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GRE Quantitative Comparisons Are Easier Than You Think
Another tip to keep in mind as you are doing quantitative comparisons is to compare rather than solve. The GRE is testing your ability to compare the quantities in the columns, NOT to do long calculations. In fact, it is a sure sign that you are doing the problem wrongly if you are doing complex calculations. Your goal should be to compare the columns.
One way to do this is to pay attention to the behavior of larger or smaller values. This means that the given columns may look very similar, but differ by a very minute aspect and your task will be to find out what that ultimately means as to which column is greater. Lets look at an example.
Notice these two columns are very similar. The only difference between them is the number in the denominator. While on the left we have 2 in the denominator, on the right we have something slightly larger 2.01. Now, if you saw this problem on test day, remember our tip: compare rather than calculate. It would be silly and time consuming to try to square the quantity in column B, but we know it is very similar to column A. If we have a slightly larger denominator, is the entire number slightly larger or slightly smaller?
Slightly smaller. Thus in column B we have a slightly smaller number being squared than column A. Thus Column B would end up being smaller when squared. So column A will always be bigger. Thus our answer is A.
This question required you to think about the behavior of numbers– what happens when a number is slightly bigger or smaller than a comparable value. Many quantitative comparisons test this, and that is why it is good to get in the habit of comparing rather than calculating.
In addition to paying attention to slight differences in the columns, it is helpful to simplify the columns as much as possible so that they look alike. This means that you use your arithmetic and algebra skills much like any other math problem, and consolidate the columns until you can compare them.
Lets say we have this as our quantitative comparison problem:
Now, initially it looks like the values would depend on what x and y are, so we would be tempted to choose D. But, if we simplify each column we may discover that we can compare them more accurately.
On the left hand side, if we remember our associative property rules, we know that we can simply drop the parentheses here and combine like terms. 3x and 5x gives us 8x, and we have a minus 5y.
On the right hand side, we need to be more careful with our parentheses, making sure to distribute the negative to each term of the parentheses. Thus we have 10x-7y-2x+2y. Combining like terms give us 8x minus 5 y.
So, lo and behold, they are exactly the same expression. Thus they are equal and our answer is C.
So you see that even if we can’t compare the columns initially, we can work with them until we can compare them. And of course, you will need to utilize your algebra and arithmetic skills here.
Another way to be able to compare the columns quickly and easily is to do the same thing to both columns. Many times, the columns cannot be directly compared unless you perform a mathematical operation on them to make them look similar.
Take this quantitative comparison question for example:
Now, to some viewers this may look daunting. For others, it may look simple. The key thing is to remember the tip of doing the same thing to both columns. Both columns have a radical: the cube root as their form. Thus, if we raised both columns to the third power, the cubed root radical would simply disappear, and our comparison would be much more simplified. So, lets do that. Cubing both sides, I am left with what was underneath the cube root sign.
We can then see that Column B is the product of two terms: the first term 3x, and the second term y squared minus 1. Perhaps we could get the same form in Column A? Let’s see how we do it:
Indeed, if we factor out an x from column A, we are left with x times y squared minus 1. This is very close to column B. Since they both have y squared minus 1, we can divide by them. Thus we have x for column A and 3x for column B. Now this is a much easier problem to handle!
At this point we do not want to divide by x because we need to consider the possible values of x. If x is negative, then column A would be larger, but if x is positive, column B is larger. Thus our answer is still D: not enough information to determine the relationship. This answer was much easier to arrive at once we simplified the problem. We did the same thing to both columns and factored until the columns were much more easily compared.
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The Savvy Way To Get Algebra Problems Right
Another useful tip to remember for these problem solving (a.k.a. discrete quantitative) questions is: If there are variables in the answer choices, plug in a workable number. This is helpful especially for those of you who would rather do arithmetic than algebra. If you choose applicable numbers for the variables, you can turn an algebra problem into an arithmetic problem, and it may streamline your work. Be on the lookout for any problem that contains variables in the answer choices. Lets see what this looks like in an example.
Now, this problem is not hard algebraically if you want to do it that way, but plugging in numbers will definitely be simpler and is especially helpful if you don’t have a clue how to set up this problem.
So, we only have one variable in this problem: f, so lets pick a value that we could use for the length of the string. An easy value would be 10 or 100, but here is an important step. If we look at the answer choices, we can see that if we are going to test them, we need a nice number divisible by 4 if we wanted to work more quickly on choices B and E. So it would be good to pick a number like 40. (If you don’t see this initially, it’s fine… The technique will work if you choose any number, but it is helpful if you look ahead.)
So, lets say this string is 40 feet long. If we cut it according to the problem, we will have one piece at 10 feet and the other at 30 feet. Now, the question asks what is the length of the longer piece. Well, with the number that we picked, the longer piece is 30?
All we have to do now is plug in our chosen value of 40 for f into the answer choices and see which one produces 30.
In choice A, we get 80. That’s not 30, so it’s out. In choice B we get 10. So that’s out. Choice C we get 78, no good. Choice D we get 120, way to high. So hopefully its going to work out for E! Indeed it does… We get 30 for choice E. This matches our scenario so it is the answer. The length of the longest side is 30.
What’s good about this strategy is that you don’t have to spend time trying to come up with an algebraic equation to express the problem. All you have to do is pick a workable number and plug in. From there it’s just arithmetic to match your prediction. So, remember this tip for test day. When you see variables in the answer choices, try to plug in a workable number.
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See How Easily You Can Read Long Passages With These Tips
These steps we took for reading comprehension are the same for short passages as they are for long passages. The difference is, in long passages, you want to make sure you find the main point of each paragraph so that you know what the author is doing over the span of the entire passage. The structure and logic of the passage will emerge nicely if you do this.
So this time, lets examine a longer passage. Before we look at the passage, we want to glance at the first question. “The author reports which of the following about drinks made from cocoa beans” We don’t need to read the answer choices, but now we know we want to be on the lookout for cocoa beans. This looks like a detail question, as it involves specific information from the passage.
In order to see what the author is doing across the entire passage, we need to make a note of what he is doing in each paragraph. So what could we say is the main point of the 1st paragraph?
Well, very simply, it introduces the three main worldwide favorite non-alcoholic beverages, with tea, coffee, and cocoa beans at the top. It looks like tea and coffee are normally neck and neck at the top, but coffee has the edge in international commerce. (If it helps, you can practice jotting down on scratch paper what is going on in each paragraph. In the interests of time, though, it is best to learn to do it in your head for test day.) So with these two short notes before us we can easily recall what the first paragraph is about.
Lets keep reading on to the second paragraph… This second paragraph is about coffee. The main point of it seems to be coffee’s universal appeal, everyone drinks it from the “most fashionable” to the “most hardworking.” There definitely seems to be a positive tone to this paragraph as the author touts the drink as having a place in the “rational diet of all civilized people on the earth.” This is quite a far-reaching positive statement, so we can rest assured the author has a positive attitude towards coffee. (Our short hand notes about this paragraph would just say P2 coffee= universal appeal, everyone drinks it, and the tone is +.) Notice too, that this idea turned out to be the first sentence of the paragraph. Often times the main point of the paragraph will reside in the first 1 or 2 sentences of that paragraph.
Moving on to the third paragraph, the main point seems to be the opposition to coffee. The author lists how coffee has endured prejudices and superstitions, as well as political and fiscal restrictions, but nevertheless “triumphantly moved on” past these oppositions. So the main point here is just the opposition to coffee and that it overcame. (Thus, our shorthand notes would be something like: “opposition to coffee which is religious, political, medical, yet it is triumphant.”) Notice that the author’s attitude towards coffee in this paragraph is a pronounced positive. Talking about a bean as being triumphant certainly exhibits an affirmative sentiment!
Notice then, we followed not only the content of the passage, but also what the author was doing. In the first paragraph, there is an intro to the world’s favorite beverages. In the second, the author discusses coffee’s universal appeal. And in the final paragraph, the author discusses coffee’s triumph over opposition. Over the course of the passage, the author demonstrates his affirmation of coffee, whereas in the beginning, he only seemed to be neutral.
So, we have just read the passage critically, there is one more thing for us to do, and that is to record the author’s intention or purpose. What is he doing with what he says, or what is the purpose of the passage as a whole?
Using the notes we’ve gathered, we can see that the author writes “To affirm (+) coffee a world favorite beverage, universal in appeal, and triumphant in its popularity” (The “+” sign just signifies that the tone is positive.)
With practice you will be able to do this process in your mind, and you will be able to see the general layout of a passage without getting bogged down by the details. It may be helpful to write your notes down in the beginning, though, just as you get the hang of it. Armed with this analysis, then, we can turn to the questions.
Our first question asks about cocoa beans.
Do you remember where we saw cocoa beans?
Back in the first paragraph was the only place the author mentioned them. He says cocoa beans are a distant third in the favorite beverage category. He really doesn’t mention anything else. So we would predict something like cocoa beans were “behind coffee and tea”, or “in the list of favorite beverages”, something like that.
Looking at the answer choices, do we see one that matches our prediction? Yes, choice C- “They are not quite on the same level as coffee and tea.”
Choice A is wrong because it goes directly against what is stated in the passage.
Choice B is wrong because the author does not say anything with regards to it being pleasurable.
Choice D won’t work because it is obviously wrong. The author does not make a single negative comment in the entire passage.
Choice E tests a detail from the first paragraph. We are told all three drinks enjoy world-wide consumption, so this answer is wrong.
So, as you see, predicting an answer choice led us rather quickly to the answer, and was very simple to do once we’ve read the passage critically.
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A Very Effective Tip For Doing Quick Calculations On GRE Math
This question asks, “Which item gave Company Z the most revenue per unit sold in 1998?” Now, if you are quick to try and find the answer, perhaps you would go to the circle graph because it shows percent of total sales in 1998, and then you would try and find a way to convert the percentages to dollar amounts and so on…
But let’s just pause for a minute and ask ourselves: Are we told anywhere in these two charts the price of a pair of shoes or the price of a shirt or handbag? No. We are not told anywhere how much they cost per unit. In the left hand chart, all we are given is total sales in a dollar amount. And in the right hand chart, all we are given is the percentage of total sales. It may be that one pair of shoes cost 500 dollars or one shirt costs 5 dollars. We are not told. Our answer, then, is D. We cannot determine the answer from the information given.
Occasionally you may see a problem like this, in which one of the answer choices is “it cannot be determined.” The test maker is seeing whether you have completely interpreted the given information and are aware of the scope and implications of the information.
If you have been viewing our GRE course, then you will have seen several key steps demonstrated on these types of questions. In summary, then, let’s review the important tips to remember when it comes to data interpretation.
First, as we have stated before, read carefully and use your finger to direct your attention. The cause of most careless mistakes in the data interpretation questions is a failure to pay proper attention to the wording of the question and the part of the chart to which it refers. Take your time to make sure you are directing your efforts in the proper path.
Second, be prepared to convert from percentages to numbers and vice versa. You will need to be very comfortable with percents, decimals, and fractions on test day. These fundamental arithmetic skills are absolutely crucial.
Third, eliminate untenable answers. If you have been viewing the rest of this GRE course, you will know that this is one of the most far-reaching GRE strategies. Untenable just means unreasonable or not able to be defended logically. To eliminate untenable answers means to eliminate answer choices that cannot be correct based on logical reasoning from the problem. We saw that earlier when, if the shoes cost 5000 and were 15% of the total, then an item which is 27% of the total must be bigger than 5000.
Lastly, estimate when necessary using 10% as a tool. Taking 10% of anything is very simple, just move the decimal point one place to the left. If you can do that, you can double what you find to get 20% or take half of it to get to 5%. (So if I needed to know 5% of 635. I could easily just take 10% of it, giving me 63.5, then I could estimate half of it, which would be a little over 31.5.) This is a very helpful tool to use on Data Interpretation problems.
We encourage you to sign-in to our GRE course and review the data interpretation module in totality to be ready for test day! 
You Don’t Have To Be Smart On GRE Data Interpretations
What we want to do is make sure we read carefully and use our finger to direct our eye. In other words, because of the very nature of referring to charts, these questions will require slow reading in order to follow them. Because of this, a good method is to use your finger to point back to the chart that the question is referring to, and the point which they are referring to. Lets demonstrate what we mean by this with a question on our previous chart.
This is a fairly straightforward problem if we have read actively. Notice that the question asks regarding the sales of multiple years, from 1996 to 1998, thus we know we are interested in the left hand chart. It is helpful to put your finger on the left hand chart just so you know you are not dealing with the pie chart. And we know we are only interested in 1996-1998. So we only need 3 out of the 4 years from the chart.
Also, we are interested in shoe sales increase, so we are interested in the blue colored columns, and remember, just the columns from 1996 and 1998 to calculate the percent increase.
As you read the problem carefully, using your finger to direct your eye, you want to identify in your mind the areas of the chart that you will be using to calculate the answer.
Once you have done this, it is a simple calculation. In 1996 it looks like we had 2 and a half thousand dollars in sales for shoes, and in 1998, we had 5 thousand dollars. The formula for percentage increase is Difference Over Original. The increase over that two year period was 2.5, and our original value was 2.5, so our increase was 1.0 or 100%. Choice D is our final answer.
Here is the scratchwork:
Notice that choice A is a trap because it is the quantity that sales increased in that period in thousands. This just goes to show you that each word in a data interpretation is very important… if the question had just asked for the increase in shoe sales, we would have had a different answer.
Let’s try another problem.
This question asks, “What was the average yearly shirt sales from 1995-1998?”, so it is talking about a multi-year value so we are again interested in the left hand chart. And we are interested in Shirt sales, so now we are interested in the red colored columns. And we want to know the average for these 4 years.
So lets list the yearly values. In 1995, it looks like it was 2.5. Many times on the GRE you will have to estimate the value by following your finger over to the proper axis. This one looks like it it about halfway in between the 2 and the 3. In 1996, the red column looks like 4.5; In 1997, it is right on the 3. And in 1998 it is 4.
We need to keep in mind that these values all represent thousands of dollars, but we can perform the average formula and then just multiply by 1000 to find our actual answer. Average is equal to the sum of terms over number of terms. 2.5 plus 4.5 plus 3 plus 4 is 14. Divided by 4 is 3.5, or 3500. So D (3500) is our answer.
Here is our scratchwork.
In order to train your eye to focus on the correct aspects of the data, we encourage you to sign-in to our animated GRE Course, which provides animated walk-throughs of these problems that are easy to follow.
