’s say 7^² is equal to 50. Therefore (7^²)^² is equal to 50^² or 2500. 2500 can also be represented as 2.5 x 10^³. So when we take 2500^² or 7^⁸ we can convert 2500 into 2.5 x 10^3 and we have (2.5 x 10^³)^². Again, because we are approximating let’s round 2.5 down to 2. Now we have (2 x 10^³)^² = 4 x 10^⁶ = 7^⁸ . This figure is almost as large as 10^7. Since we are comparing 7^¹⁰ to 10^⁷ you can see that 7^¹⁰ will be much larger. Granted, this method still involves a decent amount of calculation. Another technique we can apply is pattern recognition. For example, we can use smaller numbers that adhere to the pattern above. So let’s compare 2^⁵ to 5^². Notice that I’ve kept a similar pattern to the original question: x^^y vs. y^^x. , where y = x + 3. In this case we get 2^⁵ = 32 and 5^² = 25. Notice that the number with the greater exponent is greater. We should try one more set of numbers just to be sure, 3^{^6} vs. 6^³. Notice that this time the difference between 3^⁶ and 6^³ is even greater than that between 2^⁵ and 5^². That is, the difference between x^{^y} and y^^x where y = x + 3 increases the larger the numbers we plug in. Therefore 7^¹⁰ will be much greater than 10^⁷. The answer is (B).

Vocabulary in Context with GRE Preparation

Hello Everyone! All you GRE Aspirants – Are you in good shape? Holiday season is approaching and most of you must have finished your exams, so this is an appropriate time to hang around with friends and have a great time. Even the winter has started to show its charm. Days are becoming shorter and shorter. Sun refuses to wake up from its slumber even till 10 in the morning. So, what has all this got to do with GRE? I just want to say that this is the ideal time to develop a laid back attitude and to water down the hard work that you must have put in, in the previous months. Though holidays are around, spend some time for GRE prep. If not doing some serious study, try to read some good articles or books that may keep you vocabulary fresh in your mind. I stumbled upon an article during my regular readings and I thought that I should share the same with you. This one is from the New York Times entitled A Nose For Words. In this article, the author talks about his first exposure to vocabulary and how he develops an affinity towards it. So, if you are one of those students, who just despair at the mention of some unwieldy words like hortatory, cleave, recondite, my advice for you is to read this article.