{"id":12368,"date":"2019-04-04T19:38:35","date_gmt":"2019-04-04T19:38:35","guid":{"rendered":"https:\/\/www.manhattanprep.com\/gre\/?p=12368"},"modified":"2024-11-13T21:42:59","modified_gmt":"2024-11-13T21:42:59","slug":"gre-quantitative-comparisons-tips","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gre\/blog\/gre-quantitative-comparisons-tips\/","title":{"rendered":"Top 10 GRE Quantitative Comparisons Tips"},"content":{"rendered":"

\"Top<\/p>\n

Good news: GRE Quantitative Comparisons aren\u2019t like anything you had to do in math class. Mastering these tricky problems is a quick way to improve your GRE Quant score without a ton of computation. Get started with our 10 best GRE Quantitative Comparison tips! Then, once you\u2019re done reading, check out the <\/span>GRE Math Strategy Guide<\/span><\/a> for even more.<\/span><\/p>\n

1. Memorize the answer choices on GRE Quantitative Comparisons.<\/b><\/h4>\n

The answer choices are always the same!<\/span><\/a> If you save ten seconds on each Quantitative Comparison (QC) problem by not rereading them, that\u2019s more than a minute saved per Quant section.<\/span><\/p>\n

2. (D) doesn\u2019t stand for \u2018don\u2019t know.\u2019<\/b><\/h4>\n

On GRE Quantitative Comparison problems, answer choices (A),(B), and (C) are pretty straightforward. Then, choice (D) comes out of left field with this: <\/span><\/p>\n

The relationship cannot be determined from the information given.<\/span><\/p>\n

How are you supposed to prove that you <\/span>can\u2019t<\/span><\/i> determine something? Here\u2019s the secret: you aren\u2019t. You can imagine that (D) says this, instead:<\/span><\/p>\n

Quantity A is bigger sometimes, and Quantity B is bigger sometimes.<\/span><\/p>\n

Thinking about it this way will keep things concrete and straightforward. Is Quantity A <\/span>always<\/span><\/i> bigger, no matter what you do? Then pick answer (A). Is Quantity B always bigger? Pick answer (B). But does it go one way in one situation and the opposite way in another? Pick answer (D). (<\/span>By the way, you should also pick (D) if the quantities are sometimes equal and sometimes not equal<\/span><\/a>!)<\/span><\/p>\n

3. Make smart, fast guesses on GRE Quantitative Comparisons.<\/b><\/h4>\n

You\u2019re going to guess on the GRE.<\/span><\/a> The number-one trick for guessing on Quantitative Comparisons? Know which answers to eliminate before you guess. <\/span><\/p>\n

On some GRE QC problems, the two quantities are definite values. They might be values that you and I can\u2019t calculate, like in this problem:<\/span><\/p>\n

Quantity A: <\/b>79<\/span>43<\/sup><\/span><\/p>\n

Quantity B: <\/b>80<\/span>31<\/sup><\/span><\/p>\n

Even though those are huge numbers, they\u2019re both just numbers, not variables or expressions. If both quantities refer to specific numbers, choice (D) can\u2019t be the right answer! Either one of the numbers is bigger than the other, or they\u2019re both equal. Eliminate answer (D) and make a guess.<\/span><\/p>\n

In some cases, you can also tell that the answer shouldn\u2019t be choice (C). Maybe you have no idea whether 79<\/span>43<\/sup><\/span> is bigger or smaller than 80<\/span>31<\/sup><\/span>. But with some logic, you can tell that they <\/span>can\u2019t<\/span><\/i> be equal. After all, 80<\/span>31<\/sup><\/span> has to end in a 0, and 79<\/span>43<\/sup><\/span> definitely doesn\u2019t. Eliminate choice (C) before guessing.<\/span><\/p>\n

Finally, this might seem silly, but be careful not to guess any answer you\u2019ve already eliminated. Suppose that you\u2019re working on a tough Quantitative Comparison problem, and you\u2019ve figured out that Quantity A is <\/span>sometimes<\/span><\/i> bigger. Now you\u2019re running out of time, and you can\u2019t decide whether Quantity B is sometimes bigger, too. You need to make a guess, but don\u2019t make a guess that contradicts what you already figured out. Since A is sometimes bigger, you can definitely eliminate answers (B) and (C) before guessing.<\/span><\/p>\n

4. Simplify everything.<\/b><\/h4>\n

To start any GRE Quantitative Comparison problem, <\/span>breathe and simplify<\/b><\/a>. That\u2019s not a meditation mantra! It\u2019s actually a problem-solving technique. A lot of Quantitative Comparison problems are hard because the information is given to you in an overly-mathematical or complicated form. Simplify the given information and each quantity as much as possible. A good starting point is to try making the two quantities look as similar as possible. For instance, if one contains decimals and the other contains fractions, convert both to the same form before you keep working.<\/span><\/p>\n

Once everything is simplified, the answer might jump out at you! But if it doesn\u2019t, keep reading\u2026<\/span><\/p>\n

5. Try to prove (D).<\/b><\/h4>\n

If you\u2019ve simplified as much as you can, and it isn\u2019t clear which quantity is greater, the next step is to try proving answer (D). The method for doing that is called <\/span>case testing<\/b>. You do it by considering different situations and thinking about which quantity would be greater. Here\u2019s an example:<\/span><\/p>\n

3x<\/em><\/span>\u00b2<\/span> + 5y<\/em><\/span>\u00b2<\/span> > 200<\/span><\/p>\n

x<\/span><\/em>\u00b2<\/span> + y<\/em><\/span>\u00b2<\/span> = 61<\/span><\/p>\n

Quantity A<\/b>: y<\/em><\/span><\/p>\n

Quantity B<\/b>: 3<\/span><\/p>\n

Remember tip number 4 first: simplify! You can simplify the given information into a single inequality: <\/span><\/p>\n

3x<\/em><\/span>\u00b2<\/span> + 5y<\/em><\/span>\u00b2<\/span> > 200<\/span><\/p>\n

3(61\u2013y<\/em><\/span>\u00b2<\/span>) + 5y<\/em><\/span>\u00b2<\/span> > 200<\/span><\/p>\n

183 + 2y<\/em><\/span>\u00b2<\/span> > 200<\/span><\/p>\n

2y<\/em><\/span>\u00b2<\/span> > 17<\/span><\/p>\n

y<\/span><\/em>\u00b2<\/span> > 8.5<\/span><\/p>\n

It looks a lot better, but the answer isn\u2019t completely obvious. The next step is to look at different cases, and the goal when you do that is to prove answer (D). That means proving that Quantity A is bigger sometimes, and Quantity B is bigger other times (alternatively, that they\u2019re sometimes equal, and sometimes different).<\/span><\/p>\n

You already know that y<\/em><\/span>\u00b2<\/span> has to be bigger than 8.5. Start by showing that y can be bigger than 3, since that\u2019s easier! y<\/em> could definitely be 100, 1,000, or even 1,000,000. So, in some cases, y<\/em> is bigger than 3. <\/span><\/p>\n

The next step is to try to show that y<\/em> could be smaller than, or equal to, 3. It turns out that y<\/em> can equal 3, because 3<\/span>\u00b2<\/span> is greater than 8.5. At this point, you\u2019ve successfully proven answer (D): y<\/em> is sometimes equal to 3, and sometimes greater than 3, and since it can go either way, (D) is the right answer. Keep moving!<\/span><\/p>\n

6. Get organized.<\/b><\/h4>\n

Case testing is sometimes a lot more complicated than that. Get organized about it by creating a chart on your scratch paper. <\/span><\/p>\n

\"Manhattan<\/p>\n

Keep everything neat and clear by creating a column on your paper for each value you might have to calculate, and a different row for each case you test. If you need to do additional math, do it off to one side, or above or below your chart.<\/span><\/p>\n

7. Simple first, then weird.<\/b><\/h4>\n

Start by testing a simple scenario, whatever is easier to prove or makes the math more straightforward. We did that in the problem from tips 4 and 5, when we said that <\/span>y<\/span><\/i> could equal 100 or 1,000. Those are simple, round numbers, and since they\u2019re very large, it\u2019s easy to tell that y<\/em><\/span>\u00b2<\/span> is large as well. Don\u2019t think that you need to come up with really exciting cases to test right away. Start with a simple case and just see what happens, then eliminate as many answers as possible on that basis.<\/span><\/p>\n

8. Weird cases? Try ZONEF for QC problems.<\/b><\/h4>\n

Not sure what values to test while solving a GRE Quantitative Comparison problem?<\/span>\u00a0ZONEF is a mnemonic that stands for \u201czero, one, negatives, extremes, fractions,\u201d and it can help remind you which cases are most likely to help you prove answer (D).<\/span><\/p>\n

9. Compare, don\u2019t calculate.<\/b><\/h4>\n

You can solve some GRE Quantitative Comparisons problems with much less math than you\u2019d expect. Here\u2019s an example:<\/span><\/p>\n

A certain class consists of 14 undergraduate students and 9 graduate students. The undergraduates earned an average grade of 70% on the final exam, and the graduates earned an average grade of 80%. <\/span><\/p>\n

Quantity A: <\/b>The average grade earned by the entire class on the final exam<\/span><\/p>\n

Quantity B: <\/b>76%<\/span><\/p>\n

You don\u2019t need to know the exact average grade: you only need to know whether it\u2019s higher or lower than 76%. Before you calculate, pause and reason about the problem. The average should be closer to 70% than to 80%, because there were more undergrads than grads. So it\u2019ll definitely be lower than 76%, and the answer has to be (B).<\/span><\/p>\n

In some GRE Quantitative Comparison problems, you have no choice but to calculate! But in a lot of them, you can get away with just comparing the two values. It doesn\u2019t matter what the exact values are if you can tell which one has to be bigger. Put that calculator away!<\/span><\/p>\n

10. Pay attention to constraints\u2026and non-straints.<\/b><\/h4>\n

A \u201cconstraint,\u201d in a GRE Quantitative Comparison problem, is any extra piece of info that you\u2019re given about the values involved. For instance, \u201cy<\/em> is even\u201d is a constraint. So are \u201cx<\/em> is a positive integer\u201d and \u201ck<\/em> is less than 1.\u201d There are even implied constraints: if somebody has <\/span>b<\/span><\/i> bananas or <\/span>c<\/span><\/i> children, you can safely assume that <\/span>b<\/span><\/i> and <\/span>c<\/span><\/i> are integers!<\/span><\/p>\n

If a QC problem includes a constraint, always jot it down on your paper. Many of these problems are designed so that the answer comes out differently if you ignore the constraint! The test writers are hoping to trap people who don\u2019t notice, or forget about, a constraint. <\/span><\/p>\n

You should also train yourself to notice constraints that <\/span>aren\u2019t<\/span><\/i> there. If a problem doesn\u2019t tell you that <\/span>x<\/span><\/i> and <\/span>y<\/span><\/i> have to be positive, it\u2019s possible that something interesting will happen when you make them negative! If a problem doesn\u2019t say that all of the numbers are integers, check what happens when you use fractions! And if there isn\u2019t a constraint, anything is fair game, and a great test taker knows when to get creative.<\/span><\/p>\n

Bonus: <\/b>Quantitative Comparisons are usually pretty short problems. That makes it tempting to dive into a problem without slowing down and thinking it through first. But, in our experience, slowing down at the beginning of a GRE Quantitative Comparison problem pays off. Take the extra few seconds to tidy your scratch work and really read everything in the problem. It might make you a little slower on each problem, but it\u2019ll pay off when you avoid getting confused and bogged down.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Good news: GRE Quantitative Comparisons aren\u2019t like anything you had to do in math class. Mastering these tricky problems is a quick way to improve your GRE Quant score without a ton of computation. Get started with our 10 best GRE Quantitative Comparison tips! Then, once you\u2019re done reading, check out the GRE Math Strategy […]<\/p>\n","protected":false},"author":99,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,474284,921840,421,6,7,9,530104,733445],"tags":[1363318,1363317,127411],"yst_prominent_words":[1362788,1363303,1363298,1363305,1362627,1363294,1363289,1363293,1363292,1363306,1363290,1363291,1363295,1363299,1363304],"class_list":["post-12368","post","type-post","status-publish","format-standard","hentry","category-challenge-problems","category-current-studiers","category-gre-prep-2","category-gre-quant-2","category-gre-strategies","category-how-to-study","category-math-gre-strategies","category-quantitative-comparison-math-gre-strategies","category-study-tips-2","tag-case-testing","tag-gre-quantitative-comparisons-tips","tag-zonef"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/12368","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/users\/99"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/comments?post=12368"}],"version-history":[{"count":6,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/12368\/revisions"}],"predecessor-version":[{"id":13044,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/12368\/revisions\/13044"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/media?parent=12368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/categories?post=12368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/tags?post=12368"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/yst_prominent_words?post=12368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}