Quiz3_solutions

Quiz3_solutions - MATH 2602 — Quiz 4% 3 - May 27, 2009...

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Unformatted text preview: MATH 2602 — Quiz 4% 3 - May 27, 2009 lieu J Each problem is ten points. Show all of your work, and try to be as neat as possible. Points may be deducted if solutions are unclear. Use the back of the paper if you need more space. Name: Problem 1. H011: many numbers between 1 and 1000 (inclusive) are divisible by at least one of 3, .4, 6, and 7? ( You may leave your answer as a sum of fractions.) Lair (lit (:3! X" ((300 I éx‘w'e/EX :léXé “3001 9,331; ;}x(: iéxégiooo tL/R’JE/yila/x? Signal: (2%? le $451040 ' ‘l/ X’l/y’ K/Y/fi/‘Kz ‘ lSrgU 87 .u S; U €21:l(“3‘3 “5“?“r‘ié’wlk’3lWE :lgilllgwlgfilgwg l - $L _l+_\l§;.., iii?” _ ' *l 333’“! g 3i l as,“ “lgflbl” lglfi‘l 51% H mm; jellilwiofswfglotfi _ t h gene-H‘Wa‘lmi is. w w» n...” .— ‘Szalléeril‘l \gfidbr?lwlggcqtha?’l fi—I jig! E “553 L a m a” “L Lie-m- tin—Lew an * “fibril? . Problem 2. There are ten people in a room, some of whom decide to shake hands by way of introduction. Show that at least two people shake the same number of hands. (For example, there may be two people that have shaken the hands of exactly flue other people.) Hint 1: What is the maximum number of hands shaken? Hint 2: Can the maximum and minimum be achieved simultaneously? mxo‘n‘o \X‘fl E’l‘ii‘flh W‘l‘l‘éfifl {Fill lib fill-7- ‘? é: 2'“ I“ lbw“: be new {rada‘bfia‘wal Cure Q “Ni pl {EggeChlVE‘kfi if: is me a isms . Ci New W < 9:» _ . , a i‘ocfiies C) Mamba) Alexi. e. omits-a n an fa Mléfif“ poi gm 9.: '5 howl an Qe.:-<’“'5~és‘€“i “ Siam Wit “My” lgfif‘ so hfil‘i‘mb Laa‘iwifrhe l? RmKQGS’i‘ % €73 filfiflmfile flwrnlcei elf mangle beige? Limbs Nil“ “ll”? ‘1‘?“{7b‘3ellmfimk . ‘ g \ q \ ‘ I ‘ =. 7 ~’\ \ gm '7? ,7 "fi‘: "’~. “3% a": k P—lbifii i‘fia lac-:6 ml 313 a fit: in» b43312, QM l *3 'Q’VC "W (a m ‘* ' i .44 - “5“”. my, 52‘le j b‘fi W, Va? "blew-(“e 1 WWW l3??— “5W’“§“‘-i’”'£?"§3 “3“” ~35” alga “fir-Q Eon}? {1's '1 twink i" web?» N'al'fi ' llflfi “"‘A‘ flag} “4‘ 3 ""‘x (Sufism MATH 2602 — Quiz 7% 3 - May 27, 2009 ,s , ‘l ‘3 _ gage \i“ flak Each problem is ten points. Show all of your work, and try to be as meat as possible. Points may be deducted if solutions are unclear. Use the back of the paper if you need more space. Name: Problem 1. How many numbers between 1 and 1000 (inclusive) are divisible by at least one of 3, 4, 6', and 7? (You may leave your answer as a sum of fractions.) W i E whence n “five. Mme «MW! if:ng 95$ gawk} _ a ‘ r . ‘a V" “'. it“ MN, m . . i l ' '{r V; ‘3‘ r a" u a a" . \*_:' "j: f‘j-W,‘~_I : 4'39 we; A ._ an b6 4. is.) kW ,YN...\ i l in m __ Wk .3 ewj $37 2&1. .i ,JL U‘ .3. a 1 “"43 l N e m a. 1 We .u--- l. E “W x *‘l We 95 wee-m -. is km um “3. fig 4 Z " “‘5 nth ii: é/x may? 7 “mm (M I f a N 0"” '5' 9 WA LU \Wl‘i“ 5‘11“: (“as be game 3%}? la? Problem 2. There are ten people in a room, some of whom decide to shake hands .by way of introduction. Show that at least two people shake the same number of hands. (For example, there may be two people that have shaken the hands of exactly five other people.) Hint 1: What is the maximum number of hands shaken? Hint 2: Can the mam-imam and minimum be achieved simultaneously? figwe— " l0 <3. ewea lake seas. Ere ‘% lW‘i witfll “(13 . w - .. s. 3n“- .. . x a. ‘: x 7‘ r i m fl ggg W Ellfifq‘bvg_ Q kéfig {:33 3 all”; . l ' l ' all ‘ fflflwfifi T. “‘34; agaéxg ‘ 4; \f’xfi' 2': fl; ml»: \f‘mwm. §$fl§ l I r m \ l L“ Shale-eve“ 3‘ (We ‘Eflififfl' film 2“: .oéloml mom nee my flawl- I Elsewieg ‘ w, .ad'" . namw‘ ' p. F. ii‘ .. lg . _ I) ., _ "La, I. -’ i f. “e. a , .‘s J. all i if? WE”...>€’% a a. few “iii e \ em» ell qua-e _‘ " ...
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Quiz3_solutions - MATH 2602 — Quiz 4% 3 - May 27, 2009...

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