{"id":5250,"date":"2015-04-23T08:43:11","date_gmt":"2015-04-23T15:43:11","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=5250"},"modified":"2019-07-24T20:36:04","modified_gmt":"2019-07-24T15:06:04","slug":"gmat-quant-3-mistakes-in-even-odd-number-properties-questions","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/gmat-quant-3-mistakes-in-even-odd-number-properties-questions\/","title":{"rendered":"GMAT Quant | 3 mistakes in Even-Odd Questions | Number Properties"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">8<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span><p>When it comes to &#8216;Even &#8211; Odd&#8217;, it&#8217;s not just an issue on Delhi roads, but also in your GMAT Quant section.\u00a0Even-Odd numbers is deemed to be among the easier concepts on the GMAT Quant, and yet, come 700+ level questions from this concept, many students get them wrong. Our Subject Matter Experts have closely studied the mistakes that students make in Even-Odd questions \u2013 from the doubts they ask in Even-Odd questions in our internal forums, and from the mistakes made by 2000+ students in our recurring Number Properties Live Classroom.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-5221\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2015\/04\/Final-Hero-e1429798696174.png\" alt=\"gmat quant number properties practice questions even odd\" width=\"765\" height=\"300\" \/><\/p>\n<p>For better understanding, we have outlined in this article:<\/p>\n<ul>\n<li>3 primary pitfalls of GMAT Quant Even-Odd questions<\/li>\n<li>How to avoid these pitfalls<\/li>\n<li>Illustrative GMAT Number properties (Odd-Even) questions<\/li>\n<li>Takeaways<\/li>\n<li>GMAT Number properties ( Even-Odd) practice questions<\/li>\n<\/ul>\n<h2>3 Primary Pitfalls of GMAT Quant Even-Odd Questions<\/h2>\n<p>What we have observed is that there are three primary pitfalls that students fall into, in Even-Odd questions:.<\/p>\n<ol>\n<li><strong>Getting intimidated by complex expressions<\/strong><\/li>\n<li><strong>Wasting time on unimportant terms<\/strong><\/li>\n<li><strong>Getting stumped in division<\/strong><\/li>\n<\/ol>\n<h3>1.\u00a0\u00a0\u00a0 Getting intimidated by complex expressions<\/h3>\n<p><span style=\"text-decoration: underline;\"><strong>What we mean<\/strong><\/span><\/p>\n<p>A few Even-Odd questions may have scary-looking expressions. For example, consider this question<\/p>\n<p><strong>P1.1<\/strong><strong>\u00a0\u00a0\u00a0 If j is a positive integer, is (j<sup>3<\/sup>-27)<sup>2<\/sup>(j<sup>3<\/sup>+1)<sup>3<\/sup> odd?<\/strong><\/p>\n<p>Did you feel a bit nervous reading this question? Well, that is the first pitfall that you have to guard against. Because, if you let yourself become nervous, you will:<\/p>\n<ol style=\"list-style-type: lower-roman;\">\n<li><span style=\"line-height: 1.714285714; font-size: 1rem;\">Either leave the question without answering<\/span><\/li>\n<li><span style=\"font-size: 1rem; line-height: 1.714285714;\">Or you will panic; panic clouds our ability to think rationally and so, increases our chances of making an error.<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>For example, in your panic, you may scramble to remember and apply the formula for a<sup>3<\/sup> + b<sup>3<\/sup> on the terms of this expression, and then, realize, much to your dismay, that you\u2019ve complicated the question even further L<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>So, as you can see, \u2018getting intimidated by complex expressions\u2019 is indeed a dangerous pitfall.<\/p>\n<h2>What can you do to avoid this pitfall?<\/h2>\n<p>The next time you face such a question in GMAT Quant section and notice your heartbeat increasing, take a deep breath and tell yourself,<\/p>\n<p style=\"text-align: center;\"><span style=\"background-color: #ccffcc;\"><strong><em>\u201cSince this is a GMAT Quant question, it can be simplified elegantly.\u201d<\/em><\/strong><\/span><\/p>\n<p>This is true! The beauty of official GMAT questions is that no matter how complex they look, they can always be simplified to a couple of cases.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-5222\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2015\/04\/Pitfall-1-e1429798804799.png\" alt=\"gmat quant number properties practice questions even odd\" width=\"550\" height=\"284\" \/><\/p>\n<h3>Illustrative Example<\/h3>\n<p><em>So, let\u2019s think through the question we posed above and see how it can be simplified.<\/em><\/p>\n<p><strong><em><span style=\"text-decoration: underline;\">1<sup>st<\/sup> Simplification <\/span><\/em><\/strong><\/p>\n<p><em>The given expression is (j<sup>3<\/sup>-27)<sup>2<\/sup>(j<sup>3<\/sup>+1)<sup>3<\/sup><\/em><\/p>\n<p><em>You\u2019re probably familiar with the property that <\/em><strong><em>the power of a number doesn\u2019t impact the even-odd nature of the number.<\/em><\/strong><\/p>\n<ul>\n<li><em>(Even)<sup>n<\/sup>, where n is a positive integer = Even<\/em><\/li>\n<li><em>Similarly, (Odd)<sup>n<\/sup> = Odd<\/em><\/li>\n<\/ul>\n<p><em>So,\u00a0<\/em><em style=\"line-height: 1.714285714; font-size: 1rem;\">(j<sup>3<\/sup> \u2013 27)<sup>2<\/sup> will have the same even-odd nature as (j<sup>3<\/sup> \u2013 27). Similarly, (j<sup>3<\/sup> + 1)<sup>3<\/sup> will have the same even-odd nature as (j<sup>3<\/sup>+1)<\/em><\/p>\n<ol style=\"list-style-type: lower-roman;\">\n<li><em style=\"line-height: 1.714285714; font-size: 1rem;\">j<sup>3<\/sup> will have the same even-odd nature as j itself.<\/em><\/li>\n<\/ol>\n<p><em>So, using this property, we\u2019ve done the first level of simplification: now, we only have to determine the even-odd nature of this, simpler expression: (j-27)(j + 1)<\/em><em>\u00a0<\/em><\/p>\n<p><strong><em><span style=\"text-decoration: underline;\">2<sup>nd<\/sup> Simplification <\/span><\/em><\/strong><\/p>\n<p><em>The simpler expression is a product of 2 terms: (j \u2013 27) and (j+1)<\/em><\/p>\n<p><em>When will the product of 2 terms be odd? Only if each of the 2 terms are themselves odd. If even one of these terms is even, the product will be even.<\/em><\/p>\n<p><em>So, to answer the question, we need to know: <strong><span style=\"text-decoration: underline;\">are each of the 2 terms odd<\/span><\/strong>?<\/em><\/p>\n<p><em>So, from the earlier situation of dealing with the product as a whole, we are now dealing with individual terms only: (j \u2013 27) and (j + 1)<\/em><\/p>\n<p><strong><em><span style=\"text-decoration: underline;\">Getting to the answer<\/span><\/em><\/strong><\/p>\n<p><em>Now, j can either be Even or Odd.<\/em><em>\u00a0<\/em><\/p>\n<p><em><span style=\"text-decoration: underline;\">Case 1: j is odd<\/span><\/em><\/p>\n<p><em>In this case, j + 1 = Odd + Odd = Even<\/em><\/p>\n<p><em>And j &#8211; 27 = Odd &#8211; Odd = Even<\/em><\/p>\n<p><em>Since both the terms are Even, the answer in this case will be NO, the given expression in not odd.<\/em><\/p>\n<p><em><span style=\"text-decoration: underline;\">Case 2: j is even<\/span><\/em><\/p>\n<p><em>In this case, j + 1 = Even + Odd = Odd<\/em><\/p>\n<p><em>And, j &#8211; 27 = Even &#8211; Odd = Odd<\/em><\/p>\n<p><em>Since both the terms are odd, the answer in this case will be YES, the given expression is odd<\/em><\/p>\n<p><em>So, as you can see, using this step-wise approach, we\u2019ve been able to simplify the question to this:<\/em><\/p>\n<p><em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>Is j even?<\/strong><\/em><\/p>\n<h2>Takeaway<\/h2>\n<p><span style=\"background-color: #ffff99;\"><strong>Use the properties of Even-Odd combinations to simplify scary-looking expressions.<\/strong> Have the confidence that all Even-Odd questions in the GMAT can be easily simplified. Don\u2019t get intimidated by complex expressions in Even-Odd questions and avoid the impulse to search for algebraic formulae to apply on such expressions. \u00a0<\/span><\/p>\n<h3>Test Yourself<\/h3>\n<p>You\u2019ll know that you\u2019ve learnt this lesson well, if your heart doesn\u2019t skip a beat at the first look of the following question:<\/p>\n<p><strong>P1.2<\/strong><strong>\u00a0\u00a0\u00a0 If X = P*N<sup>K<\/sup> + P where N and K are positive integers, is X divisible by 2?<\/strong><\/p>\n<p><strong style=\"line-height: 1.714285714; font-size: 1rem;\">(1) \u00a0 \u00a0 \u00a0 \u00a0<\/strong><strong style=\"line-height: 1.714285714; font-size: 1rem;\">N + KN = 915<\/strong><\/p>\n<p><strong style=\"line-height: 1.714285714; font-size: 1rem;\">(2) \u00a0 \u00a0 \u00a0 \u00a0<\/strong><strong style=\"line-height: 1.714285714; font-size: 1rem;\">P<sup>35<\/sup> + 35<sup>P<\/sup> is Even<\/strong><\/p>\n<p><a href=\"https:\/\/e-gmat.com\/blogs\/becoming-a-gmat-even-odd-champion-q1\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Solution to this GMAT Number properties odd-even question<\/a><\/p>\n<h2>2. \u00a0 \u00a0Wasting time on unimportant terms<\/h2>\n<p>What we mean<\/p>\n<p>What we mean by \u2018unimportant terms\u2019 is \u2018the terms that do not impact the Even- Odd nature of the expression. For example, consider the following question:<\/p>\n<p><strong>P2.1<\/strong><strong>\u00a0 \u00a0\u00a0<strong>If a and b are integers, is a + 8b even?<\/strong><\/strong><\/p>\n<p>In this expression, the term 8b will be even, irrespective of whether b is even or odd (because, Even*Odd = Even and Even*Even = Even). So, you should focus all your attention on analysing whether a is even or odd, because that is what will get you to the answer.<\/p>\n<p>If you fall into the pitfall of analysing the given information to determine the even-odd nature of <strong><em>b<\/em><\/strong>, then you\u2019ll be squandering your most precious resource in the GMAT \u2013 Time. Minutes frittered away thus may create a time crunch towards the end of the test, and then, coming under the pressure of the seconds ticking away, you may frantically answer even questions that you know, wrong. So, it is very important to be on strict guard against even a moment spent on unneeded analysis. And, in Even-Odd questions, it\u2019s all too easy to fall into this booby trap.<\/p>\n<h2>What can you do to avoid this pitfall?<\/h2>\n<p>In order to not waste even a second on the unimportant terms, here are a few pointers that you should use to weed out the unimportant terms in an expression:<\/p>\n<ol style=\"list-style-type: lower-roman;\">\n<li><span style=\"font-size: 1rem; line-height: 1.714285714; color: #000000;\">A term of the form (Even number)*(X) will always be even<\/span><\/li>\n<li><span style=\"color: #000000;\"><span style=\"font-size: 1rem; line-height: 1.714285714;\">In a term of the form (Even number) + X, the (Even number) plays no role in the Even-Odd nature of the term<\/span><span style=\"font-size: 1rem; line-height: 1.714285714;\">\u00a0<\/span><\/span><\/li>\n<li><span style=\"font-size: 1rem; line-height: 1.714285714; color: #000000;\">In a term of the form (Odd number)*(X), the (Odd number) plays no role in the Even-Odd nature of the term<\/span><\/li>\n<\/ol>\n<h3>Example<\/h3>\n<p><em>You\u2019ve already seen an example of the first pointer in Question P2.1<\/em><\/p>\n<p><em>Here\u2019s an example that will show all the three pointers in action<\/em><\/p>\n<p><strong>P2.2<\/strong><strong>\u00a0 \u00a0\u00a0<strong>If a, b, c and n are integers, is a + 8b + (2n+1)c even?<\/strong><\/strong><\/p>\n<p><strong><em><span style=\"text-decoration: underline;\">1<sup>st<\/sup> Pointer <\/span><\/em><\/strong><\/p>\n<p><em>The term 8b will always be even, irrespective of the value of b<\/em><\/p>\n<p><strong><em><span style=\"text-decoration: underline;\">2<sup>nd<\/sup> Pointer <\/span><\/em><\/strong><\/p>\n<p><em>In the given expression, the even term 8b doesn\u2019t impact the even-odd nature of this expression. So, the expression will have the same even-odd nature as the sum a + (2n+1)c<\/em><\/p>\n<p><strong><em><span style=\"text-decoration: underline;\">3<sup>rd<\/sup> Pointer<\/span><\/em><\/strong><\/p>\n<p><em>In the term (2n+1)c, (2n+1) is an odd number, and so plays no role in the even-odd nature of this term. So, the term (2n+1)c will have the same even-odd nature as c.<\/em><\/p>\n<p><em>So, the expression a + (2n+1)c will have the same even-odd nature as the expression a <span style=\"text-decoration: underline;\">+ c<\/span><\/em><\/p>\n<p>To some students Pitfall 2 may seem similar to Pitfall 1 because the strategy suggested to avoid Pitfall 2 (the Three Pointers) also leads to simplification of the given expression. However, even though the <em>effect <\/em>of the strategies suggested in Pitfalls 1 and 2 may be the same, the <em>problems <\/em>that these strategies tackle are different. In Pitfall 1, the problem is that a student may get intimidated by a difficult-looking expression. In Pitfall 2, on the other hand, the problem is that a student may waste time on analysing terms that do not contribute to the Even-Odd nature of an expression. These are two distinct problems, and so, Pitfalls 1 and 2 are distinct as well.<\/p>\n<h2>Takeaway<\/h2>\n<p><span style=\"background-color: #ffff99;\"><strong>When you see an expression, first use the Three Pointers to determine the unimportant terms. <\/strong>Do not waste precious time on processing the unimportant terms.<\/span><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-5223\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2015\/04\/Pitfall-2-e1429798892327.png\" alt=\"gmat quant number properties practice questions even odd\" width=\"550\" height=\"309\" \/><\/p>\n<h3>Test Yourself<\/h3>\n<p>See how much time you take on this question and if you waste time on any term that doesn\u2019t deserve it:<\/p>\n<p><strong>P2.3<\/strong><strong>\u00a0 \u00a0\u00a0<\/strong><strong style=\"line-height: 1.714285714; font-size: 1rem;\">If a, b and n are positive integers such that n = 3a \u2013 b<sup>3<\/sup>, is n<sup>2<\/sup> + 3 divisible by 2?<\/strong><\/p>\n<p><strong>(1)\u00a0 <\/strong><strong>a<sup>2<\/sup> \u2013 4b<sup>3<\/sup> \u2013 5 = 0<\/strong><\/p>\n<p><strong><strong>(2) \u00a03b<sup>3<\/sup> \u2013 a<sup>2<\/sup> + 6 = 0\u00a0<\/strong><\/strong><\/p>\n<p>(The detailed discussion of this question is available <a href=\"http:\/\/gmatclub.com\/forum\/if-a-b-and-n-are-positive-integers-such-that-n-3a-b3-195919.html\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">here<\/a>)<\/p>\n<h2>3. \u00a0 \u00a0Getting stumped in division<\/h2>\n<p><strong>What we mean<\/strong><\/p>\n<p>If A and B are given to be integers, where A &gt; B and A\/B is an integer, can you smoothly work out the relation between the even-odd nature of A, B and the integer A\/B?<\/p>\n<p>For example, consider the following question:<\/p>\n<p><strong>P3.1<\/strong><strong>\u00a0 \u00a0\u00a0<strong>If A, B and X are integers, X\/B is an even integer and XB\/(4A+1) is an integer, is XB\/(4A+1) odd?<\/strong><\/strong><\/p>\n<p>If you don\u2019t have a firm approach to deal with this and similar questions, you\u2019re bound to feel flummoxed, and then you\u2019ll:<\/p>\n<ol style=\"list-style-type: lower-roman;\">\n<li><span style=\"line-height: 1.714285714; font-size: 1rem;\">Either give up this question as too difficult<\/span><\/li>\n<li><span style=\"line-height: 1.714285714; font-size: 1rem;\">Or will gingerly try number substitution to see which values of X and B give an even value of X\/B, and then with those values of X, try to see if XB\/(4A+1)<\/span> <span style=\"line-height: 1.714285714; font-size: 1rem;\">is odd. This approach is time-consuming and error-prone, because you may miss out on some possible cases.<\/span><\/li>\n<\/ol>\n<p>Both possible actions are costly \u2013 in terms of lost score points and lost time. So, it is important to not fall prey to such questions.<\/p>\n<h2>What can you do to avoid this pitfall?<\/h2>\n<p>This pitfall is easily avoided by following the standard approach presented here \u2013<\/p>\n<p style=\"text-align: center;\"><strong>Convert the division equation into a multiplication equation.<\/strong><\/p>\n<h2>Illustrative Example<\/h2>\n<p><em>Let\u2019s illustrate this approach on question P3.1<\/em><\/p>\n<p><em>The division equation that we can write for the terms X\/B is:<\/em><\/p>\n<p><em>We can convert this equation into a multiplication equation by multiplying both sides with B. We get:<\/em><\/p>\n<p><em>X = (Even number)*B<\/em><\/p>\n<p>&#8211;&gt; \u00a0<em>X is Even\u00a0 (Refer to Pointer (i) in Pitfall 2)<\/em><\/p>\n<p><em>Now, let\u2019s write the division equation for the term (XB\/4A+1):<\/em><\/p>\n<p>XB\/(4A + 1) = integer Z (say)<\/p>\n<p><em>Converting this equation into a multiplication equation, we get:<\/em><\/p>\n<p>&#8211;&gt; \u00a0<em>XB = (4A+1)*(Z)<\/em><\/p>\n<p>&#8211;&gt; \u00a0<em>XB has the same Even-Odd nature as Z\u00a0<\/em><em style=\"line-height: 1.714285714; font-size: 1rem;\">(because 4A + 1 is odd \u2013 Refer to Pointers (ii) and (iii) in Pitfall 2)<\/em><\/p>\n<p><em>Since X is Even, XB is Even<\/em><\/p>\n<p>&#8211;&gt; \u00a0<em>Z is Even<\/em><\/p>\n<p><em>So, we see that the given expression will be Even.<\/em><\/p>\n<h2>Takeaway<\/h2>\n<p><span style=\"background-color: #ffff99;\">In Even-Odd questions that involve division, convert the division equation into multiplication equation.<\/span><\/p>\n<h3>Test Yourself<\/h3>\n<p><strong>P3.2<\/strong><strong>\u00a0 \u00a0\u00a0<strong>If x, y and z are positive integers such that x<sup>4 <\/sup>y<sup>3<\/sup> = z<sup>2<\/sup>, is x<sup>9<\/sup> \u2013 y<sup>6<\/sup> odd?<\/strong><\/strong><\/p>\n<p><strong>(1) \u00a0(<strong><strong>x<sup>4<\/sup>\u00a0y<sup>3<\/sup>)\/(<strong><strong>x<sup><span style=\"font-size: 10.5px; line-height: 0px;\">2<\/span><\/sup>\u00a0+ y<sup><span style=\"font-size: 10.5px; line-height: 0px;\">2<\/span><\/sup><\/strong><\/strong><\/strong><\/strong><strong>)can be written in the form 4k + 3, where k is a positive integer.<\/strong><\/strong><\/p>\n<p><strong>(2) \u00a0z = x + y<\/strong><\/p>\n<p>(The detailed discussion of this question is available <a href=\"http:\/\/gmatclub.com\/forum\/if-x-y-and-z-are-positive-integers-such-that-x-4-y-3-z-196033.html\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">here<\/a>)<\/p>\n<h1>Conclusion<\/h1>\n<p>Even when you know a concept, you might not be able to answer the questions that test advanced application of that concept. In this article, we saw the three pitfalls that many students fall into in Even-Odd questions. If you make a conscious effort to avoid these pitfalls, you\u2019ll find that your ability to answer 700+ level Even-Odd questions will improve significantly. As a happy co-benefit, the time you take to solve the questions will also come down.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-5224\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2015\/04\/Conclusion-e1429798931843.png\" alt=\"gmat quant number properties practice questions even odd\" width=\"700\" height=\"285\" \/><\/p>\n<p>If you wish to work further on the 3 pitfalls, please practice the 3 questions provided below.<\/p>\n<p>Wish you enjoy your journey of GMAT Prep and reach a great score on the GMAT!<\/p>\n<h2>GMAT Number properties (Even-Odd) Practice Questions<\/h2>\n<h6>Question 1<\/h6>\n<p><strong>Is the product of two integers A and B odd?<\/strong><\/p>\n<p><strong>(1)\u00a0 <\/strong><strong>A is the number of factors of N, where N is a perfect square and B = A<sup>3<\/sup> -1<\/strong><\/p>\n<p><strong>(2)\u00a0 <\/strong><strong>A is a product of two consecutive prime numbers and when\u00a0\u00a0 <\/strong><strong>\u00a0is added to A, the sum is an odd number.<\/strong><\/p>\n<p>(The detailed solution of this question is available <a href=\"http:\/\/gmatclub.com\/forum\/is-the-product-of-two-integers-a-and-b-odd-195888.html\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">here<\/a>)<\/p>\n<h6>Question 2<\/h6>\n<p><strong>If P and Q are positive integers, is the product 3P<sup>Q<\/sup> divisible by 2?<\/strong><\/p>\n<p><strong><span style=\"line-height: 1.714285714; font-size: 1rem;\">(1) \u00a06Q<\/span><sup>3<\/sup><span style=\"line-height: 1.714285714; font-size: 1rem;\"> + 2 is an even number<\/span><\/strong><\/p>\n<p><strong><span style=\"line-height: 1.714285714; font-size: 1rem;\">(2) \u00a0P + 8Q<\/span><sup>2<\/sup><span style=\"line-height: 1.714285714; font-size: 1rem;\"> is a prime number<\/span><\/strong><\/p>\n<p>(The detailed solution of this question is available <a title=\"Becoming a GMAT Even-Odd Champion: Q2\" href=\"https:\/\/e-gmat.com\/blogs\/becoming-a-gmat-even-odd-champion-q2\/\" target=\"_blank\" rel=\"noopener noreferrer\" data-wpel-link=\"internal\">here<\/a> )<\/p>\n<h6>Question 3<\/h6>\n<p><strong>Is 3a + 2b + 5c even if 0&lt;a&lt;b&lt;c and a, b and c are integers?<\/strong><\/p>\n<p><strong><span style=\"line-height: 1.714285714; font-size: 1rem;\">(1) \u00a09a+7c is not even<\/span><\/strong><\/p>\n<p><strong><span style=\"line-height: 1.714285714; font-size: 1rem;\">(2) \u00a0a<\/span><sup>3<\/sup><span style=\"line-height: 1.714285714; font-size: 1rem;\">*(c-1)<\/span><sup>2<\/sup><span style=\"line-height: 1.714285714; font-size: 1rem;\"> is odd<\/span><\/strong><\/p>\n<p>(The detailed solution of this question is available <a title=\"Becoming a GMAT Even-Odd Champion: Q3\" href=\"https:\/\/e-gmat.com\/blogs\/becoming-a-gmat-even-odd-champion-q3\/\" target=\"_blank\" rel=\"noopener noreferrer\" data-wpel-link=\"internal\">here<\/a>)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When it comes to &#8216;Even &#8211; Odd&#8217;, it&#8217;s not just an issue on Delhi roads, but also in your GMAT Quant section.\u00a0Even-Odd numbers is deemed to be among the easier concepts on the GMAT Quant, and yet, come 700+ level questions from this concept, many students get them wrong. Our Subject Matter Experts have closely [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[60,61],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Krishna Chaitanya","author_link":"https:\/\/e-gmat.com\/blogs\/author\/krishnae-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>GMAT Quant | 3 mistakes in Even-Odd Questions | Number Properties | e-GMAT<\/title>\n<meta name=\"description\" content=\"When it comes to &#039;Even - Odd&#039;, it&#039;s not just an issue on Delhi roads but also in your GMAT Quant section.\u00a0&#039;Even-Odd numbers&#039; topic of Number properties is deemed to be among the easier concepts on the GMAT Quant, and yet, come 700+ level questions from this concept, many students get them wrong.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/e-gmat.com\/blogs\/gmat-quant-3-mistakes-in-even-odd-number-properties-questions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Quant | 3 mistakes in Even-Odd Questions | Number Properties\" \/>\n<meta property=\"og:description\" content=\"When it comes to &#039;Even - 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