{"id":10112,"date":"2017-03-15T17:00:05","date_gmt":"2017-03-15T17:00:05","guid":{"rendered":"http:\/\/www.manhattanprep.com\/gre\/?p=10112"},"modified":"2019-08-30T16:38:57","modified_gmt":"2019-08-30T16:38:57","slug":"tackling-gre-word-problems-one-thing-at-a-time","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gre\/blog\/tackling-gre-word-problems-one-thing-at-a-time\/","title":{"rendered":"Tackling GRE Word Problems: One Thing at a Time"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-10165\" src=\"http:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2017\/03\/3-15-17-social-1.png\" alt=\"Manhattan Prep GRE Blog - Tackling GRE Word Problems: One Thing at a Time by Neil Thornton\" width=\"1200\" height=\"628\" srcset=\"https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2017\/03\/3-15-17-social-1.png 1200w, https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2017\/03\/3-15-17-social-1-300x157.png 300w, https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2017\/03\/3-15-17-social-1-768x402.png 768w, https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2017\/03\/3-15-17-social-1-1024x536.png 1024w\" sizes=\"auto, (max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><b><i>Did you know that you can attend the first session of any of our online or in-person GRE courses absolutely free? We\u2019re not kidding! <\/i><\/b><a id=\"bloglink\" href=\"https:\/\/www.manhattanprep.com\/gre\/classes\/\" target=\"_blank\"><b><i>Check out our upcoming courses here<\/i><\/b><\/a><b><i>.<\/i><\/b><\/p>\n<hr \/>\n<p><span style=\"font-weight: 400;\">\u201cThe man who moves a mountain begins by carrying away small stones.\u201d -Confucius<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Recently, one of my students emailed me the following question. I imagine at some point in your GRE practice you\u2019ve run into the same issue:<\/span><!--more--><\/p>\n<p><i><span style=\"font-weight: 400;\">\u201cI\u2019m still having a hard time tackling Quant problems. I\u2019ll read the question and sort-of know what it\u2019s asking me, but by the time I start figuring it out I run out of time and need to just pick something and move on.\u00a0I just don\u2019t know how\/where to start or how to get quicker at it. My guess is that I just need to practice, practice, practice. But I wanted to just reach out and see what you thought and see if you had any suggestions.\u201d<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">If that sounds familiar, you\u2019re facing one of the most common problems on GRE Quant. Yes: practice, practice, practice (and learn your mechanics and times tables). However, you may also want to shift the way you look at longer Quant problems. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">You, like many students, may be trying to plan your way through the <\/span><i><span style=\"font-weight: 400;\">whole<\/span><\/i><span style=\"font-weight: 400;\"> question before you write anything on your scratch paper, trying to \u201cset it up\u201d entirely in your mind before you get to work. Therefore, you end up stuck, with no idea how you\u2019re going to begin to put it all together, much less get to the end of the problem. This holistic \u201cdoing math in space\u201d method will sometimes work with very easy one-step problems, but not with anything more complicated.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The best GRE word problems are elegant little puzzle boxes (really, I love them). You won\u2019t even know what step two is asking until you solve step one. Therefore, relax. Just focus on the first sentence, or even just the first phrase, or one tiny piece in the middle you know you can handle. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Each step, ask yourself: <\/span><b>What can I write down? What formulas and rules apply? What math can I do right now? What else do I know?<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Take the following (made up) problem: <\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">The area of a right triangle is 24 square inches. The base of the triangle is two inches longer than the height. What is its hypotenuse?<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">If you try to set up that whole problem \u201cholistically,\u201d you might get some awful unsolvable quadratic garbage: \u00bd(x)(x+2) = 24??? And then maybe Pythagoras? (x)^2 + (x+2)^2 = c^2????? Ugh. No.<\/span><\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/giphy.com\/embed\/KrLqtbe8PGEDe\" width=\"480\" height=\"327\" frameBorder=\"0\" class=\"giphy-embed\" allowFullScreen><\/iframe><\/p>\n<p><a href=\"http:\/\/giphy.com\/gifs\/meme-ahora-no-por-favor-porfavor-KrLqtbe8PGEDe\"><\/a><\/p>\n<p><span style=\"font-weight: 400;\">You barely need ANY algebra to solve GRE word problems like this. Just focus ONLY on the first bit, work out what you know, and go from there:<\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">The area of a right triangle is 24 square inches\u2026<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">STOP! Don\u2019t read more than that! Breathe. Draw the triangle. Make sure it\u2019s marked as a right triangle. Write down the formula you know: \u00bd * b * h = 24 and get to work. Oh, okay\u2026 that means b * h must be 48. What else do I know? 48 might be 1 * 48, 2 * 24, 3 *16, 4 * 12, or 6 * 8\u2026<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Stay there in the space after the period and do as much work as you can. Squeeze every drop out of the one little piece of the puzzle you CAN solve, and only then move on to the next step.<\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">The base of the triangle is two inches longer than the height.<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">Now, add that to what you already know. Interesting. You already know 48 could mean 1 * 48, 2 * 24, 3 *16, 4 * 12, or 6 * 8, so\u2026 Oh, hey! The only combination that works is 6 and 8 (8 is 2 more than 6). Wait, which one is longer? The base? So that must mean the base is 8 and the height is 6. Add that info to your figure. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Then, and only then, face the final question:<\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">What is the hypotenuse?<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">I could work out the Pythagorean theorem or (with practice) recognize that this is a classic 3:4:5 right triangle times 2, or 6:8:10. So the hypotenuse must be 10. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">And you\u2019re done. The answer is 10. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">What\u2019s the lesson? <\/span><b>Take it in tiny bite-sized pieces and you will avoid all kinds of headache.<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Let\u2019s look at another one:<\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">Yumiko spends 1\/5 of her monthly income on rent. She then spends 3\/8 of the remainder on food<\/span><\/i><span style=\"font-weight: 400;\">. <\/span><i><span style=\"font-weight: 400;\">After that, she puts 1\/3 of what\u2019s left over into a savings account. What fraction of her income does she put into savings each month? <\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">Holistically\/algebraically, this is a nightmare: Is it x &#8211; \u00a0(1\/5)(3\/8)(1\/3)(x)? Is it (1\/3)(3\/8)(4\/5)(x)? Who knows? Who cares? (Both of those are wrong, by the way)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">If the problem starts with an unknown amount, \u201c<\/span><i><span style=\"font-weight: 400;\">Yumiko spends 1\/5 of her monthly income on rent<\/span><\/i><span style=\"font-weight: 400;\">\u201d (income is unknown) and only asks you for a fractional answer, the easiest thing to do is to make up your own \u201csmart number.\u201d [You\u2019ll learn this and all kinds of other great techniques in <\/span><a id=\"bloglink\" href=\"https:\/\/www.manhattanprep.com\/gre\/prep\/complete-course\/\" target=\"_blank\"><span style=\"font-weight: 400;\">our classes<\/span><\/a><span style=\"font-weight: 400;\">.]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Look at the fractions in the problem (1\/5, 3\/8, 1\/3). I\u2019ll start with a nice easy multiple of those denominators for Yumiko\u2019s income (5 * 8 * 3 = $120) and get to work. But on ONLY the first bit.<\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">Yumiko spends 1\/5 of her monthly income on rent.<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">Don\u2019t read further. Do your math. Okay, that means she spends 1\/5 of $120, or $24 on rent. What else do I know? She must have $96 remaining.<\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">She then spends 3\/8 of the remainder on food<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">Okay. 3\/8 of that $96 is going to be $36. So now, she has 96 \u2013 36 = $60 left over.<\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">After that, she puts 1\/3 of what\u2019s left over into a savings account. <\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">What\u2019s 1\/3 of $60? $20 goes into her savings account. Then, and only then, tackle the question. <\/span><\/p>\n<p style=\"padding-left: 30px;\"><i><span style=\"font-weight: 400;\">What fraction of her income does she put into savings each month? <\/span><\/i><\/p>\n<p><span style=\"font-weight: 400;\">$20 out of $120 is 20\/120, which reduces to 1\/6. Therefore, the answer is 1\/6!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">And yes: practice. Notice the real key to speed is your ability to do the little pieces quickly and accurately (factor 48, get 3\/8 of 96). For now, relax. Take your time on every practice problem, but get confident that you CAN solve the little pieces. Even if you don\u2019t know how you\u2019re going to get there, confidently jump in anyway. Start writing and solving and tinkering. Trust that you\u2019ll get there eventually.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">And have fun. As I said, GRE word problems are often elegant little puzzles to solve, and with time you can learn to love the process of taking them apart. ?<\/span><\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/giphy.com\/embed\/3GnCVaJAGhfJ6\" width=\"480\" height=\"357\" frameBorder=\"0\" class=\"giphy-embed\" allowFullScreen><\/iframe><\/p>\n<p><a href=\"http:\/\/giphy.com\/gifs\/memory-puzzle-chimp-3GnCVaJAGhfJ6\"><\/a><\/p>\n<hr \/>\n<p><b><i>Find Neil\u2019s musings helpful? We all do. Don\u2019t forget that you can join him twice monthly for a free hour and a half study session in <\/i><\/b><a id=\"bloglink\" href=\"https:\/\/www.manhattanprep.com\/gre\/mondays-with-neil\/\" target=\"_blank\"><b><i>Mondays with Neil<\/i><\/b><\/a><b><i>.<\/i><\/b><\/p>\n<hr \/>\n<p><b><i><a href=\"https:\/\/www.manhattanprep.com\/gre\/mondays-with-neil\/?utm_source=manhattanprep.com%2Fgre%2Fblog&#038;utm_medium=blog&#038;utm_content=GRE%20Blog%20Mondays%20with%20Neil%20Plug&#038;utm_campaign=GRE%20Blog%20Product%20Push\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-9096 size-thumbnail\" src=\"https:\/\/d27gmszdzgfpo3.cloudfront.net\/gre\/wp-content\/uploads\/sites\/19\/2016\/06\/neil-thornton-150x150.png\" alt=\"Neil Thornton Instructor Headshot\" width=\"150\" height=\"150\" \/><\/a><\/i><\/b><i><em><strong>When not onstage telling jokes, <a href=\"https:\/\/www.manhattanprep.com\/instructors\/neil-thornton\/\" target=\"_blank\">Neil Thornton<\/a> loves teaching you to beat the GRE and GMAT.<\/strong> Since 1991, he\u2019s coached thousands of students through the GRE, GMAT, LSAT, MCAT, and SAT, and trained instructors all over the United States. He scored 780 on the GMAT, a perfect 170Q\/170V on the GRE, and a 99th-percentile score on the LSAT. <a href=\"https:\/\/www.manhattanprep.com\/gre\/classes\/#instructor\/35\" target=\"_blank\">Check out Neil\u2019s upcoming GRE course offerings here<\/a>\u00a0or join him for a free online study session twice monthly in\u00a0<a href=\"https:\/\/www.manhattanprep.com\/gre\/mondays-with-neil\/\" target=\"_blank\">Mondays with Neil<\/a>.<\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Did you know that you can attend the first session of any of our online or in-person GRE courses absolutely free? We\u2019re not kidding! Check out our upcoming courses here. \u201cThe man who moves a mountain begins by carrying away small stones.\u201d -Confucius Recently, one of my students emailed me the following question. I imagine [&hellip;]<\/p>\n","protected":false},"author":23,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,474284,921840,421,6,7,9,733445],"tags":[1362372],"yst_prominent_words":[],"class_list":["post-10112","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-study-tips-2","tag-gre-word-problem"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/10112","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\/23"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/comments?post=10112"}],"version-history":[{"count":7,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/10112\/revisions"}],"predecessor-version":[{"id":10167,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/10112\/revisions\/10167"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/media?parent=10112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/categories?post=10112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/tags?post=10112"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/yst_prominent_words?post=10112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}