![\"GMAT](\"https:\/\/www.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2019\/12\/mprep-blogimages-wave1-24-e1575900924807.png\")
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What if I told you that you could have five extra minutes on the quantitative section of the GMAT? Would you be interested?<\/span><\/p>\n Good, because this is going to get a little technical. I\u2019m also going to assume you\u2019ve had some experience with Data Sufficiency problems on the GMAT Math section. You should also have practiced testing cases to solve these problems: <\/span>here\u2019s a good introduction to that strategy<\/span><\/a> in case you\u2019re unfamiliar.<\/span><\/p>\n <\/p>\n Now, to save yourself the five minutes I promised, you have to understand something I\u2019m naming the Moliski Theorem. Though I\u2019ve heard it discussed by several people, I\u2019m naming it after my colleague Liz Moliski, who was the first person I saw actually float this idea while teaching a class. The theorem applies to any Data Sufficiency question that has a <\/span>yes\/no answer<\/span><\/a>. For example, the theorem is applicable to this Data Sufficiency question:<\/span><\/p>\n Did Rocky the dog eat more dog treats this year than he did last year?<\/span><\/p>\n It is not, however, applicable to this question, since the question asks for a specific value:<\/span><\/p>\n How many dog treats did Rocky the dog eat this year?<\/span><\/p>\n Here\u2019s the Moliski theorem, put simply: Attempt to find one concrete example of the statement where the answer to the question is \u201cno.\u201d If you can find such an example, the statement is not sufficient. If you can\u2019t find such an example, the statement <\/span>is<\/span><\/i> sufficient.<\/span><\/p>\n That\u2019s it! Is your mind blown yet? Cause mine is.<\/span><\/p>\n You see, up until I saw Liz teach, I\u2019d always assumed you needed <\/span>two<\/span><\/i> concrete examples of the statement that got you two different answers to the question in order to show that the statement is not sufficient. Defining those examples was time-consuming. The Moliski theorem not only obviates the need for the second example, it also makes it extremely simple to define the single example you\u2019re looking for. Since I now only need to define and find half the examples than I did before, I have been able to solve Data Sufficiency problems in half the time that it took me previously, going from two minutes (on average) down to one. I have seen at least five yes\/no Data Sufficiency questions on each of my <\/span>practice tests<\/span><\/a>, meaning this idea has bought me at least five full minutes of extra time.<\/span><\/p>\n I\u2019m going to show you a Data Sufficiency problem. Try to solve it on your own first. Then we\u2019ll apply the Moliski theorem.<\/span><\/p>\n If x and y are integers, is the product xy even?<\/span><\/i><\/p>\n Remember, the Moliski theorem says we should attempt to find examples where the answer to the question is \u201cno.\u201d In this case, that means we <\/span>don\u2019t<\/span><\/i> actually want the product <\/span>xy<\/span><\/i> to be even; we want that product to be odd.<\/span><\/p>\n Now let\u2019s find our examples. Can I find an example of statement (1), which says <\/span>x<\/span><\/i> \u2013 <\/span>y<\/span><\/i> < 3, where the product <\/span>xy<\/span><\/i> is odd? Sure I can: 7 and 5, for example. 7 \u2013 5 is 2, that\u2019s less than 3. The product 7 \u00b7 5 is 35, which is odd. Statement (1) is therefore not sufficient.<\/span><\/p>\n Moving on to statement (2): I want to find numbers where <\/span>x<\/span><\/i> + <\/span>y<\/span><\/i> is odd, and also where the product <\/span>xy<\/span><\/i> is odd. Well that\u2019s impossible, since if <\/span>x<\/span><\/i> + <\/span>y<\/span><\/i> is odd, then one or the other must be even, meaning when I multiply them together, there\u2019s no way I\u2019ll ever get an odd number. Since I couldn\u2019t find my example, statement (2) <\/span>is<\/span><\/i> sufficient. Now we know that the correct answer is (B).<\/span><\/p>\n Are you excited yet? Try this super-tough problem:<\/p>\n Is x > 0?<\/i><\/p>\n The Moliski theorem tells us we\u00a0don\u2019t<\/i>\u00a0want\u00a0x<\/i>\u00a0to be greater than 0; we want it to be less than 0. In other words, we want\u00a0x<\/i>\u00a0to be negative.<\/p>\n Try to find a negative number\u00a0x<\/i>\u00a0that would make statement (1) true. So, I know that\u00a0x\u00b2<\/i>\u00a0< 9. Can\u00a0x<\/i>\u00a0be negative? Sure, as long as it\u2019s a negative fraction like\u00a0\u20131\/2. Statement (1) is not sufficient.<\/p>\n Now try to find a negative number for\u00a0x<\/i>\u00a0that would make statement (2) true. If\u00a0x\u00b3<\/i>\u00a0>\u00a0x<\/i>, can\u00a0x<\/i>\u00a0be negative? There\u2019s no reason to reinvent the wheel, let\u2019s just use\u00a0x<\/i>\u00a0=\u20131\/2\u00a0again. If you cube that, it\u2019s greater than what you started with. So statement (2) is also not sufficient.<\/p>\n And oh, by the way, since\u00a0\u20131\/2\u00a0is an example that satisfies both statements, and gives us the \u201cno\u201d answer we\u2019re looking for, the correct answer to this question is (E).<\/p>\n LET\u2019S GOOOOOOO<\/span><\/p>\n Occasionally, the Moliski theorem fails. Here\u2019s an example:<\/span><\/p>\n Is x > 10?<\/span><\/i><\/p>\n Both of these statements are sufficient on their own to answer the question, so the correct answer is (D), but the Moliski theorem would lead you to decide they are not (and would therefore lead you to incorrect answer (E)). These statements are each sufficient because the answer to the question is <\/span>always<\/span><\/i> \u201cno,\u201d meaning they technically <\/span>do<\/span><\/i> provide us enough information to answer that question. Liz mentioned this possibility in her class, noting that if you want to be thorough and precise, you should find a \u201cyes\u201d case <\/span>after<\/span><\/i> you\u2019ve found a \u201cno\u201d case.<\/span><\/p>\n Don\u2019t, however, let the rain fall on your parade quite yet. The \u201calways no\u201d situation is <\/span>exceedingly rare;<\/span><\/i> in my professional experience, it shows up on roughly 1% of all Data Sufficiency questions (probably even fewer, to be honest). So, we are still looking at a strategy that works 99+% of the time and saves you 5+ minutes: personally, I\u2019m willing to accept that risk.<\/span><\/p>\n Finally, here\u2019s what I think is the true genius of the Moliski theorem: It sidesteps the single most common error I see my students make when tackling Data Sufficiency problems, which is to misinterpret the question as a rule. By explicitly hunting for a \u201cno\u201d answer, the Moliski theorem forces you to consider that negative possibility right upfront, so that you don\u2019t have to remember to look for it later when you\u2019re already knee-deep in a fog of calculations and algebra.<\/span><\/p>\n When I first started teaching the GMAT, I never dreamed I\u2019d see a day when I could get away with testing just one case per Data Sufficiency statement as opposed to two. Now that day is upon us. I hope your life is as changed as mine.<\/span><\/p>\n You can attend the first session of any of our online or in-person GMAT courses absolutely free! We\u2019re not kidding. <\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n What if I told you that you could have five extra minutes on the quantitative section of the GMAT? Would you be interested? Good, because this is going to get a little technical. I\u2019m also going to assume you\u2019ve had some experience with Data Sufficiency problems on the GMAT Math section. You should also have […]<\/p>\n","protected":false},"author":25,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[52871],"tags":[233,252,969],"yst_prominent_words":[54235,56816,54040,54184,56088,56820,56992,54535,56988,56980,56986,54561,56981,56979,54302,54054,54310,56983,56975,54301],"class_list":["post-18381","post","type-post","status-publish","format-standard","hentry","category-gmat-strategies","tag-gmat","tag-gmat-data-sufficiency","tag-gmat-data-sufficiency-strategy"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18381","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/users\/25"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=18381"}],"version-history":[{"count":7,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18381\/revisions"}],"predecessor-version":[{"id":18410,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/18381\/revisions\/18410"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=18381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=18381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=18381"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=18381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Part 1: Practical Application<\/b><\/h3>\n
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Part 2: A Small Caveat and Other Non-Essential Nerdy Stuff That You Can Read If You\u2019re Interested, but I\u2019m Mostly Writing It Because I Don\u2019t Want Liz to Get in Trouble<\/b><\/h3>\n
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Epilogue<\/b><\/h3>\n
\n![\"ryan-jacobs\"](\"https:\/\/cdn2.manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2018\/02\/ryan-jacobs-e1501597417957-150x150.png\")
Ryan Jacobs<\/a>\u00a0is a Manhattan Prep instructor based in San Francisco, California.<\/strong>\u00a0He has an MBA from UC San Diego, a 780 on the GMAT, and years of GMAT teaching experience. His other interests include music, photography, and hockey.\u00a0Check out Ryan\u2019s upcoming GMAT prep offerings here<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"