{"id":3025,"date":"2010-04-27T08:37:47","date_gmt":"2010-04-27T16:37:47","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=3025"},"modified":"2010-07-24T22:02:15","modified_gmt":"2010-07-25T06:02:15","slug":"veritas-prep-gmat-tips-range-rover","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/veritas-prep-gmat-tips-range-rover\/","title":{"rendered":"Veritas Prep GMAT Tips: Range Rover"},"content":{"rendered":"

Brian Galvin is the Director of Academic Programs at Veritas Prep, where he oversees all of the company\u2019s GMAT preparation courses<\/a>.<\/p>\n

For some of us, one of our favorite days in school was when our teacher let us use a calculator and, therefore, never had to draw out that feared long division bracket again.\u00a0 Long division is a meticulous, time consuming process and, as some of us tried to convince our grade school teachers, is a waste of paper given the numerous steps it requires a student to write down.\u00a0 So, when the GMAT asks us to conclude how many numbers in the range of 210 to 230 are prime, the thought that we may need to take numbers like 217 and divide them by 7 or 11 is frightening.<\/p>\n

There is an easier way.\u00a0 If you note that a(b+c) = ab + ac (the distributive property), then you can also find that 7 * 31 = 7(30+1) = 7(30) + 7(1).\u00a0 Furthermore, if you want to determine whether 217 is divisible by 7, you can simply subtract a big multiple of 7 (like 210) to whittle away at the larger number 217.\u00a0 217-210 leaves 7, which definitely divides by 7, so we know that 217 is divisible by 7.<\/p>\n

If you follow that logic, you are close to having a fast method for determining divisibility, and to being able to quickly check numbers to see if they are prime. Let\u2019s, again, address the question:<\/p>\n

How many prime numbers exist between 210 and 230?<\/p>\n

At first, you should recognize that you can eliminate all even numbers (they\u2019re divisible by 2) and all numbers that end in 5 (they\u2019re divisible by 5), leaving:<\/p>\n

211<\/p>\n

213<\/p>\n

217<\/p>\n

219<\/p>\n

221<\/p>\n

223<\/p>\n

227<\/p>\n

229<\/p>\n

Next, test every number for divisibility by 3, using the method that, if the sum of the digits is a multiple of 3, then that number is divisible by 3.\u00a0 This works to eliminate:<\/p>\n

213 (2+1+3 = 6) and 219 (2 +1+9 =12).\u00a0 Now we are left with:<\/p>\n

211<\/p>\n

217<\/p>\n

221<\/p>\n

223<\/p>\n

227<\/p>\n

229<\/p>\n

From here, using divisibility \u201ctricks\u201d becomes trickier.\u00a0 While there do exist tricks for 7, 11, and other numbers, they tend to be time consuming and need extra memorization without much ROI.\u00a0 A simpler check for divisibility exists for all numbers:<\/p>\n

Find a multiple of the number-in-question in the range that you are testing, and then just add\/subtract the number-in-question from that to round up all of the multiples.<\/p>\n

As we test this range for multiples of 7, the easiest multiple of 7 to note is 210.\u00a0 If 210 is a multiple of 7, then adding 7, and adding it again, will again produce multiples of 7:<\/p>\n

210<\/p>\n

217<\/p>\n

224<\/p>\n

At this point, we have already eliminated 210 and 224 (both even), so the only new number to eliminate is 217, leaving:<\/p>\n

211<\/p>\n

221<\/p>\n

223<\/p>\n

227<\/p>\n

229
\nNext, we will test for divisibility by 11 using the same system.\u00a0 Our \u201canchor\u201d will be 220 (the product of 11 and 20), which means that the next-closest multiples of 11 are 209 (220-11) and 231 (220+11), both of which fall outside the range in question. Here, we cannot eliminate any new values.<\/p>\n

Next, test for divisibility by 13, again finding a number \u201cin the range\u201d and working from there.\u00a0 Here, it is easiest to use 260 as our \u201canchor\u201d, and then work down to our range from there.\u00a0 Subtracting 13 from 260, we find that the following are multiples of 13:<\/p>\n

247, 234, 221, 208<\/p>\n

221 is\u00a0in our range, so we can eliminate it, and we are left with the rest as prime numbers:<\/p>\n

211, 223, 227, 229<\/p>\n

Note that this approach also helps to avoid having to individually test each of the remaining numbers.\u00a0 If we know that they are not divisible by 2, 3, 5, 7, 11, or 13, we know that they are \u00a0prime, as they cannot be divisible by any other number less than 16 (each of those numbers would be divisible by another in that set).\u00a0 Because 230, the upper limit of our range, is less than 162<\/sup>, then in order for a number in our range to be divisible by something greater than 16, that factor would have to be paired with something less than 16, and we have already tried each of those numbers.\u00a0 Therefore, we can conclude somewhat quickly that these four numbers are prime.<\/p>\n

In conclusion, to avoid attempting several long-division calculations when checking numbers for divisibility, or for whether they are prime, merely find a multiple of a potential factor in the range of the number(s) you are testing, and use addition and subtraction to complete the set.<\/p>\n

Read more GMAT advice on the Veritas Prep blog<\/a>. Ready to sign up for a GMAT course<\/a>? Enroll through GMAT Club and save up to $180 (use discount code GMATC10)!<\/p>\n

\"Veritas
\n<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Brian Galvin is the Director of Academic Programs at Veritas Prep, where he oversees all of the company\u2019s GMAT preparation courses. For some of us, one of our favorite days…<\/p>\n","protected":false},"author":101,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3025","post","type-post","status-publish","format-standard","hentry","category-uncategorized","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/3025","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/101"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=3025"}],"version-history":[{"count":3,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/3025\/revisions"}],"predecessor-version":[{"id":3028,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/3025\/revisions\/3028"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=3025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=3025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=3025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}