{"id":11753,"date":"2012-05-31T09:00:43","date_gmt":"2012-05-31T16:00:43","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=11753"},"modified":"2012-05-30T16:25:39","modified_gmt":"2012-05-30T23:25:39","slug":"gmat-quant-difference-of-two-squares","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/gmat-quant-difference-of-two-squares\/","title":{"rendered":"GMAT Quant: Difference of Two Squares"},"content":{"rendered":"

You may remember this formula, one of the sleekest factoring tricks in all of algebra:<\/p>\n

\"y^2<\/p>\n

This formula, called \u201cthe difference of two squares\u201d formula, is a favorite of standardized test writers.\u00a0 A simple enough pattern: see if you can detect where it shows up in the following challenging problems.<\/p>\n

 <\/p>\n

1) \u00a0\"1\/{2-sqrt{3}}\"=<\/p>\n

(A)\u00a0\"2<\/p>\n

(B)\u00a0\"2<\/p>\n

(C)\u00a0\"1\/7\"<\/p>\n

(D)\u00a0\"1\/2<\/p>\n

(E)\u00a0\"1\/2<\/p>\n

 <\/p>\n

2) What is the sum of a and b?<\/p>\n

(1)\"a<\/p>\n

(2)\"{b^2<\/p>\n

    \n
  1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.<\/li>\n
  2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.<\/li>\n
  3. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.<\/li>\n
  4. Each statement alone is sufficient to answer the question.<\/li>\n
  5. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.<\/li>\n<\/ol>\n

     <\/p>\n

    \"\"<\/a><\/p>\n

    3) \u00a0In the diagram above, \u2220A = \u2220ABC, \u2220CBD = \u2220BDC, and \u2220CBE =90\u00b0.\u00a0 If AE = 16 and DE = 4, what is the length of BE?<\/p>\n

    (A) 7<\/p>\n

    (B) 8<\/p>\n

    (C) 9<\/p>\n

    (D) 10<\/p>\n

    (E) 11<\/p>\n

     <\/p>\n

    Practice Problem Solutions<\/h2>\n

    1) This involves a relatively sophisticated trick known as \u201cmultiplying by the conjugate.\u201d\u00a0 When we have an expression of the form a+sqrt(b), the \u201cconjugate\u201d of this is a-sqrt(b).\u00a0 When we multiply a radical expression by its conjugate, we employ the difference of two squares.\u00a0 For example:<\/p>\n

    \"1\/{2-sqrt{3}}<\/p>\n

    This is answer\u00a0B<\/strong>.\u00a0 BTW, the trick of multiplying by the conjugate is at the very outside edge of what you might be expected to do the hardest GMAT math problems.<\/p>\n

     <\/p>\n

    2) The prompt of this DS problem is straightforward.<\/p>\n

    Statement #1 tells us a = 4, but we have no idea of b, so, by itself, this is not sufficient for finding the sum.<\/p>\n

    Statement #2 gives us a value for an algebraic expression that lends itself nicely to simplification.<\/p>\n

     <\/p>\n

    \"7<\/p>\n

     <\/p>\n

    Thus, the sum is 7.\u00a0 Statement #2, by itself is sufficient.\u00a0 Answer =\u00a0B<\/strong>.<\/p>\n

     <\/p>\n

    3) This is a tricky one.\u00a0 Remember, it\u2019s a diagram drawn to scale, so if all else fails, you can estimate (see this post).\u00a0 But, let\u2019s solve this with math.\u00a0 The fact that \u2220A = \u2220ABC tells us triangle ABC is isosceles, with AC = BC.\u00a0 The fact that \u2220CBD = \u2220BDC tells us triangle BCD is isosceles, with BC = CD.\u00a0 The fact that \u2220CBE = 90\u00b0 means that (BC)2<\/sup>\u00a0+ (BE)2<\/sup>\u00a0= (CE)2<\/sup>.\u00a0 This means<\/p>\n

     <\/p>\n

    \"(BE)^2\u00a0=<\/p>\n

    \"{}<\/p>\n

    \"{}\u00a0(substitutions from the two isosceles triangles)<\/p>\n

    \"{}<\/p>\n

    \"{}<\/p>\n

     <\/p>\n

    Answer = B<\/p>\n

     <\/p>\n

    Here\u2019s a further practice question.<\/p>\n

    https:\/\/gmat.magoosh.com\/questions\/118<\/a><\/p>\n

    This post was written by Mike McGarry, GMAT expert at\u00a0Magoosh<\/a>, and originally posted\u00a0here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    You may remember this formula, one of the sleekest factoring tricks in all of algebra: This formula, called \u201cthe difference of two squares\u201d formula, is a favorite of standardized test…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,783,243,718,717,736],"tags":[],"class_list":["post-11753","post","type-post","status-publish","format-standard","hentry","category-gmat","category-magoosh-blog","category-blog","category-data-sufficiency-gmat","category-problem-solving-gmat","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/11753","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\/133"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=11753"}],"version-history":[{"count":2,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/11753\/revisions"}],"predecessor-version":[{"id":11757,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/11753\/revisions\/11757"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=11753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=11753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=11753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}