Quiz3_solutions

# Quiz3_solutions - MATH 2602 — Quiz 4 3 lieu J Each...

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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 lieu J Each...

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