{"id":57469,"date":"2025-08-24T11:36:20","date_gmt":"2025-08-24T06:06:20","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=57469"},"modified":"2025-08-24T11:36:21","modified_gmt":"2025-08-24T06:06:21","slug":"of-the-people-who-donated-money-to-a-certain-local-theater-last-year","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/of-the-people-who-donated-money-to-a-certain-local-theater-last-year\/","title":{"rendered":"Of the people who donated money to a certain local theater last year, 1\/4 donated $20 or less&#8230;."},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">3<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<p>\ufeffOf the people who donated money to a certain local theater last year, 1\/4 donated $20 or less and 2\/3 donated more than $20 but less than $1,000. If the average (arithmetic mean) amount donated by the people who donated more than $20 but less than $1,000 was $180, what was the average amount donated by the people who donated $1,000 or more?<\/p>\n\n\n\n<p>(1) The average amount donated by the people who donated less than $1,000 was $132.<br>(2) The average amount donated by the people who donated more than $20 was $360.<\/p>\n\n\n\n<ul><li>A. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.<\/li><li>B. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.<\/li><li>C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.<\/li><li>D. EACH statement ALONE is sufficient.<\/li><li>E. Statements (1) and (2) TOGETHER are not sufficient.<\/li><\/ul>\n\n\n\n<h2>Solution:<\/h2>\n\n\n\n<h3 id=\"h-understanding-the-question\">Understanding the Question<\/h3>\n\n\n\n<p>We need to find the average donation amount for people who donated\u00a0$1,000 or more.<\/p>\n\n\n\n<h4 id=\"h-given-information\">Given Information<\/h4>\n\n\n\n<ul><li><strong>\u00a01\/4 of donors<\/strong>\u00a0gave\u00a0less than or equal to $20<\/li><li><strong>\u00a02\/3 of donors<\/strong>\u00a0gave between\u00a0$20\u00a0and\u00a0$1000\u00a0(with average\u00a0$180)<\/li><li>The remaining fraction gave\u00a0greater than or equal to $1000<\/li><li>Since\u00a01\/4 plus 2\/3 is equal to 11\/12, this means\u00a01\/12<strong>\u00a0of donors<\/strong>\u00a0gave\u00a0greater than or equal to $1000<\/li><\/ul>\n\n\n\n<h4 id=\"h-what-we-need-to-determine\">What We Need to Determine<\/h4>\n\n\n\n<p>To have sufficiency, we need to be able to calculate\u00a0<strong>one specific value<\/strong>\u00a0for the average donation of the\u00a0group that gave greater than or equal to $1000.<\/p>\n\n\n\n<h4 id=\"h-key-insight\">Key Insight<\/h4>\n\n\n\n<p>This is a weighted average problem with three distinct groups. To find the average of one group, we typically need information about either:<\/p>\n\n\n\n<ul><li>The overall average of all donors, OR<\/li><li>The combined average of groups that include our target group<\/li><\/ul>\n\n\n\n<h3 id=\"h-analyzing-statement-1\">Analyzing Statement 1<\/h3>\n\n\n\n<p>Statement 1: The average amount donated by people who donated less than\u00a0$1000\u00a0was\u00a0$132.<\/p>\n\n\n\n<h4 id=\"h-what-statement-1-provides\">What Statement 1 Provides<\/h4>\n\n\n\n<p>This gives us the combined average of the first two groups:<\/p>\n\n\n\n<ul><li>Group 1: Donors who gave\u00a0less than or equal to $20<\/li><li>Group 2: Donors who gave\u00a0$20-$1000<\/li><\/ul>\n\n\n\n<p>Together, these groups represent\u00a011\/12<strong>\u00a0of all donors<\/strong>.<\/p>\n\n\n\n<h4 id=\"h-calculation-analysis\">Calculation Analysis<\/h4>\n\n\n\n<p>Using the weighted average formula, we can find the average for the\u00a0less than or equal to $20\u00a0group.<\/p>\n\n\n\n<p>We know:<\/p>\n\n\n\n<ul><li>Combined groups (1 and 2):\u00a011\/12\u00a0of donors with average\u00a0$132<\/li><li>Group 2 alone:\u00a02\/3\u00a0of donors with average\u00a0$180<\/li><\/ul>\n\n\n\n<p>Setting up the weighted average:<\/p>\n\n\n\n<p>(1\/4 * A1 + 2\/3 *180) divided by (11\/12) = 132<\/p>\n\n\n\n<p>Converting to common denominator (12) for easier calculation:<\/p>\n\n\n\n<ul><li>(3\/12 * A1 + 8\/12*180) divided by (11\/12) = 132<\/li><li>(3A1 + 1440) divided by 11 = 132<\/li><li>3A1 + 1440 = 1452<\/li><li>3A1 = 12<\/li><li>A1 = $4<\/li><\/ul>\n\n\n\n<h4 id=\"h-why-this-isn-t-sufficient\">Why This Isn&#8217;t Sufficient<\/h4>\n\n\n\n<p>We now know:<\/p>\n\n\n\n<ul><li>Group 1 (less than or qraul to $20): average =\u00a0$4<\/li><li>Group 2 ($20 &#8211; $1000): average =\u00a0$180<\/li><li>Group 3 (greater than or equal to $1000): average = ?<\/li><\/ul>\n\n\n\n<p>Without knowing the overall average of ALL donors, we cannot determine Group 3&#8217;s average. The missing link prevents us from finding a unique value.<\/p>\n\n\n\n<p>Statement 1 is&nbsp;<strong>NOT sufficient<\/strong>.<\/p>\n\n\n\n<p><strong>This eliminates choices A and D.<\/strong><\/p>\n\n\n\n<h3 id=\"h-analyzing-statement-2\">Analyzing Statement 2<\/h3>\n\n\n\n<p><strong>Now we analyze Statement 2 independently, forgetting Statement 1 completely.<\/strong><\/p>\n\n\n\n<p>Statement 2: The average amount donated by people who donated more than\u00a0$20\u00a0was\u00a0$360.<\/p>\n\n\n\n<h4 id=\"h-what-statement-2-provides\">What Statement 2 Provides<\/h4>\n\n\n\n<p>This gives us the combined average of Groups 2 and 3:<\/p>\n\n\n\n<ul><li>Group 2: Donors who gave\u00a0$20 &#8211; $1000<\/li><li>Group 3: Donors who gave\u00a0greater than or equal to $1000<\/li><\/ul>\n\n\n\n<p>Together, these groups represent\u00a02\/3 + 1\/12 = 9\/12 = 3\/4<strong>\u00a0of all donors<\/strong>.<\/p>\n\n\n\n<h4 id=\"h-calculation-analysis-1\">Calculation Analysis<\/h4>\n\n\n\n<p>We can use the weighted average formula to find Group 3&#8217;s average.<\/p>\n\n\n\n<p>Within the &#8220;more than\u00a0$20&#8221; category:<\/p>\n\n\n\n<ul><li>Group 2:\u00a0\u00a02\/3 of all donors (which is\u00a08\/9\u00a0of this combined group)<\/li><li>Group 3:\u00a0\u00a01\/12 of all donors (which is\u00a01\/9\u00a0of this combined group)<\/li><\/ul>\n\n\n\n<p>Setting up the weighted average:<\/p>\n\n\n\n<p>(2\/3 *180 + 1\/12*A3) divided by (3\/4) = 360<\/p>\n\n\n\n<p>Converting fractions:<\/p>\n\n\n\n<ul><li>(8\/12*180 + 1\/12*A3) divided by 9\/12 = 360<\/li><li>(1440 + A3) divided by 9 = 360<\/li><li>1440 + A3 = 3240<\/li><li>A3 = $1800<\/li><\/ul>\n\n\n\n<h4 id=\"h-verification\">Verification<\/h4>\n\n\n\n<p>We found exactly one value: the average donation for the\u00a0greater than or equal to $1000\u00a0group is\u00a0$1800.<\/p>\n\n\n\n<p><strong>[STOP &#8211; Sufficient!]<\/strong><\/p>\n\n\n\n<p>Statement 2 is&nbsp;<strong>sufficient<\/strong>.<\/p>\n\n\n\n<p><strong>This eliminates choices C and E.<\/strong><\/p>\n\n\n\n<h3 id=\"h-the-answer-b\">The Answer: B<\/h3>\n\n\n\n<p>Statement 2 alone provides enough information to determine that the average donation for the greater than or equal to $1000 group is\u00a0$1800, while Statement 1 alone does not provide sufficient information.<\/p>\n\n\n\n<p><strong>Answer Choice B<\/strong>: Statement 2 alone is sufficient, but Statement 1 alone is not sufficient.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\ufeffOf the people who donated money to a certain local theater last year, 1\/4 donated $20 or less and 2\/3 donated more than $20 but less than $1,000. If the average (arithmetic mean) amount donated by the people who donated more than $20 but less than $1,000 was $180, what was the average amount donated [&hellip;]<\/p>\n","protected":false},"author":102457,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"off","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[11726,94],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Kashish Garg","author_link":"https:\/\/e-gmat.com\/blogs\/author\/kashish\/"},"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>Of the people who donated money to a certain local theater last year, 1\/4 donated $20 or less....<\/title>\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\/of-the-people-who-donated-money-to-a-certain-local-theater-last-year\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Of the people who donated money to a certain local theater last year, 1\/4 donated $20 or less....\" \/>\n<meta property=\"og:description\" content=\"\ufeffOf the people who donated money to a certain local theater last year, 1\/4 donated $20 or less and 2\/3 donated more than $20 but less than $1,000. 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