{"id":11056,"date":"2016-02-25T16:23:59","date_gmt":"2016-02-25T16:23:59","guid":{"rendered":"http:\/\/www.manhattanprep.com\/gmat\/?p=11056"},"modified":"2019-11-08T19:50:01","modified_gmt":"2019-11-08T19:50:01","slug":"decoding-divisibility-and-primes-on-the-gmat-part-2","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gmat\/blog\/decoding-divisibility-and-primes-on-the-gmat-part-2\/","title":{"rendered":"Decoding Divisibility and Primes on the GMAT \u2013 Part 2"},"content":{"rendered":"

\"DecodingDid you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We\u2019re not kidding! Check out our upcoming courses here<\/a>.<\/em><\/strong>
\n<\/em><\/strong><\/p>\n

\n

Welcome to the 2nd<\/sup> installment of our dive into Number Properties. If you haven\u2019t yet tried the first problem, start with the first article in the series<\/a>.<\/p>\n

Let\u2019s dive right into our second problem from the GMATPrep\u00ae free exams:<\/p>\n

\u201c*What is the greatest prime factor of \u00a04^17\u00a0– 2^28?<\/p>\n

\u201c(A) 2<\/p>\n

\u201c(B) 3<\/p>\n

\u201c(C) 5<\/p>\n

\u201c(D) 7<\/p>\n

\u201c(E) 11\u201d<\/p><\/blockquote>\n

You know the drill. First, what\u2019s going on?<\/p>\n

\"Glance<\/a><\/p>\n

Glance<\/i>: PS. Ugly exponents. The answer choices are small\/easy numbers.<\/p>\n

Read<\/i>: The question is pretty straightforward. Right up until we get to the ugly math. \":P\"<\/p>\n

Jot<\/i>:<\/p>\n

\"\"\"341<\/p>\n

\"\"<\/p>\n

I definitely have to think about how to approach this.<\/p>\n

\"Reflect<\/a><\/p>\n

My first thought: it\u2019s annoying that the bases are different. Oh, but I can fix that! 4 is a multiple of 2.<\/p>\n

\"341<\/p>\n

\"\"<\/p>\n

Okay\u2026now what? They probably want me to think that that\u2019s just \"2^6\", in which case the answer would be 2. But you subtract the exponents when you\u2019re dividing<\/i> the two bases. Here, the two bases are subtracted<\/i>, so subtracting the exponents is an illegal move. The answer probably isn\u2019t 2; if I get stuck and have to guess, I won\u2019t guess (A).<\/p>\n

Oh, this is ringing a bell. I\u2019ve seen something like this before. When I can\u2019t combine the terms using standard exponent rules, I should try pulling out a common term. That math is more annoying, but at least it\u2019s something I\u2019m allowed to do.<\/p>\n

\"341<\/p>\n

\"\"<\/p>\n

I\u2019ve got it! 63 = (9)(7) = (3)(3)(7). So the prime factors of the whole thing are 2, 3, and 7. The largest one is 7; that\u2019s the answer!<\/p>\n

The correct answer is (D).<\/p>\n

Even if I hadn\u2019t figured out that last part, I still could have done a decent job of making an educated guess. 2 is a trap answer, as I found earlier. And if they\u2019re asking for the \u201cgreatest\u201d number, then the answer usually won\u2019t be the greatest number given, so I wouldn\u2019t have picked (E) either. I\u2019d have guessed among (B), (C), and (D), which gives me decent odds on a problem I don\u2019t know how to solve.<\/p>\n

Key Takeaways for Divisibility and Primes on the GMAT:<\/h4>\n

(1) Exponents can be mixed in with divisibility and prime! Other topics also often get mixed up with Number Properties topics. Start looking out for other examples in your studies. (And know your exponent rules.)<\/p>\n

(2) You can sometimes cross off answers by knowing what you\u2019re not<\/i> allowed to do, as we did for answer (A). Start training yourself to think about trap answers, too, not just correct answers, and you\u2019ll turn yourself into a better educated guesser.<\/p>\n

(3) We\u2019ve got one more for you! Join us for the third, and final, installment of this series, when we\u2019ll try the hardest problem yet.<\/p>\n

* GMATPrep\u00ae questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.<\/p>\n

Keep Reading:\u00a0<\/strong>Part 3<\/a><\/p>\n

\n

Can\u2019t get enough of Stacey\u2019s GMAT mastery? Attend the first session of one of her upcoming GMAT courses<\/a> absolutely free, no strings attached. Seriously.\u00a0<\/strong><\/em><\/p>\n

\n

\"stacey-koprince\"<\/a>Stacey Koprince<\/a> is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California.<\/strong> Stacey has been teaching the GMAT, GRE, and LSAT \u00a0for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests. Check out Stacey\u2019s upcoming GMAT courses here<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We\u2019re not kidding! Check out our upcoming courses here. Welcome to the 2nd installment of our dive into Number Properties. If you haven\u2019t yet tried the first problem, start with the first article in […]<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,873,929,2,8],"tags":[61,161,233,52766,557,52765],"yst_prominent_words":[54235,53868,53653,53779,56475,56477,53877,53659,53635,53781,53775,56476,53798,54189,54292,53704,53797,55210,53784,53867],"class_list":["post-11056","post","type-post","status-publish","format-standard","hentry","category-data-suff","category-for-current-studiers","category-gmat-prep","category-how-to-study","category-quant-on-gmat","tag-algebra","tag-divisibility","tag-gmat","tag-integers","tag-number-properties","tag-primes"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/11056","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\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=11056"}],"version-history":[{"count":11,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/11056\/revisions"}],"predecessor-version":[{"id":18281,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/11056\/revisions\/18281"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=11056"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=11056"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=11056"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=11056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}