Practice GRE Quant and Verbal questions

So you’d like practice questions for the GRE?  This blog is for you!

Since you’re here for the practice, let’s go directly to our first question for today — a Quantitative Comparison question. For those not familiar, in these questions you are given information about two Quantities and asked, based on this information, to assess if one of the Quantities is greater, if both are equal, or if the relationship between them cannot be determined.

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Given information: 2m percent of 3n equals 3m percent of 2n

Quantity A:   m

Quantity B:   n

(A) Quantity A is greater.

(B) Quantity B is greater.

(C) The two quantities are equal.

(D) The relationship cannot be determined from the information given.

So, just in case you’re not familiar with the format, we can rephrase the question as ‘Given that 2m percent of 3n equals 3m percent of 2n, which is greater, m or n?’

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Now, before we jump directly into the solution, let’s take a step back. How should you go about solving Quant questions on the GRE?  Should you try to write everything as an equation? Just ‘solve it in your head’ based on basic logic? Maybe try writing down a few examples so that you have an easier time understanding what you’re dealing with?

Good question!  In fact, there is no one right way to solve a GRE question — when approaching GRE questions you need to find the approach that right for you.   Personalizing the solution methods you’ll see to your preferences and abilities is our core mantra at examPAL and is what we devote much of our effort and AI-assisted algorithms towards.  If you like the concept, and the different solutions methods presented here, check us out!

Let’s take a look at a few radically different solutions to the above question.

Solution 1: (Precise methodology)

The first solution we’ll show is what we call the Precise methodology.  These types of approaches are similar to what you would have been taught in a high school or college classroom — write down the relevant equations, work through them carefully, and arrive at the solution.  In this case, we’ll write an equation for m, an equation for n, and see if one expression is larger than the other.

So:  our given data is ‘2m percent of 3n equals 3m percent of 2n’.  Since ‘2m percent of 3n’ is written mathematically as 2m/100*3n and ‘3m percent of 2n’ is written mathematically as 3m/100*2n , then we can write 2m/100*3n=2m/100*2n  Multiplying both sides by 100 gives 2m*3n=3m*2n and dividing by 6 gives mn=mn.  But this is true always!  In other words, we have no idea if m is larger than n or the other way around!  Then (D) is our answer.

Now, let’s say that something in the above solution doesn’t click for you.  Maybe you felt confused about how to translate the given data into an equation, or maybe you didn’t really get the logical inference at the end.  Then the below solution just might be better suited to you.

Solution 2: (Alternative methodology)

Another way to solve this question is based on testing different values of m and n to see which of the answers is definitely wrong, thereby eliminating it from consideration.  Once there is only one option left, it must be the correct answer! This approach is Alternative – it helps us get to the right answer even if we don’t understand why that answer is correct.

Let’s try, for example, m = 0.  Then 2m percent of 3n is 0% of 3n which is always 0, and 3m percent of 2n is 0% of 2n which is also 0.  In other words, we can pick whichever value of n we like!  We can pick, for example, n = 0, in which case the values of m and n are equal, meaning that (A) and (B) can be eliminated.  We can also pick n = 100, in which case the value of n is larger, and (C) can be eliminated.  In other words, since none of (A), (B), or (C) is ALWAYS true, then we can eliminate all of them. The only remaining answer, (D), must be our answer.

OK, so we got lucky and managed to pick good numbers.  (We didn’t really get lucky, there is a technique to picking numbers).  But what if we don’t want to just pick numbers or just brute-force manipulate equations?  What if we really want to understand the answer to the question?

Well, in that case, check out this next solution approach:

Solution 3: (Logical methodology)

The third solution methodology we’ll show is Logical and relies on utilizing the fundamental principles underlying the question’s concepts — in this case the fact that ratios can be expanded or reduced without changing their values. In our case, we’ll expand and reduce our percentages to a common denominator, which will allow us to arrive at an immediate comparison. As a preliminary example, 10% of $100 equals 20% of $50 (both are $10).  In other words, we can take half the percentage from twice the sum, or more generally increase the percentage and reduce the sum by a constant factor.

In our question, instead of taking 2m% from 3n, we can take half of the percentage — m% — from twice the amount — 6n.  Since we’re interested in comparing apples to apples,  we’ll also bring 2n to our common denominator (of 6n).  That is, we’ll take a third of 3m% — m% — from three times 2n — 6n.  Once again, we’ve gotten back to the exact same point:  both percentages represent the exact same quantity! This gives information about m and n together, but not about each one separately, meaning that (D) is our answer.

So what have we seen so far?  We’ve seen a Quantitative Comparison question about an extremely important topic, percents and ratios. We’ve also seen several radically different approaches for solving the question.  When you go about practicing questions, make sure not to just routinely solve, but rather to actively seek out the different ways with which you could solve a given question and to figure out which of those ways fits best for you.

For more GRE Quant practice, go here.  Now, onto Verbal!

We’ll take a look at a Text Completion question. In these questions, your goal is to choose the words that complete the sentence in a grammatically correct and meaningful manner. You will get points for a question only if all of the blanks are filled in correctly.

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Politicians are often thought to be motivated solely by their personal ambition. This, however, is not always the case.  Some politicians are not (i) _____ figures, but (ii) ______ public servants with a true sense of purpose.

Blank (i)

1. equivocal
2. duplicitous
3. rancorous

Blank (ii)

1. cautious
2. obstinate
3. committed

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Solution 1: (Logical methodology)

Now, text completion questions require a mixture of vocabulary and critical analysis.  In these questions, you need to understand what the sentence is trying to say, and then find those words that give it that meaning.

Therefore, the natural approach to these questions is focused on meaning and structure – a Logical methodology.

The text opens by saying that politicians are thought to be motivated by ambition, but directly continues by telling us that this is not always the case.  The second sentence follows the first with specific examples (‘some politicians are…’) so it is natural to expect that the given examples reflect this contrast. In other words, we expect to see examples of politicians who are not motivated solely by ambition.  Then blank (i) should be a word related to ambition. Of the options, only (B) duplicitous, meaning deceitful and insincere, makes sense.  Similarly, blank (ii) should be a positive word, and the only viable option is (F) ‘committed’.

Solution 2: (Alternative methodology)

Now, sometimes it is hard to infer what the sentence is trying to say solely from the given words.  In these cases, we’ll use the answer choices to help us out. Similarly to Quant, a process where we get to the correct answer by an ‘indirect method’, and sometimes without fully understanding why that answer is correct, is an Alternative approach.

In this question, we could have started out by zooming in only on our blanks:  the first blank is ‘politicians are not ___ figures’. Looking at our options, only (B) duplicitous and (C) rancorous make sense – the first states that the politicians are deceitful and the second that they are bitter and angry. (an ‘equivocal figure’ doesn’t make sense; equivocal refers to behavior or words and not to the person themself).

Moving on to our second blank, (D) cautious and (E) obstinate do not make sense – how do they contrast someone who is deceitful or angry? (F) committed does make sense – the politicians do not lie and manipulate (i.e. are not duplicitous), but rather commit themselves to the public and to their purpose.  So (B) and (F) are our best best, and reading the whole sentence with these two choices shows that it makes sense.

OK, so that was an example of Text Completion question.  As before, we saw two fundamentally different approaches for solution.  The first was ‘top-down’: we broke down the logic of the sentence, inferred what sorts of words we were looking for, and then picked those words that best fit our prediction.  The second was ‘bottom-up’: we saw which words fit the immediate context of blank (i), used these words to help find the words that fit blank (ii), and finished by reading the entire sentence to make sure that our top picks made sense.

Take home messages:

In both questions, our focus was not only on finding the right answer, but also on understanding the different methodologies available. Building up your ‘mental toolbox’, i.e. increasing the number of ways you can approach a given question is extremely important, and should be high on your list of priorities when practicing for the GRE.

Want more practice questions and more question-solving strategies?  Check out our free trial here!