{"id":13510,"date":"2022-07-16T21:42:00","date_gmt":"2022-07-16T16:12:00","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=13510"},"modified":"2022-11-29T17:41:34","modified_gmt":"2022-11-29T12:11:34","slug":"quickly-solve-gmat-quant-questions-on-time-and-work-work-time-lcm-method","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/quickly-solve-gmat-quant-questions-on-time-and-work-work-time-lcm-method\/","title":{"rendered":"How to quickly solve GMAT Quant Questions on Time and Work"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">13<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<p><span style=\"color: #000000;\">Time and Work problems are the low-hanging fruit in the world of GMAT Quant Questions. You can easily learn and apply the concepts. The only question to ask is, &#8216;Can you solve them faster?&#8217; The answer is Yes. In this article, we&#8217;ll compare the conventional methods of solving GMAT Quant questions on Time and work with other quick and efficient methods. The other methods being the LCM method and the efficiency (work rate) method.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"1024\" height=\"589\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/How_to_quickly_solve_GMAT_Quant_Questions_on_Time_and_Work-1024x589.png\" alt=\"how to quickly solve gmat quant questions on time and work\" class=\"wp-image-13592\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/How_to_quickly_solve_GMAT_Quant_Questions_on_Time_and_Work-1024x589.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/How_to_quickly_solve_GMAT_Quant_Questions_on_Time_and_Work-300x173.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/How_to_quickly_solve_GMAT_Quant_Questions_on_Time_and_Work-768x442.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/How_to_quickly_solve_GMAT_Quant_Questions_on_Time_and_Work-1080x621.png 1080w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/How_to_quickly_solve_GMAT_Quant_Questions_on_Time_and_Work.png 1600w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><span style=\"color: #000000;\">In this article, we will further explain the concept of time and work with illustrative examples. Here are the key points of the article.<\/span><\/p>\n\n\n\n<ul class=\"has-text-color\" style=\"color:#00aeef\"><li><span style=\"color: #00aeef;\"><a style=\"color: #00aeef;\" href=\"#index-1\">Learn <\/a>to solve GMAT Quant Questions on Time and Work quickly<\/span><\/li><li><span style=\"color: #00aeef;\"><a style=\"color: #00aeef;\" href=\"#index-2\">The conventional method of solving Time and Work Problems<\/a><\/span><\/li><li><span style=\"color: #00aeef;\"><a style=\"color: #00aeef;\" href=\"#index-3\">Solving Time and Work problems by LCM Method<\/a><\/span><\/li><li><span style=\"color: #00aeef;\"><a style=\"color: #00aeef;\" href=\"#index-4\">Efficiency (work rate) method to solve Time and Work problems<\/a><\/span><\/li><li><span style=\"color: #00aeef;\"><a style=\"color: #00aeef;\" href=\"#takeaways\">Takeaways from the article<\/a><\/span><\/li><\/ul>\n\n\n\n<h2 id=\"index-1\"><span style=\"color: #000000;\">What will you learn from this article<\/span><\/h2>\n\n\n\n<p><span style=\"color: #000000;\">In this article, you will learn:<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">The application of LCM to solve Time and Work questions<\/span><\/li><li><span style=\"color: #000000;\">A comparative study of methods of solving Time and Work problems \u2013 by using the fraction and by using the LCM method, which one should be used and when?<\/span><\/li><li><span style=\"color: #000000;\">How to define efficiency and how to implement it in a problem?<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">In this article, we have only used official sources to help you understand the above aspects. Also, at the end of the article, we have provided some practice questions where you can apply your learning from the article.<\/span><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong><a href=\"https:\/\/e-gmat.com\/blogs\/gmat-710-wharton-first-time-test-takers-story\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">Guillermo scored a Q50 and got an admit from the Wharton School<\/a> . Read his amazing success story on how <a href=\"https:\/\/e-gmat.com\/blogs\/working-professionals-gmat-study-plan-balancing-work-gmat\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">he managed his work and preparation with a rock-solid study plan.<\/a><\/strong><\/p><p>You too can save 60+ hours of GMAT preparation with a well crafted, personlised study plan. Learn the other benefits of a <strong><a href=\"https:\/\/e-gmat.com\/blogs\/gmat-study-plan-benefits-study-plans-100-score-improvement\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">well defined study plan<\/a><\/strong> in this article.<\/p><p>We can help you with a detailed study plan, customized according to your strengths and weaknesses. Create you study plan today in just 3 steps:<\/p><\/blockquote>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/5ftgtAl_3C0? rel=0\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer rel=0; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\"><\/iframe>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-f48bcf80-f1e9-4a57-9842-17e92c7ccfcb\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/create-study-plan\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium ub-button-flex-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 576, 512\"><path fill=\"currentColor\" d=\"M144.3 32.04C106.9 31.29 63.7 41.44 18.6 61.29c-11.42 5.026-18.6 16.67-18.6 29.15l0 357.6c0 11.55 11.99 19.55 22.45 14.65c126.3-59.14 219.8 11 223.8 14.01C249.1 478.9 252.5 480 256 480c12.4 0 16-11.38 16-15.98V80.04c0-5.203-2.531-10.08-6.781-13.08C263.3 65.58 216.7 33.35 144.3 32.04zM557.4 61.29c-45.11-19.79-88.48-29.61-125.7-29.26c-72.44 1.312-118.1 33.55-120.9 34.92C306.5 69.96 304 74.83 304 80.04v383.1C304 468.4 307.5 480 320 480c3.484 0 6.938-1.125 9.781-3.328c3.925-3.018 97.44-73.16 223.8-14c10.46 4.896 22.45-3.105 22.45-14.65l.0001-357.6C575.1 77.97 568.8 66.31 557.4 61.29z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Create your Personalized Study Plan<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<p><\/p>\n\n\n\n<h2 id=\"index-2\">The conventional<span style=\"color: #000000;\"> method of solving Time and Work Problems<\/span><\/h2>\n\n\n\n<p><span style=\"color: #000000;\">In time and work problem, where people with different constant efficiencies do a certain work, we assume the total work to be constant. Mostly we solve these questions assuming the total work to be 1 unit.&nbsp;Let\u2019s look at the following example:<\/span><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p><strong><em>For any strategic advice for GMAT or MBA Admissions, write to us at&nbsp;<a href=\"mailto:acethegmat@e-gmat.com\">acethegmat@e-gmat.com<\/a>.&nbsp;<a href=\"https:\/\/e-gmat.com\/free-trial-registration\/?channel=blogsin_article&amp;utm_source=blogs&amp;utm_medium=in_article&amp;utm_campaign=free_trial&amp;utm_content=about_the_gmat&amp;utm_term=blogs_in_article\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">Take a free trial&nbsp;<\/a><\/em><em>and get unlimited access to concept files, live sessions, and practice questions.<\/em><\/strong><\/p><\/blockquote>\n\n\n\n<h4><span style=\"color: #000000;\">Example 1<\/span><\/h4>\n\n\n\n<p><span style=\"color: #000000;\"><strong>It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?<\/strong><\/span><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"513\" height=\"251\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-1.png\" alt=\"gmat quant questions on gmat time and work\" class=\"wp-image-13521\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-1.png 513w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-1-300x147.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-1-510x251.png 510w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/figure>\n\n\n\n<h5><span style=\"color: #000000;\">Solution 1A &#8211; Conventional Method<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">Here it is given that two machines, working independently with their different constant efficiency, complete a large production order in 4 hours and 3 hours respectively.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">As the total work done by both the machines are same, the work is constant<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">Let us assume the total work of the production order is 1 unit. Therefore, we can say:<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">1st machine in 4 hours can complete 1 unit of work<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, 1st machine in 1 hour can complete 1\/4 units of work<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Similarly, 2nd machine in 3 hours can complete 1 unit of work<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, 2nd machine in 1 hour can complete 1\/3 units of work<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">If both the machines work together simultaneously, then in 1 hour they will complete (1\/4 + 1\/3) = [(3+4)\/12] units of work = 7\/12 units of work<\/span><\/li><li><span style=\"color: #000000;\">As the machines can complete 7\/12 units of work in 1 hour time, to complete the whole work of 1 unit, they will take [1\/(7\/12)] hours = 12\/7 hours<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Hence, working together, both the machines will take (12\/7) hours to complete the production order.<\/strong><\/span><\/p>\n\n\n\n<h5><span style=\"color: #339966;\"><strong>Important Observations<\/strong><\/span><\/h5>\n\n\n\n<p><span style=\"color: #339966;\">At the beginning of the solution, we have assumed the total constant work to be 1 unit.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #339966;\">Important thing one can observe here is that assuming the total work to be 1 unit or x units can make life difficult for us \u2013 because, when we calculate the 1-day work of that person or machine, chances are very high that we will be getting fractional values<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #339966;\">Now we all know, dealing with fractional calculations can be difficult and it increases the chances of making an error to a great extent. But the question is how we can avoid it?<\/span><\/p>\n\n\n\n<p><span style=\"color: #339966;\">Again, if you look carefully, the 1-day work of a person or a machine is calculated as the ratio of total work and the time taken.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #339966;\">Therefore, if the assumed value of the total work is a multiple of the time taken, then the 1- day work will certainly be an integer value<\/span><\/li><li><span style=\"color: #339966;\">So, when we are assuming a value for the total work, we need to consider such a value which should be a multiple of the time taken by the different parties working on that job<\/span>\n<ul>\n<li><span style=\"color: #339966;\">In other words, the assumed value of the total work can be taken as the least common multiple (LCM) of the given individual time taken by the persons or machines working on that job<\/span><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p><span style=\"color: #339966;\">Let us try to solve the same question using the method that we just mentioned.<\/span><\/p>\n\n\n\n<h5><span style=\"color: #000000;\">Solution 1B &#8211; Changing the total work value<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">Let us assume the total work of the production order is 12 units. Therefore, we can say:<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">In 4 hours 1st machine can complete 12 units of work<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, in 1 hour 1st machine can complete 3 units of work<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Similarly, 2nd machine in 3 hours can complete 12 units of work<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, in 1 hour 2nd machine can complete 4 units of work<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">If both the machines work simultaneously together, in 1 hour they will complete (3 + 4) units of work = 7 units of work<\/span><\/li><li><span style=\"color: #000000;\">As the complete work is 12 units, to complete the order they need to do total 12 units of work together<\/span><\/li><li><span style=\"color: #000000;\">Combined together, the machines are completing 7 units of work in 1 hour<\/span><\/li><li><span style=\"color: #000000;\">Therefore, the machines will complete 12 units of work together in (12\/7) hours<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Hence, working together, both the machines will take (12\/7) hours to complete the production order.<\/strong><\/span><\/p>\n\n\n\n<h5><span style=\"color: #000000;\">Takeaways<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">If we compare the methods explained above, fundamentally they are same, with some difference in value-wise derivation. But the most important thing to observe is that there are no fractional intermediate calculations involved in the second solution.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">As the total work is assumed to be the LCM of 3 and 4, we are avoiding the fractional calculation, and thus, saving the overall calculation time.<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">Let us take another example to validate this learning:<\/span><\/p>\n\n\n\n<div style=\"height:34px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4><span style=\"color: #000000;\">Example 2<\/span><\/h4>\n\n\n\n<p><span style=\"color: #000000;\"><strong>One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3&nbsp;<\/strong><strong>hours. If both pipes are used together, how long will it take to fill 2\/3<\/strong>&nbsp;<strong>rd of the tank?<\/strong><\/span><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"517\" height=\"240\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-2.png\" alt=\"gmat quant questions on gmat time and work\" class=\"wp-image-13522\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-2.png 517w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-2-300x139.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/figure>\n\n\n\n<h5><span style=\"color: #000000;\">Solution 2A &#8211; Conventional Method<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">In this question, it is given that one inlet pipe can fill an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours.<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">As the capacity of the tank remains the same, let\u2019s assume the capacity of the tank is 1 unit.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">As the 1st pipe takes 5 hours to fill 1 unit,<\/span>\n<ul>\n<li><span style=\"color: #000000;\">In 1 hour it will fill 1\/5 units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Similarly, the 2nd pipe takes 3 hours to fill 1 unit<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, in 1 hour it will fill 1\/3 units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">If both pipes are used together, in 1 hour they will fill = (1\/5 + 1\/3) units = (3+5)\/15 units = 8\/15 units<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Hence to fill 2\/3rd of the tank, they will take = (2\/3) \/ (8\/15) = 2\/3 x 15\/8 = 5\/4 hours<\/strong><\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">Let&#8217;s try solving this question with the LCM method<\/span><\/p>\n\n\n\n<h5><span style=\"color: #000000;\">Solution 2B &#8211; LCM Method<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">As the capacity of the tank remains the same, let\u2019s assume the capacity of the tank is 15 units.<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">[notice that 15 = LCM (3,5)]<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">As the 1st pipe takes 5 hours to fill 15 units,<\/span>\n<ul>\n<li><span style=\"color: #000000;\">In 1 hour it will fill 3 units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Similarly, the 2nd pipe takes 3 hours to fill 15 units<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, in 1 hour it will fill 5 units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">If both pipes are used together, in 1 hour they will fill = (3 + 5) units = 8 units<\/span><\/li><li><span style=\"color: #000000;\">The total work to be completed = (2\/3 x 15) = 10 units<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Hence, to fill 2\/3rd of the tank, they will take = 10\/8 hours = 5\/4 hours<\/strong><\/span><\/p>\n\n\n\n<h5><span style=\"color: #000000;\">Takeaways<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">As you can see, both the problems can be solved using the conventional method as well as the LCM method. However, application of LCM method significantly decreases the calculation related, and therefore the time taken to solve a particular question becomes less.<\/span><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Also, read our article on <a href=\"https:\/\/e-gmat.com\/blogs\/gmat-probability-3-deadly-mistakes-to-avoid-gmat-quant\/\" target=\"_blank\" rel=\"noreferrer noopener\" data-wpel-link=\"internal\">how to avoid the 3 most common mistakes in Probability<\/a><\/p><\/blockquote>\n\n\n\n<div style=\"height:34px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 id=\"index-3\"><span style=\"color: #000000;\">Solving Time and Work problems by LCM Method<\/span><\/h2>\n\n\n\n<p><span style=\"color: #000000;\">In the following questions, we will solve the GMAT Quant Questions on Time and Work by applying the LCM method only.<\/span><\/p>\n\n\n\n<h4><span style=\"color: #000000;\">Example 3<\/span><\/h4>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 3 hours, and Machine B can fill the same lot in x hours. If A and B worked alternatively, while each work for 1 hour at a time, the total work gets completed in 4 hours. What is the value of x?<\/strong><\/span><\/p>\n\n\n\n<h5><span style=\"color: #000000;\">&nbsp;Solution<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">In this question, it is given that machine A can fill a production lot in 3 hours, and machine B can fill the same production lot in x hours when they are working alone.<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">However, they will take 4 hours to complete the job, when they are working alternatively for 1 hour each.<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">Let us assume the total work to be 3x units (LCM of 3 and x)<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">As machine A takes 3 hours to fill 3x units<\/span>\n<ul>\n<li><span style=\"color: #000000;\">In 1 hour it will fill (3x\/3) units = x units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Similarly, machine B takes x hours to fill 3x units<\/span>\n<ul>\n<li><span style=\"color: #000000;\">In 1 hour it will fill (3x\/x) units = 3 units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">It is also given that; machine A and machine B, working alternatively, take 4 hours to fill 3x units<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Therefore, in 2 hours\u2019 time they will fill = (x + 3) units<\/span><\/li>\n<li><span style=\"color: #000000;\">Hence, in 1 hour the production lot they fill = 1\/2 X (x+3) units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Now we can say in 4 hours,<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Units filled by A + units filled by B = total production units<\/span><\/li>\n<li><span style=\"color: #000000;\">Or, 4 x 1\/2 x (x+3) = 3x<\/span><\/li>\n<li><span style=\"color: #000000;\">Or, 2x + 6 = 3x<\/span><\/li>\n<li><span style=\"color: #000000;\">Or, x = 6 hours<\/span><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Hence, the value of x is 6.<\/strong><\/span><\/p>\n\n\n\n<h5><span style=\"color: #000000;\">Key Takeaways<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">Unlike the previous questions, in this question, we have a variable defined as x. Even in such case, we can apply the LCM method, as we did in the solved example, to get a quick and accurate answer.<\/span><\/p>\n\n\n\n<div style=\"height:34px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4><span style=\"color: #000000;\">Example 4<\/span><\/h4>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Working at a constant rate, pump X pumped out half of the water in a flooded basement in 4 hours. Then pump Y was started and the two pumps, working independently at their respective constant rates, pumped out the rest of the water in 3 hours. How many hours would it have taken pump Y, operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?<\/strong><\/span><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"512\" height=\"254\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-3.png\" alt=\"gmat quant questions on gmat time and work\" class=\"wp-image-13523\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-3.png 512w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-3-300x149.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-3-510x254.png 510w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/figure>\n\n\n\n<p><span style=\"color: #000000;\">Solution<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">In this question, there are two pumps working separately at their own constant rate.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">Pump X cleared half of the water present in the flooded basement in 4 hours<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Therefore, to clear all the water, pump A would have taken twice the amount of time, i.e. 8 hours<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">After pump X worked for 4 hours, pump Y also started working, and together they took 3 hours to clear the remaining half of the water<\/span>\n<ul>\n<li><span style=\"color: #000000;\">As they took 3 hours to clear half the total amount of water, they would have taken double of that time, e. 6 hours, to clear the whole water<\/span><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">With this inference, we actually have a simple problem, which is very similar to the previous ones that we solved.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">Pump X takes 8 hours to clear the whole water<\/span><\/li><li><span style=\"color: #000000;\">Pump X and Y together take 6 hours to clear the whole water<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">Let us assume the total amount of water to be 24 units<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">In 8 hours, pump X clears 24 units,<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, in 1 hour, pump X clears 24\/8 units = 3 units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Similarly, in 6 hours. pump Y clears 24 units<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, in 1 hour, pump X and Y together clear 24\/6 units = 4 units<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Now in 1 hour, out of the 4 units of water cleared by pump X and Y together, 3 units were cleared by X only<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Therefore, the amount of water cleared by Y in <\/span>1 hour<span style=\"color: #000000;\"> = (4 \u2013 3) unit = 1 unit<\/span><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">As pump Y can clear 1 unit of water in 1 hour, it will take 24\/1 hours = 24 hours to clear the whole amount of water, when working alone at its constant rate.<\/span><\/p>\n\n\n\n<h5><span style=\"color: #339966;\"><strong>Important Observations<\/strong><\/span><\/h5>\n\n\n\n<p><span style=\"color: #339966;\">Apart from the usual application of the LCM method, another distinct observation we can do from this question, which is applicable to the previous question also. Let us see that:<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #339966;\">X can complete the whole work alone in 8 hours<\/span><\/li><li><span style=\"color: #339966;\">Y can complete the whole work alone in 24 hours<\/span><\/li><li><span style=\"color: #339966;\">X and Y together can complete the whole work in 6 hours<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #339966;\">It is noticeable that the time taken by them together to complete the work is much less than their individual time. This is happening because of their difference in individual efficiencies.<\/span><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Also, read our article on <a href=\"https:\/\/e-gmat.com\/blogs\/gmat-geometry-questions-most-common-mistakes\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">how to avoid the 3 most common mistakes in Geometry<\/a><\/p><\/blockquote>\n\n\n\n<div style=\"height:34px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 id=\"index-4\"><span style=\"color: #000000;\">Efficiency (work rate) method to solve Time and Work problems<\/span><\/h2>\n\n\n\n<p><span style=\"color: #000000;\">As we know, efficiency essentially means the rate of work, i.e. the amount of work done in unit time.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">The more time one takes to complete a job, the less efficient the person is.<\/span><\/li><li><span style=\"color: #000000;\">Similarly, the less time one takes to complete a job, the more efficient the person is. Therefore, we can say that efficiency is inversely proportional to the time taken to complete the work.<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">In a given scenario, efficiency can be used to explain the work rate either of an individual or of a group consists of similar objects. For a group, it is generally assumed that everyone within that group has the same efficiency.<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">Let us take an example of a time and work problem, which relates to the concept of efficiency:<\/span><\/p>\n\n\n\n<h4><span style=\"color: #000000;\">Example 5<\/span><\/h4>\n\n\n\n<p><span style=\"color: #000000;\"><strong>At a loading dock, each worker on the night crew loaded <span style=\"font-size: 11.6667px;\">3\/4<\/span><\/strong>&nbsp;<strong>as many boxes as each worker&nbsp;<\/strong><strong>on the day crew. If the night crew has <\/strong><span style=\"font-size: 11.6667px;\"><strong>4\/5<\/strong>&nbsp;<\/span><strong>as many workers as the day crew, what fraction of&nbsp;<\/strong><strong>all the boxes loaded by the two crews did the day crew load?<\/strong><\/span><\/p>\n\n\n\n<h5><span style=\"color: #000000;\">Solution<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">In this question, we have two separate groups of people to consider.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">Each member within the group has the same efficiency as other members<\/span><\/li><li><span style=\"color: #000000;\">However, group-wise the efficiencies are different from each other<\/span>\n<ul>\n<li><span style=\"color: #000000;\">This means that everyone in the night crew has the same efficiency and everyone in the day crew has the same efficiency. However, the efficiency of the day and night crew, in this case, is different.<\/span><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">Let us look at the problem in detail.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" width=\"508\" height=\"247\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-4.png\" alt=\"gmat quant questions on gmat time and work\" class=\"wp-image-13524\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-4.png 508w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2018\/07\/gmat-quant-questions-time-and-work-4-300x146.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/figure>\n\n\n\n<p><span style=\"color: #000000;\">It is given that there are two groups of workers \u2013 one operates at daytime and the other one operates at night time.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">Each worker on the night crew loaded 3\/4 as many boxes as each worker on the day crew<\/span>\n<ul>\n<li><span style=\"color: #000000;\">This statement defines the <strong>difference in efficiency of each worker <\/strong>belonging&nbsp;to the&nbsp; night crew and the day crew<\/span><\/li>\n<li><span style=\"color: #000000;\">If we assume that each worker in the day crew loaded 4 boxes, then each worker in the night crew must have loaded 4x (3\/4) boxes = 3 boxes<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">It is also given that night crew has 4\/5 as many workers as the day crew<\/span>\n<ul>\n<li><span style=\"color: #000000;\">If we assume that there are 5 workers on the day crew, then there will be 5x 4\/5 = 4 workers in the night crew<\/span><\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">[notice that we have intentionally assumed the number of box loaded and the number of day crew workers as 4 and 5, to avoid any fractional calculation. Both the numbers could have been assumed as 1 or any other number \u2013 the end result would have been same, but may lead to fractional calculations]<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">We can show the whole data in the following table:<\/span><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><span style=\"color: #000000;\">&nbsp;<\/span><\/td><td>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">Day Crew<\/span><\/p>\n<\/td><td>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">Night Crew<\/span><\/p>\n<\/td><\/tr><tr><td><span style=\"color: #000000;\">Number of boxed loaded per worker (X)<\/span><\/td><td>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">4<\/span><\/p>\n<\/td><td>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">3<\/span><\/p>\n<\/td><\/tr><tr><td><span style=\"color: #000000;\">Number of workers in the crew (N)<\/span><\/td><td>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">5<\/span><\/p>\n<\/td><td>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">4<\/span><\/p>\n<\/td><\/tr><tr><td><span style=\"color: #000000;\">Total boxes loaded (X \u00d7 N)<\/span><\/td><td>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">4 \u00d7 5 = 20<\/span><\/p>\n<\/td><td>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">3 \u00d7 4 = 12<\/span><\/p>\n<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><span style=\"color: #000000;\">As we can see, total boxes loaded by day crew are 20 and by night crew is 12. Hence, the boxes loaded by day crew as the fraction of all the boxes loaded by both the crew = [20\/(20+12)] = 20\/32 = 5\/8<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">Let us take one last example to demonstrate the application of efficiency:<\/span><\/p>\n\n\n\n<h4><span style=\"color: #000000;\">Example 6<\/span><\/h4>\n\n\n\n<p><span style=\"color: #000000;\">M<strong>achines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?<\/strong><\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\"><strong>(1) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.<\/strong><\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\"><strong>(2) Machine Y, working alone, fills a production order of twice the size in 6 hours.<\/strong><\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">Option choices:<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">A)&nbsp; &nbsp; &nbsp;Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">B)&nbsp; &nbsp; &nbsp;Statement (2) ALONE is sufficient, but statement (1) alone is not&nbsp;sufficient<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">C)&nbsp; &nbsp; &nbsp;BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is&nbsp;sufficient<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">D)&nbsp; &nbsp; &nbsp;EACH statement ALONE is&nbsp;sufficient<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\">E)&nbsp; &nbsp; &nbsp;Statements (1) and (2) TOGETHER are NOT&nbsp;sufficient<\/span><\/p>\n\n\n\n<h5><span style=\"color: #000000;\">Solution<\/span><\/h5>\n\n\n\n<p><span style=\"color: #000000;\">In this question, two machines X and Y, with different efficiency, can work on a certain job.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">The question asks the number of extra hours that machine Y takes to complete the job when working alone, compared to the time taken by machine X to complete the same job, working alone.<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">As no other information was provided in the question stem, we will analyze the given statements<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Analysing Statement 1:<\/strong><\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">As per the information given in statement 1, machines X and Y, working together, fill a production order of the same size in two-thirds the time that machine X, working alone, does.<\/span><\/li><li><span style=\"color: #000000;\">If we assume that machine X, working alone, takes &#8216;t&#8217; hours to complete the job, then from statement 1 we can say<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Machine X and Y, working together, complete the whole work in (2\/3)t hours<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">As both the machines work on their constant efficiencies throughout, we can say in (2\/3)t hours&nbsp;machine X can complete 2\/3 rd of the total work<\/span><\/li><li><span style=\"color: #000000;\">Therefore, in that (2\/3)t hours, machine Y completes 1\/3 rd of the total work<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, machine Y can complete the total work in (2\/3)t \u00d7 3 hours = 2t hours<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">But we cannot deduce the exact value of t from this statement<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Hence, statement 1 is not sufficient to answer the question.<\/strong><\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Analysing Statement 2:<\/strong><\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">As per the information <\/span>given<span style=\"color: #000000;\"> in statement 2, machine Y, working alone, fills a production order of twice the size in 6 hrs<\/span><\/li><li><span style=\"color: #000000;\">Hence, if we consider a production order of the original volume, machine Y will take 3 hours to complete it<\/span><\/li><li><span style=\"color: #000000;\">But from this statement, we cannot figure out any information regarding the work rate or time <\/span>taken<span style=\"color: #000000;\"> by X to complete the work<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\">Hence, statement 2 is not sufficient to answer the question.<\/span><\/p>\n\n\n\n<p><span style=\"color: #000000;\"><strong>Combining Both Statements:<\/strong><\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">If we consider both statements together, we can say machine Y takes 2t hours to complete the whole job, which is equal to 3 hours<\/span>\n<ul>\n<li><span style=\"color: #000000;\">Hence, the value of t = 3\/2 hours<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">We also know that machine X takes t hours to complete the whole job working alone<\/span>\n<ul>\n<li><span style=\"color: #000000;\">As we already know t is equal to 3\/2 hours, we can say machine X takes 3\/2 hours to complete the job working alone<\/span><\/li>\n<\/ul>\n<\/li><li><span style=\"color: #000000;\">Therefore, machine Y takes (3 &#8211; (3\/2)) hours = 3\/2 hours more than what machine X takes to complete the work, working individually<\/span><\/li><\/ul>\n\n\n\n<p><span style=\"color: #000000;\"><strong>As information from both the statements <\/strong>is<strong> required to solve the question, we can say the correct answer choice is Option C.<\/strong><\/span><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Also, read our article on <a href=\"https:\/\/e-gmat.com\/blogs\/permutation-combination-avoid-3-mistakes-gmat\/\" data-wpel-link=\"internal\" target=\"_blank\" rel=\"noopener noreferrer\">how to avoid the 3 most common mistakes in Permutations and Combinations.<\/a><\/p><\/blockquote>\n\n\n\n<div style=\"height:34px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 id=\"takeaways\"><span style=\"color: #000000;\">Takeaways from this article<\/span><\/h2>\n\n\n\n<p><span style=\"color: #000000;\">To quickly solve GMAT Quant Questions on Time and Work, please refer to the following takeaways and keep them in mind.<\/span><\/p>\n\n\n\n<ul><li><span style=\"color: #000000;\">In Time and Work problems where we are supposed to assume the value of total work, it is always a good practice to assume the total work as the LCM of the given days (or any multiple of LCM), rather than assuming the total work as 1 unit \u2013 as it decreases the complex calculations involved with fractions<\/span><\/li><li><span style=\"color: #000000;\">LCM method can still be applied when one of the data points are given in terms of variable<\/span><\/li><li><span style=\"color: #000000;\">Efficiency is inversely proportional to the time&nbsp;taken<\/span><\/li><li><span style=\"color: #000000;\">When working in groups, all are considered to be equally efficient within a group, whereas people have different efficiencies across groups<\/span><\/li><\/ul>\n\n\n\n<p>Read our next article on 3 deadly mistakes you need to avoid in Time and Work Problems<\/p>\n\n\n\n<p><\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Questions on time and work are very commonly asked on the GMAT. Ace GMAT Quant by <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\">signing up for our free trial<\/a> and get access to 400+ questions. 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You can easily learn and apply the concepts. The only question to ask is, &#8216;Can you solve them faster?&#8217; The answer is Yes. In this article, we&#8217;ll compare the conventional methods of solving GMAT Quant questions on Time and work [&hellip;]<\/p>\n","protected":false},"author":102406,"featured_media":42587,"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":[94,60,102],"tags":[],"featured_image_src":"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2021\/07\/How_to_quickly_solve_GMAT_Quant_Questions_on_Time_and_Work-1024x589-1.png","author_info":{"display_name":"Suheb Hussain","author_link":"https:\/\/e-gmat.com\/blogs\/author\/syede-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>How to quickly solve GMAT Quant Questions on Time and Work | e-GMAT<\/title>\n<meta name=\"description\" content=\"Time and Work problems are the low hanging fruit in the world of GMAT Quant Questions. 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