A is the smallest positive integer which when divided by 9 and 12 leaves remainder 8. B is the smallest positive integer which when divided by 9 and 12 leaves remainder 5. Which one of the following is the value of A \u2013 B ?<\/p>\n
[amp_mcq option1=”3″ option2=”2″ option3=”1″ option4=”0″ correct=”option1″]<\/p>\n
B is the smallest positive integer which when divided by 9 and 12 leaves remainder 5.
\nThis means B $\\equiv$ 5 (mod 9) and B $\\equiv$ 5 (mod 12).
\nEquivalently, B – 5 is divisible by both 9 and 12. Therefore, B – 5 must be a multiple of LCM(9, 12) = 36.
\nSo, B – 5 = 36m for some integer m. B = 36m + 5.
\nWe are looking for the smallest positive integer B.
\nIf m=0, B = 36(0) + 5 = 5. Check: $5 \\div 9$ gives remainder 5, $5 \\div 12$ gives remainder 5. 5 is a positive integer.
\nSo, B = 5.<\/p>\n
Finally, we need to find the value of A – B:
\nA – B = 8 – 5 = 3.<\/section>\n","protected":false},"excerpt":{"rendered":"
A is the smallest positive integer which when divided by 9 and 12 leaves remainder 8. B is the smallest positive integer which when divided by 9 and 12 leaves remainder 5. Which one of the following is the value of A \u2013 B ? [amp_mcq option1=”3″ option2=”2″ option3=”1″ option4=”0″ correct=”option1″] This question was previously … <\/p>\n