{"id":2872,"date":"2010-04-13T11:53:03","date_gmt":"2010-04-13T19:53:03","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=2872"},"modified":"2010-04-14T09:19:08","modified_gmt":"2010-04-14T17:19:08","slug":"veritas-prep-gmat-tips-it%e2%80%99s-hip-to-be-square","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/veritas-prep-gmat-tips-it%e2%80%99s-hip-to-be-square\/","title":{"rendered":"Veritas Prep GMAT Tips: It\u2019s Hip to be Square"},"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

Jaime Escalante<\/a>, the famed calculus teacher and subject of the movie Stand and Deliver, famously told his students \u201ccalculus doesn\u2019t need to be made easy; it\u2019s easy already\u201d.\u00a0 To paraphrase the late icon, there are no \u201ctricks\u201d to success on the GMAT; math in itself is clever enough.<\/p>\n

Sure, there are countless ways to save time and cut corners on the GMAT, but none is inherently \u201ctricky\u201d.\u00a0 Each of these methods just takes advantage of the beauty of math.\u00a0 As you attempt to maximize your efficiency and accuracy on the GMAT, and ultimately your score, embrace these shortcuts for what they are, but also learn to appreciate the logic behind them.\u00a0 Knowing that each of these tricks has a logical foundation in math, you can use that understanding to apply that logic to solve several problems.\u00a0\u00a0 Consider an example of a pretty elegant \u201ctrick\u201d that could help you on the GMAT:<\/p>\n

Say you needed to find the square of 31. Rather than stack up 31 *31 and plunge through the math, you could use a fairly clever \u201ctrick\u201d to calculate it quite efficiently.\u00a0 Because 30*30 is 900, you can simply add 30 and 31 to determine that 31-squared is 961.\u00a0 Why?<\/p>\n

If you have 30*30 and need to get to 31*31, you might first start by adding 30 to that initial 30*30.\u00a0 Adding an extra 30 means that you have 31 30s, or 31*30.\u00a0 You could also, then, consider 31*30 to mean that you have 30 31s.\u00a0 To get another \u2013 to have 31 31s, or 31*31 \u2013 you\u2019d need to add one more 31.\u00a0 So, you\u2019d add 31 to get there, and you\u2019d have 31*31.<\/p>\n

Reiterating those steps, you took 30*30, then added 30 (itself) and 31 (the next integer) to it to determine that 31-squared is 961.\u00a0 Essentially, the rule for finding the next square in the sequence is:<\/p>\n

Take the previous square, then add its square root plus that square root + 1.<\/p>\n

Or, more theoretically, n-squared = (n-1)-squared + (n-1) + n.<\/p>\n

This property may well save you some time and arduous calculation in a situation like 31-squared, but its application may prove even more helpful (and definitely more fascinating):<\/p>\n

The squares of integers increase by adding consecutive odd integers.<\/p>\n

Think about it; to replicate the pattern of squares:<\/p>\n

1, 4, 9, 16, 25, 36, 49, 64, 81, 100<\/p>\n

You add:<\/p>\n

3 (to get from 1 to 4), 5 (to get from 4 to 9), 7 (9 to 16), 9 (16 to 25), 11, 13, 15, 17, and 19<\/p>\n

Why is this true?<\/p>\n

Let\u2019s use 25, or 5-squared, as our starting point.\u00a0 To get to 6-squared, we need to add 5, then add 6, which means we add 11.\u00a0 To get to 7-squared, we\u2019ll add 6 again (which is now our \u201cbase\u201d number, or n), then add n+1, which is 7.\u00a0 6+7 is 13.\u00a0 Each time we do this, we\u2019re adding two consecutive integers (and the sum of consecutive integers is always odd), and we\u2019re just moving up each integer by one, so we\u2019re adding another 1+1 to what we previously added.\u00a0 That pattern will go on forever; to get to 27-squared, we can start by knowing that 25-squared is 625.\u00a0 To get to 26-squared, we\u2019d add 25+26, or 51, then to go up one more square, to 27-squared, we\u2019d just add another 53.\u00a0 Essentially, we\u2019re taking 625 and adding 51, then 53; so, we can take 625, add 104, and get 729 as 27-squared.<\/p>\n

This \u201ctrick\u201d can be a time-saver on test day, but if you have to think about it to know why it works, you also put yourself in a position to better attack the Number Properties and Sequences concepts that the GMAT tends to use as the bases of some of its tougher questions.\u00a0 Several GMAT questions will ask you to \u201cspot the pattern\u201d \u2013 either explicitly or as a way to more efficiently tackle a seemingly labor-intensive problem \u2013 and there are few better ways to develop that skill than by checking each \u201ctrick\u201d you come across to see why such a pattern holds.<\/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<\/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. Jaime Escalante, the famed calculus teacher and subject of…<\/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-2872","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\/2872","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=2872"}],"version-history":[{"count":4,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/2872\/revisions"}],"predecessor-version":[{"id":2878,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/2872\/revisions\/2878"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=2872"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=2872"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=2872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}