![\"Manhattan](\"http:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2017\/07\/mental-math-magic-neil-thornton-gre.png\")
<\/p>\n<\/p>\n
You can attend the first session of any of our online or in-person GRE courses absolutely free. Ready to take the plunge? <\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n <\/i><\/b>Quick! How long did it take you to figure those out using mental math? Did you need a pencil or a calculator? Are you 100% sure you\u2019re right? Do you know a way to check your answers? Do you <\/span>still<\/span><\/i> not know the results? (Okay, lazybones: 108, 729, 14, 58).<\/span><\/p>\n If you\u2019re like most students, your major concern about the Quant section of the GRE is <\/span>time<\/span><\/i>. You could get way more questions right if you only had more <\/span>time<\/span><\/i>. <\/span><\/p>\n The GRE is never as easy as knowing 12 x 9 = 108. However, a single tough GRE problem may require a handful of little calculations, each of which can eat up precious time. If you know 12 x 9 = 108, you\u2019re done in seconds. If you have to pop out the calculator and key in each number carefully, you\u2019ve added 30 seconds for each calculation, or several MINUTES to each problem\u2014time you just don\u2019t have. <\/span><\/p>\n Yes, you have a calculator, but you can\u2019t rely on it. You MUST know your basic times tables. 2 x 1, 2 x 2, 2 x 3\u20267 x 8, 7 x 9\u2026all the way to 12 x 12 (at least).<\/span><\/p>\n Write the numbers 1 through 12 across the top of a piece of paper. Then 1 through 12 down the left-hand side. Get to work filling in the grid with all those multiples. Next week, mix up the numbers, or fill the spaces in randomly. Once you have them locked, add 13s and 14s to the mix. Can you count up by 17s? 19s?<\/span><\/p>\n Make flashcards of the tough ones. Download iPhone apps. Run through your 7\u2019s as you\u2019re walking to work. 42\u202649\u202656\u202663\u2026<\/span><\/p>\n Addition of all single-digit numbers: 1+1 to 9+9 Rules of divisibility: Can you look at a number and tell whether it\u2019s divisible by 2, 3, 4, 5, 6, 8, 9, or 10? Check out our <\/span>Number Properties Strategy Guide<\/span><\/a> for all of these rules. <\/span><\/p>\n Perfect squares: 1\u00b2<\/span>, 2\u00b2<\/span>, 3\u00b2<\/span>\u2026 all the way to 20\u00b2 Powers of 2: 2\u00b9<\/span>\u00a0to 210 Lock these in and you\u2019ll be saving 10 seconds here, 30 seconds there, all of which will add up to finishing way more problems than your competition. Even if you don\u2019t have everything perfect, all the effort will be worth it. Other people will see 243 and not know what to do (is it prime? What?). You\u2019ll see 243 and think \u201cHmm, that looks like one of those powers I memorized. Okay, the digits add up to 9, so that\u2019s a multiple of 9\u2026so it must be a power of 3. Which one? Well, 81 is 3<\/span>4<\/sup><\/span>, so 243 must be 3<\/span>5<\/sup><\/span>!\u201d<\/span><\/p>\n After you have the basics memorized, you can get to all the ways to impress your friends (if they\u2019re not already impressed by 14 x 14 = 196). I\u2019ll show you more tools and tricks for mental math magic in future articles, but let\u2019s learn the first principle of quick mental math: Go Left to Right.<\/span><\/p>\n When you learned so-called \u201clong\u201d multiplication in grade school, you learned a RIGHT to LEFT technique that is practical on paper (and very useful on the GRE), but nearly impossible to perform in your head. Take 23 x 9:<\/span><\/p>\n 23 Notice, old-school multiplication goes right to left. \u201cWhat is 3 times 9? 27? Okay, carry the 2\u2026 What is 2 times 9? 18, add the 2 to get 20. So 207.\u201d That\u2019s cool. Good to know, but you can actually do this in your head (with maybe a little help from your pencil) if you go LEFT to RIGHT instead.<\/span><\/p>\n 23 x 9.<\/span><\/p>\n Think of 23 as 20 plus 3. Now multiply things left to right. 20 x 9 is 180. Store that or write it down. Now 3 x 9 = 27. Add 180 to 27 and you get 207. Way easier. No need to \u201ccarry\u201d anything. <\/span><\/p>\n Let\u2019s try a tougher one\u2014253 x 4.<\/span><\/p>\n Think of that 253 as 200+50+3.<\/span><\/p>\n 200 x 4 = 800 Add \u2018em up and you get 1012!<\/span><\/p>\n Remember 12 x 9? If I don\u2019t have it memorized, I can use the left to right technique: <\/span><\/p>\n 10 x 9 = 90 Therefore 12 x 9 = 108. But how can I be relatively sure that I didn\u2019t make a mistake?<\/span><\/p>\n First, I make sure I\u2019m in the right range by rounding the numbers to easy things (10, 100, 25). <\/span><\/p>\n 9 is a little less than 10. 12 is a little more than 10. 10 x 10 = 100, so I know I\u2019m looking for a number close to 100. 108 is close enough. <\/span><\/p>\n 23 x 9? 9 is close to 10, so I\u2019m looking for an answer less than 230. 207 is close enough.<\/span><\/p>\n 253 x 4? 253 is very close to 250, so I\u2019m looking for something close to 1000. 1012 is close enough.<\/span><\/p>\n Multiples of 9 are a little magical. To check whether a number is divisible by 9, add all the digits together. If you get 9 or a multiple of 9, you know you have a multiple of 9. <\/span><\/p>\n 12 x 9 = 108. Add those digits together: 1+0+8 = 9. I\u2019m pretty sure I have it right. If I get 107, the digits add up to 8, so I know I made a mistake.<\/span><\/p>\n Wait, does 9\u00b3<\/span>\u00a0= 719? Or 721? Or 729? The only one in which the digits add up to a multiple of 9 is 729. 7+2+9 = 18, so that\u2019s probably it. Also, 10 x 10 x 10 is 1000, so 729 is in the right ballpark. 243 would be way too low.<\/span><\/p>\n You can\u2019t spend all day every day doing GRE problems without going a little crazy, but you can have fun throughout the day practicing your mental math. As you\u2019re walking and driving, do your times tables, run through your perfect cubes. Add up groceries in your head. Estimate the tax. Practice ballparking to divide the dinner check by the number of people at the table; estimate the tip. <\/span><\/p>\n Whenever you see a number (an address, an area code), double it, triple it, multiply it by 7. Check to see what it\u2019s divisible by. (I used to live in New Orleans, area code 504. 504 is divisible by 2, 3, 4, 6, and 9. And 504 x 7 is 3528, or is it?)<\/span><\/p>\n A week or two of this kind of practice can cut your calculation time (not to mention your stress levels) in half or more. Do it! Have fun. <\/span><\/p>\n More to come! ?<\/span><\/p>\n Want more guidance from our GRE gurus? You can attend the first session of any of our online or in-person GRE courses absolutely free! We\u2019re not kidding. <\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n You can attend the first session of any of our online or in-person GRE courses absolutely free. Ready to take the plunge? Check out our upcoming courses here. Quick! What is 12 x 9? What is 9\u00b3? What is the square root of 196? What is 95 \u2013 37?<\/p>\n","protected":false},"author":23,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,474284,921840,421,6,7,9,10,154333],"tags":[1362455],"yst_prominent_words":[],"class_list":["post-10530","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-gre-basic-math","category-taking-the-gre-2","tag-mental-math"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/10530","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=10530"}],"version-history":[{"count":2,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/10530\/revisions"}],"predecessor-version":[{"id":10547,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/10530\/revisions\/10547"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/media?parent=10530"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/categories?post=10530"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/tags?post=10530"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/yst_prominent_words?post=10530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n
\n<\/span>What is 12 x 9?
\n<\/span>What is 9\u00b3<\/span>?
\n<\/span>What is the square root of 196?
\n<\/span>What is 95 \u2013 37?<\/span><\/p>\nPhase 1: Memorize Your Basics<\/b><\/h4>\n
Other Basics to Know<\/b><\/h4>\n
\n<\/span>Subtraction of all \u201cteens\u201d: 11 \u2014 2, 11 \u2014 3\u2026 18 \u2014 9, etc.<\/span><\/p>\n
\n<\/span>Perfect cubes: 1\u00b3<\/span>\u00a0to 10\u00b3<\/span><\/p>\n
\n<\/sup><\/span>Powers of 3: 3<\/span>1<\/sup><\/span> to 3<\/span>6<\/sup><\/span> (Note that 3<\/span>6<\/sup><\/span> is the same as 9<\/span>3<\/sup><\/span>. Why would that be?)
\n<\/span>Powers of 5: 5<\/span>1\u00a0<\/sup><\/span>to 5<\/span>4<\/sup><\/span><\/p>\nPhase 2: Mental Math Magic<\/b><\/h4>\n
\n<\/span>x 9<\/span><\/p>\n
\n<\/span>50 x 4 = 200
\n<\/span>3 x 4 = 12<\/span><\/p>\nPhase 3: Check Your Work<\/b><\/h4>\n
\n<\/span>2 x 9 = 18<\/span><\/p>\nBallpark<\/b><\/h4>\n
Check Divisibility<\/b><\/h4>\n
Practice and Play<\/b><\/h4>\n
\n
\n![\"Neil](\"https:\/\/d27gmszdzgfpo3.cloudfront.net\/gre\/wp-content\/uploads\/sites\/19\/2016\/06\/neil-thornton-150x150.png\")
<\/a><\/i><\/b>When not onstage telling jokes,\u00a0Neil Thornton<\/a>\u00a0loves teaching you to beat the GRE and GMAT.<\/strong>\u00a0Since 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.\u00a0Check out Neil\u2019s upcoming GRE course offerings here<\/a>\u00a0or join him for a free online study session twice monthly in\u00a0Mondays with Neil<\/a>.<\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"