{"id":93119,"date":"2025-06-01T11:42:15","date_gmt":"2025-06-01T11:42:15","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93119"},"modified":"2025-06-01T11:42:15","modified_gmt":"2025-06-01T11:42:15","slug":"if-the-sum-of-five-consecutive-even-numbers-is-equal-to-the-product-of","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-sum-of-five-consecutive-even-numbers-is-equal-to-the-product-of\/","title":{"rendered":"If the sum of five consecutive even numbers is equal to the product of"},"content":{"rendered":"

If the sum of five consecutive even numbers is equal to the product of first five natural numbers, then which one of the following is the largest of those even numbers ?<\/p>\n

[amp_mcq option1=”30″ option2=”24″ option3=”26″ option4=”28″ correct=”option4″]<\/p>\n

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This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe product of the first five natural numbers (1, 2, 3, 4, 5) is $1 \\times 2 \\times 3 \\times 4 \\times 5 = 120$. Let the five consecutive even numbers be represented as $x-4, x-2, x, x+2, x+4$, where $x$ is the middle number. The sum of these five consecutive even numbers is $(x-4) + (x-2) + x + (x+2) + (x+4) = 5x$. We are given that this sum is equal to the product of the first five natural numbers, so $5x = 120$. Solving for $x$, we get $x = 120 \/ 5 = 24$. The five consecutive even numbers are $24-4=20$, $24-2=22$, $24$, $24+2=26$, and $24+4=28$. The largest of these even numbers is 28.
\n<\/section>\n
\n– First five natural numbers are 1, 2, 3, 4, 5. Their product is 120.
\n– Consecutive even numbers differ by 2. Representing them around the middle term simplifies the sum calculation.
\n– If the middle term is $x$, the sum of five consecutive even numbers is $5x$.
\n<\/section>\n
\nUsing $x-4, x-2, x, x+2, x+4$ simplifies the sum calculation as the constant terms cancel out. Alternatively, if the first even number is $a$, the numbers are $a, a+2, a+4, a+6, a+8$. Their sum is $5a+20$. So $5a+20 = 120$, $5a = 100$, $a=20$. The numbers are 20, 22, 24, 26, 28. The largest is $a+8 = 20+8 = 28$.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

If the sum of five consecutive even numbers is equal to the product of first five natural numbers, then which one of the following is the largest of those even numbers ? [amp_mcq option1=”30″ option2=”24″ option3=”26″ option4=”28″ correct=”option4″] This question was previously asked in UPSC CISF-AC-EXE – 2022 Download PDFAttempt Online The product of the … <\/p>\n

Detailed SolutionIf the sum of five consecutive even numbers is equal to the product of<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1089],"tags":[1108,1102],"class_list":["post-93119","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIf the sum of five consecutive even numbers is equal to the product of<\/title>\n<meta name=\"description\" content=\"The product of the first five natural numbers (1, 2, 3, 4, 5) is $1 times 2 times 3 times 4 times 5 = 120$. Let the five consecutive even numbers be represented as $x-4, x-2, x, x+2, x+4$, where $x$ is the middle number. The sum of these five consecutive even numbers is $(x-4) + (x-2) + x + (x+2) + (x+4) = 5x$. We are given that this sum is equal to the product of the first five natural numbers, so $5x = 120$. Solving for $x$, we get $x = 120 \/ 5 = 24$. The five consecutive even numbers are $24-4=20$, $24-2=22$, $24$, $24+2=26$, and $24+4=28$. The largest of these even numbers is 28. - First five natural numbers are 1, 2, 3, 4, 5. Their product is 120. - Consecutive even numbers differ by 2. Representing them around the middle term simplifies the sum calculation. - If the middle term is $x$, the sum of five consecutive even numbers is $5x$.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-sum-of-five-consecutive-even-numbers-is-equal-to-the-product-of\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the sum of five consecutive even numbers is equal to the product of\" \/>\n<meta property=\"og:description\" content=\"The product of the first five natural numbers (1, 2, 3, 4, 5) is $1 times 2 times 3 times 4 times 5 = 120$. Let the five consecutive even numbers be represented as $x-4, x-2, x, x+2, x+4$, where $x$ is the middle number. The sum of these five consecutive even numbers is $(x-4) + (x-2) + x + (x+2) + (x+4) = 5x$. We are given that this sum is equal to the product of the first five natural numbers, so $5x = 120$. Solving for $x$, we get $x = 120 \/ 5 = 24$. The five consecutive even numbers are $24-4=20$, $24-2=22$, $24$, $24+2=26$, and $24+4=28$. The largest of these even numbers is 28. - First five natural numbers are 1, 2, 3, 4, 5. Their product is 120. - Consecutive even numbers differ by 2. Representing them around the middle term simplifies the sum calculation. - If the middle term is $x$, the sum of five consecutive even numbers is $5x$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-sum-of-five-consecutive-even-numbers-is-equal-to-the-product-of\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:42:15+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"If the sum of five consecutive even numbers is equal to the product of","description":"The product of the first five natural numbers (1, 2, 3, 4, 5) is $1 times 2 times 3 times 4 times 5 = 120$. Let the five consecutive even numbers be represented as $x-4, x-2, x, x+2, x+4$, where $x$ is the middle number. The sum of these five consecutive even numbers is $(x-4) + (x-2) + x + (x+2) + (x+4) = 5x$. We are given that this sum is equal to the product of the first five natural numbers, so $5x = 120$. Solving for $x$, we get $x = 120 \/ 5 = 24$. The five consecutive even numbers are $24-4=20$, $24-2=22$, $24$, $24+2=26$, and $24+4=28$. The largest of these even numbers is 28. - First five natural numbers are 1, 2, 3, 4, 5. Their product is 120. - Consecutive even numbers differ by 2. Representing them around the middle term simplifies the sum calculation. - If the middle term is $x$, the sum of five consecutive even numbers is $5x$.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/if-the-sum-of-five-consecutive-even-numbers-is-equal-to-the-product-of\/","og_locale":"en_US","og_type":"article","og_title":"If the sum of five consecutive even numbers is equal to the product of","og_description":"The product of the first five natural numbers (1, 2, 3, 4, 5) is $1 times 2 times 3 times 4 times 5 = 120$. Let the five consecutive even numbers be represented as $x-4, x-2, x, x+2, x+4$, where $x$ is the middle number. The sum of these five consecutive even numbers is $(x-4) + (x-2) + x + (x+2) + (x+4) = 5x$. We are given that this sum is equal to the product of the first five natural numbers, so $5x = 120$. Solving for $x$, we get $x = 120 \/ 5 = 24$. The five consecutive even numbers are $24-4=20$, $24-2=22$, $24$, $24+2=26$, and $24+4=28$. The largest of these even numbers is 28. - First five natural numbers are 1, 2, 3, 4, 5. Their product is 120. - Consecutive even numbers differ by 2. Representing them around the middle term simplifies the sum calculation. - If the middle term is $x$, the sum of five consecutive even numbers is $5x$.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-sum-of-five-consecutive-even-numbers-is-equal-to-the-product-of\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:42:15+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-sum-of-five-consecutive-even-numbers-is-equal-to-the-product-of\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-sum-of-five-consecutive-even-numbers-is-equal-to-the-product-of\/","name":"If the sum of five consecutive even numbers is equal to the product of","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:42:15+00:00","dateModified":"2025-06-01T11:42:15+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The product of the first five natural numbers (1, 2, 3, 4, 5) is $1 \\times 2 \\times 3 \\times 4 \\times 5 = 120$. Let the five consecutive even numbers be represented as $x-4, x-2, x, x+2, x+4$, where $x$ is the middle number. The sum of these five consecutive even numbers is $(x-4) + (x-2) + x + (x+2) + (x+4) = 5x$. We are given that this sum is equal to the product of the first five natural numbers, so $5x = 120$. Solving for $x$, we get $x = 120 \/ 5 = 24$. The five consecutive even numbers are $24-4=20$, $24-2=22$, $24$, $24+2=26$, and $24+4=28$. The largest of these even numbers is 28. - First five natural numbers are 1, 2, 3, 4, 5. Their product is 120. - Consecutive even numbers differ by 2. 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