{"id":16650,"date":"2019-08-13T07:54:04","date_gmt":"2019-08-13T12:54:04","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=16650"},"modified":"2020-09-11T20:41:26","modified_gmt":"2020-09-11T20:41:26","slug":"gmat-quantitative-symbolism","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/gmat\/gmat-quantitative-symbolism\/","title":{"rendered":"GMAT Quantitative: Symbolism"},"content":{"rendered":"
\n
\nFor the most part,\u00a0GMAT math<\/a>\u00a0is high school math. This is a helpful mantra for many math-phobic test takers, who remind themselves (correctly!) that if they could do the math back when they were sixteen, they can do it today, too. But occasionally, the GMAT will throw something at you that you\u2019ve never seen before, a weird symbol or other doohickey that looks like it came from outer space. Here is an example:
\nIf\u00a0x<\/em>\u263cy = 4xy<\/em>\u00a0\u2013\u00a0x<\/em>\/y<\/em>, for all\u00a0x\u00a0<\/em>and for all\u00a0y<\/em>\u2260<\/em>0,\u00a0<\/em>then\u2026.
\nOkay, what\u2019s \u263c? Certainly nothing you learned in school. But fortunately:
\n 
\n

Rule 1: The problem will always tell you what the symbols mean.<\/h4>
<\/div><\/div><\/div>
\nYou aren\u2019t expected to know \u263c at a glance. It\u2019s defined for you. That first part of the sentence, the equation for\u00a0x<\/em>\u263cy<\/em>, is that definition. This is tricky, because the equals sign in the definition is the same symbol in every algebraic equation. But in reality, the = in this problem doesn\u2019t mean \u201cequals.\u201d
\n

Rule 2: An = in the definition of a symbol should be read as \u201c<\/span>is defined as.\u201d<\/span><\/h4>
<\/div><\/div><\/div>
\nIn other words, in \u2018real\u2019 math, \u263c is meaningless. So\u00a0the GMAT\u00a0testmaker has to give that symbol a definition. Paraphrasing the question above into English, we get the following: \u201cWhen two numbers are connected by the \u263c sign, that operation is defined as four times the product of those two numbers, minus the first over the second.\u201d\u00a0 Or perhaps more simply: \u201cWhen two numbers are on either side of the \u263c, we plug the first number into every\u00a0x<\/em>\u00a0in the definition in the question stem and we plug the second number into every\u00a0y<\/em>\u00a0in that definition.\u201d
\nSo if we see them complete version of the problem:
\nIf\u00a0x<\/em>\u263cy = 4xy<\/em>\u00a0\u2013\u00a0x<\/em>\/y<\/em>, for all\u00a0x\u00a0<\/em>and for all\u00a0y<\/em>\u2260<\/em>0,\u00a0<\/em>then 6\u263c3 equals
\nThen the problem, despite looking intimidating at first, turns out to be quite simple.
\n

Rule 3: The vast majority of symbolism problems test no math more complex than simple substitution.<\/h4>
<\/div><\/div><\/div>
\nWe follow the instructions in the question stem, as we paraphrased them. If it\u2019s easier for you to think of the \u263c as a process, than follow the rules for the process as you paraphrased them. If it\u2019s easier to wrap your head around substitution, then substitute for\u00a0x\u00a0<\/em>and\u00a0y<\/em>. The final math is the same either way:
\n6\u263c3 = 4*6*3 \u2013 6\/3 = 72 \u2013 2 = 70
\nAnd on\u00a0test-day, we get the points for a correct answer just like that.
\nDon\u2019t let yourself get intimidated by strange symbols. These problems are testing your flexibility\u2014your ability to understand new definitions and apply them. And as long as you remember the three rules of symbolism in this article, you\u2019ll be able to answer any weird signs or operations that the\u00a0GMAT\u00a0throws at you.
\n 
\n

Practice Question<\/h3>
<\/div><\/div><\/div>
\nHere is one more chance to try the same skills on a slightly tougher problem. Good luck!
\n\t
\t\t

\nFor all numbers\u00a0a\u00a0<\/em>and\u00a0b<\/em>, the operation\u00a0&& is defined by\u00a0a&&b\u00a0<\/em>= (a<\/em>\u00a0+ 2)(b<\/em>\u00a0\u2013 3).
\nIf 3&&\u00a0x<\/em>\u00a0= \u201345, then\u00a0x<\/em>\u00a0=
\n(A)\u00a0\u00a0\u00a0 \u201315
\n(B)\u00a0\u00a0 \u00a0\u20136
\n(C)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3
\n(D)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6
\n(E) \u00a0\u00a0\u00a0\u00a0\u00a0 15<\/p>\n<\/div><\/div>
\n

Solution<\/h4>
<\/div><\/div><\/div>
\nAnalyze:\u00a0<\/strong>What do the answer choices represent?\u00a0<\/em>The value of\u00a0x\u00a0<\/em>when it is part of the operation described in the stem.
\nOutline the information in the stem.\u00a0<\/em>The operation shows what we do with two numbers,\u00a0a\u00a0<\/em>and\u00a0b<\/em>.
\nThe stem tells us\u00a0that when we substitute 3 for\u00a0a\u00a0<\/em>and\u00a0x\u00a0<\/em>for\u00a0b<\/em>, the operation will equal \u201345.
\nTask:\u00a0<\/strong>How do we use the operation in the stem to get a value for x?\u00a0<\/em>Just do the substitution and simplify, isolating\u00a0x<\/em>.
\nApproach Strategically:<\/strong>
\nReplace\u00a0a\u00a0<\/em>with 3 and\u00a0b\u00a0<\/em>with\u00a0x<\/em>, and then solve for\u00a0x<\/em>.
\n(3 + 2)(x\u00a0<\/em>\u2013 3) = \u201345
\n5(x\u00a0<\/em>\u2013 3) = \u201345
\nx\u00a0<\/em>\u2013 3 = \u20139
\nx\u00a0<\/em>= \u20136
\nThat gives us (B) as the correct answer.
\nConfirm:\u00a0<\/strong>Plug 3 in for\u00a0a\u00a0<\/em>and \u20136 in for\u00a0b\u00a0<\/em>in the operation and FOIL: (3 + 2)(\u20136 \u2013 3) = (\u201318) \u2013 9 \u2013 12 \u2013 6 = \u201345.
\n
\t\t\t

<\/span><\/p>\n<\/div>\n\t\t<\/div>

\t\t\t

<\/span><\/p>\n<\/div>\n\t\t<\/div><\/div>\n<\/div>\n<\/div>\n

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

For the most part,\u00a0GMAT math\u00a0is high school math. This is a helpful mantra for many math-phobic test takers, who remind themselves (correctly!) that if they could do the math back when they were sixteen, they can do it today, too. But occasionally, the GMAT will throw something at you that you\u2019ve never seen before, a […]<\/p>\n","protected":false},"author":1,"featured_media":27623,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[55],"tags":[56,80],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/16650"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=16650"}],"version-history":[{"count":2,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/16650\/revisions"}],"predecessor-version":[{"id":34920,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/16650\/revisions\/34920"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/27623"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=16650"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=16650"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=16650"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}