{"id":7423,"date":"2014-10-15T19:21:43","date_gmt":"2014-10-15T19:21:43","guid":{"rendered":"http:\/\/www.manhattanprep.com\/gre\/?p=7423"},"modified":"2019-08-30T16:43:02","modified_gmt":"2019-08-30T16:43:02","slug":"gre-geometry-impossible-task","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gre\/blog\/gre-geometry-impossible-task\/","title":{"rendered":"GRE Geometry: The Impossible Task"},"content":{"rendered":"

\"GRE-Geometry-tips-and-help\"<\/a>In one of my recent classes, I told the students \u201cYou\u2019ll never know how to answer a geometry question.\u201d\u00a0 The reaction was fairly predictable: \u201cWhy would you say that?!?\u00a0 That\u2019s so discouraging!!\u201d<\/p>\n

Of course, I certainly was NOT<\/b> trying to discourage them.\u00a0 I used that statement to illustrate that geometry questions are often a type of quantitative question that can feel immensely<\/i> frustrating!\u00a0 You know what shape you have, you know what quantity the question wants, but you have no idea how to solve for that quantity.<\/p>\n

This is what I meant when I said you\u2019ll never know how to answer these questions. That \u201cleap\u201d to the correct answer is impossible.\u00a0 You can\u2019t get to the answer in one step, but that\u2019s all right: you\u2019re not supposed to!<\/p>\n

(An important aside: if you\u2019ve read my post regarding calculation v. principle<\/a> on the GRE, you should be aware that I am discussing the calculation heavy geometry questions in this post.)<\/p>\n

The efficient, effective approach to a calculation-based geometry question is NOT to try and jump to the final answer, but instead to simply move to the next \u201cpiece\u201d.\u00a0 For example, let\u2019s say a geometry question gives me an isosceles triangle with two angles equaling x<\/i>.\u00a0 I don\u2019t know what x<\/i> is, and I don\u2019t know how to use it to find the answer to the question.\u00a0 But I DO<\/b> know that the third angle is 180-2x<\/i>.<\/p>\n

That\u2019s the game.\u00a0 Find the next little piece.\u00a0 And the piece after that.\u00a0 And the piece after that.\u00a0 Let\u2019s see an example.<\/p>\n

\"2014-10-15_1513\"<\/a><\/p>\n

The correct response to this problem is \u201cBu-whah???\u00a0 I know nothing about the large circle!\u201d<\/p>\n

But you do know the area of the smaller circle.\u00a0 What piece will that give you?\u00a0 Ok, you say, area gives me the radius.\u00a0 A = pi*r^2, so pi = pi*r^2, so r^2 = 1, so r = 1.\u00a0 Done, and let\u2019s put that in the diagram.
\n
\n(By the way, did you build your own diagram on your paper?\u00a0 I suppose you could try to do this all in your head, but\u2026 why do you hate yourself?)<\/p>\n

So now we have the radius, so that gives the diameter.\u00a0 D = 2.\u00a0 Let\u2019s put that in the diagram.<\/p>\n

\"2014-10-15_1513\"<\/a><\/p>\n

Now what?\u00a0 Well, looks like that diameter is also the length of a side of that square.\u00a0 What else can you draw?\u00a0 What if you draw the diagonal of the square, and solve for that?\u00a0 Now you can either use the Pythagorean theorem, or you can just know that the sides of a 45 : 45 : 90 triangle always follow the proportion x : x : ?2.\u00a0 And you can put that in your diagram.<\/p>\n

\"2014-10-15_1513\"<\/a><\/p>\n

At which point, you have the diameter of the larger circle, which will give you the radius, which will give you the area.<\/p>\n

But how do I get fast at this?\u00a0 That took forever!<\/b><\/p>\n

Good question!\u00a0 You get faster with practice: practice beyond the bounds of the question.\u00a0 Can you find the area of the square?\u00a0 What about the difference between the area of the square and the area of the larger circle?\u00a0 What about the circumference of the circles?\u00a0 Or the perimeter and area of the right triangle formed by the diameter of the square?<\/p>\n

Whenever you review a geometry problem, try to do more!\u00a0 More than what the question asked, with more shapes.<\/p>\n

Go beyond the question.\u00a0 What if you drew a line segment from Q to R?\u00a0 What kind of triangles will you create?\u00a0 What is the measure of the central angles?\u00a0 The measure of angle PQO? Can you solve for the length of PQ?<\/p>\n

This, my GRE compatriots, is how you get fast.<\/p>\n

\"GRE\"<\/p>\n

\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"

In one of my recent classes, I told the students \u201cYou\u2019ll never know how to answer a geometry question.\u201d\u00a0 The reaction was fairly predictable: \u201cWhy would you say that?!?\u00a0 That\u2019s so discouraging!!\u201d Of course, I certainly was NOT trying to discourage them.\u00a0 I used that statement to illustrate that geometry questions are often a type […]<\/p>\n","protected":false},"author":87,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,6,9],"tags":[105,1362338,133,158,169,366],"yst_prominent_words":[],"class_list":["post-7423","post","type-post","status-publish","format-standard","hentry","category-geometry-gre-math","category-gre-strategies","category-math-gre-strategies","tag-geometry","tag-grad-school","tag-gre","tag-gre-prep","tag-gre-strategy","tag-test-prep"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/7423","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/users\/87"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/comments?post=7423"}],"version-history":[{"count":6,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/7423\/revisions"}],"predecessor-version":[{"id":7505,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/7423\/revisions\/7505"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/media?parent=7423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/categories?post=7423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/tags?post=7423"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/yst_prominent_words?post=7423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}