Data Sufficiency<\/a> question.\u00a0 How to determine this without a calculator?<\/p>\n <\/p>\n
The Easy Rules<\/h2>\n
First of all, it’s probably obvious that all even numbers are divisible by 2.\u00a0 Furthermore, 2 is the only even prime number: all other positive even integers are divisible by 2, so all other prime numbers are odd.<\/p>\n
A number that ends with a 5 or a 0 is divisible by 5.\u00a0 A two digit number in which the first and last digits are the same is divisible by 11.<\/p>\n
With 4, there’s an interesting pattern.\u00a0 Think of the one-digit numbers that are multiples of 4: those are 0, 4, and 8.\u00a0 If the last digit is 0, 4, or 8, and the tens digit is even<\/em>, then the number is divisible by 4.\u00a0 If the last digit is even but not one of those — viz. 2 or 6, the one-digit even numbers that are not<\/em> multiples of 4 \u2013 and the tens digit is odd<\/em>, then the number is divisible by 4.<\/p>\n <\/p>\n
The Pattern with 3<\/h2>\n
The rule for 3 is a bit different from the rules for other numbers.\u00a0 You simply add up the digits.\u00a0 If the sum of the digits is divisible by 3, then the original number is divisible by 3.\u00a0 For example, consider the number 285 —- 2 + 8 + 5 = 15, which is divisible by 3, so that means 285 must be divisible by 3.\u00a0 Consider the number 2012 —- 2 + 0 + 1 + 2 = 5, which is not divisible by 3, so that means 2012 is not divisible by 3.<\/p>\n
That pattern also works with 9 — if the sum of the digits is divisible by 9, then the original number is divisible by 9.\u00a0 For example, the next year that will be a multiple of 9 is 2016, because 2 + 0 + 1 + 6 = 9.<\/p>\n
<\/p>\n
Testing Prime Numbers<\/h2>\n
The GMAT occasionally will have questions that require you to figure out whether larger two-digit numbers are prime.\u00a0 It will not ask you to figure out whether numbers greater than 100 are prime.\u00a0 For numbers less than 100, two-digit numbers, it’s enough to check whether it divisible by any single digit prime number {2, 3, 5, 7}.\u00a0 Any two-digit number not divisible by one of those four must be prime.<\/p>\n
Back to our set above:<\/p>\n
S = {71, 73, 75, 77, 79, 81, 83, 85, 87, 89}<\/p>\n
All odds, so no multiples of 2.The numbers 75 and 85 are obviously divisible by 5, so those are not prime.<\/p>\n
S = {71, 73, __, 77, 79, 81, 83, __, 87, 89}<\/p>\n
The number 77 = 7*11.\u00a0 Once we have that multiple of 7, we add and subtract 7 to find other multiples of 7: { . . . . 70, 77, 84, 91, . . . }\u00a0 We see that 77 is the only multiple of 7 on this list.<\/p>\n
S = {71, 73, __, __, 79, 81, 83, __, 87, 89}<\/p>\n
Now we need a multiple of 3.\u00a0 We notice that, with 81, 8+1=9, which is divisible by 3, so 81 must be divisible by 3.\u00a0 We add and subtract 3 repeatedly to get other multiples of three: { . . . 69, 72, 75, 78, 81, 84, 87, 90, . . .}.\u00a0 Just to double-check 87, we see 8+7=15, which is divisible by 3, so of course 87 is divisible by 3.\u00a0 We can eliminate<\/p>\n
S = {71, 73, __, __, 79, __, 83, __, __, 89}<\/p>\n
The remaining five numbers must be prime.\u00a0 Indeed, each one is a prime number.<\/p>\n
<\/p>\n
Here’s a free GMAT Problem Solving question on which you can practice these skills:\u00a0http:\/\/gmat.magoosh.com\/questions\/850<\/a><\/p>\nThat question will be followed by a full video explanation when you submit your answer. Good luck!<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
Improve your Mental Math Fact: On the GMAT, you do not get a calculator. Actually, on the new IR questions coming this summer, there will be an onscreen calculator, but for the ordinary Quantitative questions, for the foreseeable future, you will be doing those without a calculator of any sort. Consider the following question: S […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[112],"tags":[],"ppma_author":[13209],"class_list":["post-1096","post","type-post","status-publish","format-standard","hentry","category-math"],"acf":[],"yoast_head":"\n
GMAT Divisibility Rules and Shortcuts - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gmat\/gmat-divisibility-rules-and-shortcuts\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Divisibility Rules and Shortcuts\" \/>\n<meta property=\"og:description\" content=\"Improve your Mental Math Fact: On the GMAT, you do not get a calculator. Actually, on the new IR questions coming this summer, there will be an onscreen calculator, but for the ordinary Quantitative questions, for the foreseeable future, you will be doing those without a calculator of any sort. 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He was also featured as \"member of the month\" for over two years at <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/1096","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=1096"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/1096\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=1096"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=1096"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=1096"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=1096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}