{"id":92627,"date":"2025-06-01T11:29:25","date_gmt":"2025-06-01T11:29:25","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92627"},"modified":"2025-06-01T11:29:25","modified_gmt":"2025-06-01T11:29:25","slug":"suppose-p-and-q-are-distinct-two-digit-numbers-consisting-of-the-same","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/suppose-p-and-q-are-distinct-two-digit-numbers-consisting-of-the-same\/","title":{"rendered":"Suppose P and Q are distinct two-digit numbers consisting of the same"},"content":{"rendered":"

Suppose P and Q are distinct two-digit numbers consisting of the same digits. Then P-Q is<\/p>\n

[amp_mcq option1=”a prime number” option2=”an even number” option3=”an odd number” option4=”divisible by 9″ correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2019<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is (D) divisible by 9. Let the two distinct two-digit numbers be P and Q, formed by the digits ‘a’ and ‘b’. Since they are distinct two-digit numbers consisting of the same digits, the digits must be distinct (a \u2260 b) and non-zero (otherwise one number would be a single digit). Let P = 10a + b and Q = 10b + a (where a and b are single digits from 1-9, a \u2260 b).
\n<\/section>\n
\n– The difference P – Q = (10a + b) – (10b + a) = 9a – 9b = 9(a – b).
\n– Since ‘a’ and ‘b’ are distinct digits, (a – b) is a non-zero integer.
\n– Therefore, the difference P – Q is always a multiple of 9.
\n– Any multiple of 9 is divisible by 9.
\n<\/section>\n
\nLet’s test the other options with an example: P=72, Q=27. P-Q = 72-27 = 45.
\n– Is 45 a prime number? No.
\n– Is 45 an even number? No.
\n– Is 45 an odd number? Yes. But consider P=31, Q=13. P-Q = 31-13 = 18, which is even. So it’s not always odd.
\n– Is 45 divisible by 9? Yes (45 \/ 9 = 5).
\nThe property P-Q = 9(a-b) guarantees divisibility by 9 for any pair of distinct two-digit numbers formed by swapping two distinct digits (assuming both digits are non-zero to ensure two distinct two-digit numbers, or carefully considering the case with digit 0, which would mean numbers like 20 and 02, but 02 is not a two-digit number, confirming our assumption that both digits must be non-zero).
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Suppose P and Q are distinct two-digit numbers consisting of the same digits. Then P-Q is [amp_mcq option1=”a prime number” option2=”an even number” option3=”an odd number” option4=”divisible by 9″ correct=”option4″] This question was previously asked in UPSC CISF-AC-EXE – 2019 Download PDFAttempt Online The correct answer is (D) divisible by 9. Let the two distinct … <\/p>\n

Detailed SolutionSuppose P and Q are distinct two-digit numbers consisting of the same<\/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":[1119,1102],"class_list":["post-92627","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1119","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nSuppose P and Q are distinct two-digit numbers consisting of the same<\/title>\n<meta name=\"description\" content=\"The correct answer is (D) divisible by 9. Let the two distinct two-digit numbers be P and Q, formed by the digits 'a' and 'b'. Since they are distinct two-digit numbers consisting of the same digits, the digits must be distinct (a \u2260 b) and non-zero (otherwise one number would be a single digit). Let P = 10a + b and Q = 10b + a (where a and b are single digits from 1-9, a \u2260 b). - The difference P - Q = (10a + b) - (10b + a) = 9a - 9b = 9(a - b). - Since 'a' and 'b' are distinct digits, (a - b) is a non-zero integer. - Therefore, the difference P - Q is always a multiple of 9. - Any multiple of 9 is divisible by 9.\" \/>\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\/suppose-p-and-q-are-distinct-two-digit-numbers-consisting-of-the-same\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Suppose P and Q are distinct two-digit numbers consisting of the same\" \/>\n<meta property=\"og:description\" content=\"The correct answer is (D) divisible by 9. Let the two distinct two-digit numbers be P and Q, formed by the digits 'a' and 'b'. Since they are distinct two-digit numbers consisting of the same digits, the digits must be distinct (a \u2260 b) and non-zero (otherwise one number would be a single digit). Let P = 10a + b and Q = 10b + a (where a and b are single digits from 1-9, a \u2260 b). - The difference P - Q = (10a + b) - (10b + a) = 9a - 9b = 9(a - b). - Since 'a' and 'b' are distinct digits, (a - b) is a non-zero integer. - Therefore, the difference P - Q is always a multiple of 9. - Any multiple of 9 is divisible by 9.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-p-and-q-are-distinct-two-digit-numbers-consisting-of-the-same\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:29:25+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":"Suppose P and Q are distinct two-digit numbers consisting of the same","description":"The correct answer is (D) divisible by 9. Let the two distinct two-digit numbers be P and Q, formed by the digits 'a' and 'b'. Since they are distinct two-digit numbers consisting of the same digits, the digits must be distinct (a \u2260 b) and non-zero (otherwise one number would be a single digit). Let P = 10a + b and Q = 10b + a (where a and b are single digits from 1-9, a \u2260 b). - The difference P - Q = (10a + b) - (10b + a) = 9a - 9b = 9(a - b). - Since 'a' and 'b' are distinct digits, (a - b) is a non-zero integer. - Therefore, the difference P - Q is always a multiple of 9. - Any multiple of 9 is divisible by 9.","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\/suppose-p-and-q-are-distinct-two-digit-numbers-consisting-of-the-same\/","og_locale":"en_US","og_type":"article","og_title":"Suppose P and Q are distinct two-digit numbers consisting of the same","og_description":"The correct answer is (D) divisible by 9. Let the two distinct two-digit numbers be P and Q, formed by the digits 'a' and 'b'. 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Let P = 10a + b and Q = 10b + a (where a and b are single digits from 1-9, a \u2260 b). - The difference P - Q = (10a + b) - (10b + a) = 9a - 9b = 9(a - b). - Since 'a' and 'b' are distinct digits, (a - b) is a non-zero integer. - Therefore, the difference P - Q is always a multiple of 9. - Any multiple of 9 is divisible by 9.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-p-and-q-are-distinct-two-digit-numbers-consisting-of-the-same\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:29:25+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\/suppose-p-and-q-are-distinct-two-digit-numbers-consisting-of-the-same\/","url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-p-and-q-are-distinct-two-digit-numbers-consisting-of-the-same\/","name":"Suppose P and Q are distinct two-digit numbers consisting of the same","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:29:25+00:00","dateModified":"2025-06-01T11:29:25+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is (D) divisible by 9. Let the two distinct two-digit numbers be P and Q, formed by the digits 'a' and 'b'. Since they are distinct two-digit numbers consisting of the same digits, the digits must be distinct (a \u2260 b) and non-zero (otherwise one number would be a single digit). 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