{"id":3916,"date":"2010-07-28T14:39:37","date_gmt":"2010-07-28T22:39:37","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=3916"},"modified":"2010-07-28T14:45:28","modified_gmt":"2010-07-28T22:45:28","slug":"veritas-prep-gmat-tips-think-globally-act-locally-number-properties-the-al-gore-way","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/veritas-prep-gmat-tips-think-globally-act-locally-number-properties-the-al-gore-way\/","title":{"rendered":"Veritas Prep GMAT Tips: Think Globally, Act Locally: Number Properties the Al Gore Way"},"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 anyone who wants to change the world, doing so can seem like an insurmountable task.\u00a0 The Catch-22, however, is that a world of individuals overwhelmed by the specific inability of each to change will miss out on opportunities to make incremental individual differences that sum to marked progress.\u00a0 Environmentalists like Al Gore (and his less-famous but probably more-impactful counterparts) have struggled with this concept for years \u2013 how can they mobilize individuals collectively toward an individually-overwhelming goal?<\/p>\n

You\u2019ll likely feel the same about some questions on the GMAT.\u00a0 Many questions feature uncomfortably high numbers for exactly that purpose \u2013 a freakishly large number can certainly overwhelm a test-taker as the task becomes much less tangible, the same way that problems that feature a mass of variables can do the same thing.<\/p>\n

To combat these questions, think like an environmentalist: Think Globally, but Act Locally.<\/p>\n

This mantra was enacted by the environmental community to encourage people to take pride in their small, individual activities that, if undertaken collectively, would extrapolate to mass change.\u00a0 On the GMAT, you\u2019ll have opportunities to do the same, by testing the ways that numbers\u00a0 interact with small, \u201clocal\u201d numbers, and then extrapolating those learnings to the larger, more abstract numbers in question.<\/p>\n

Consider the question:<\/p>\n

The sum of the digits of integer z is 186, and z = 10n<\/sup> \u2013 4. What is the value of positive integer n?<\/p>\n

A)\u00a0\u00a0\u00a0\u00a0 19<\/p>\n

B)\u00a0\u00a0\u00a0\u00a0\u00a0 20<\/p>\n

C)\u00a0\u00a0\u00a0\u00a0\u00a0 21<\/p>\n

D)\u00a0\u00a0\u00a0\u00a0 22<\/p>\n

E)\u00a0\u00a0\u00a0\u00a0\u00a0 23<\/p>\n

Taking 10 to any of the exponents provided in the answer choices will create a massive number hardly worth the time it would take to write on your noteboard (a process that will likely be fraught with error as you attempt to keep track of 19 zeroes).\u00a0 However, we know what 10n<\/sup> \u2013 4 will look like simply by taking a few, smaller numbers that are easier to jot down:<\/p>\n

10^\u00b3 = 1000, so 10^3<\/sup> \u2013 4 = 996<\/p>\n

10^4= 10000, so 10^4 <\/sup>\u2013 4 = 9996<\/p>\n

As we look at these numbers, we can find some patterns.\u00a0 When n = 3, the result is 996, or a 6 in the units place preceded by two 9s (a total of 3 digits).\u00a0 When n = 4, we just add another 9 to the left, and we have 9996, or a 6 preceded by three 9s (a total of 4 digits).<\/p>\n

We know that the larger the value of n the more zeroes we\u2019ll add to that term, and then the more 9s we\u2019ll have to begin z.\u00a0 Accordingly, z will be composed of several 9s with a 6 on the end.\u00a0 The question becomes just how many 9s we\u2019ll need.\u00a0 Judging from the pattern above, we know that the value of z will have n number of digits \u2013 the same number of digits as the value of the exponent.\u00a0 We also know that one of those digits will be 6, while the others are 9.<\/p>\n

To get the digits to sum to 186, we know that the units digit of 6 in 999\u2026.96 will account for 6, and the rest of the sum will be comprised of the 9s.\u00a0 if we take off that 6, the sum of the remaining digits \u2013 the 9s\u00a0 - is 180, and 180\/9 means that we need 20 9s.\u00a0 To have 20 9s and then a 6, we need a total of 21 digits, and judging from the above pattern we know then that we need n to be 21. The correct answer is C.<\/p>\n

On questions like this that deal with massive numbers, you\u2019re well-served to find out what that large number will look like by using smaller versions of it to establish patterns and relationships that you can then carry forward.\u00a0 Much like an environmentalist, think about the big picture while taking smaller, more manageable steps, and you\u2019ll find that the process is much smoother.<\/p>\n

Read more GMAT advice in our GMAT lesson booklets<\/a> which are now available for individual purchase.\u00a0 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. For anyone who wants to change the world, doing…<\/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-3916","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\/3916","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=3916"}],"version-history":[{"count":3,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/3916\/revisions"}],"predecessor-version":[{"id":3919,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/3916\/revisions\/3919"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=3916"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=3916"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=3916"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}