sum of the ages

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sairakesh: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sun Sep 14, 2008 8:33 am; Location: hyderabad

by sairakesh » Wed Jul 01, 2009 5:26 am

The sum of the ages of 22 boys and 24 girls is 160.What is the sum of ages of one boy plus one girl, if all the boys are of the same age and all the girls are of the same age, and only full years are counted?
1.6
2.7
3.5
4.8
5.9

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Source: Beat The GMAT — Problem Solving | Wed Jul 01, 2009 5:26 am

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Wed Jul 01, 2009 6:40 am

This is more of a guess and check question.

X= Age of one boy
Y= Age of one girl

22X+24Y=160

We want X+Y=?

Just to make the numbers more simpler and easier to work with, let's factor out a 2.

2(11X+12Y)=160

11X+12Y=80

X=4--> 12Y=36--> Y=3

X+Y=4+3=7 B

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shanmugam.d: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Thu Apr 30, 2009 1:32 pm; Thanked: 2 times

by shanmugam.d » Wed Jul 01, 2009 8:15 am

to continue with trueplayer:
11X+12Y=80 to find the combination which makes up 80
just list multiples of 11: 11 22 33 44 55
multiple of 12: 12 24 36 48 56
the combination is: 4 & 3 hence: 4+3 = 7 (B)

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ajlcalbanese1: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun May 17, 2009 1:32 pm; Location: Texas; GMAT Score:390

maybe if we find x first?

by ajlcalbanese1 » Wed Jul 01, 2009 8:51 am

if we have:
22X+24Y=160

can we find the value for X and then substitute in the ecuation?

22x=160-24y

x=160-24y/22

22(160-24y/22)=160

and from here find the value of y and substitute in the ecuation?

would that work? any comments about my aproach?

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scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Wed Jul 01, 2009 11:22 am

22B+24G=160
=>11B+12G=80

80 is even, 12G is even=> 11B must be even (E+E=E)
since B, G must be integers,
G=(80-11B)/12 must be an integer

let B be 2, (B must be even)=>G=(80-22)/12=58/12 not an integer
let B be 4, (G=80-44)/12=36/12=3 integer. bingo!

so B+G=4+3=7

hence, B

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sairakesh: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sun Sep 14, 2008 8:33 am; Location: hyderabad

thanks

by sairakesh » Thu Jul 02, 2009 5:37 am

thanks a lot for ur help.

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ghacker: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Jun 03, 2009 8:04 pmFollowed by: 1 member; Thanked: 18 times

by ghacker » Thu Jul 02, 2009 8:31 am

Another way

Girls = G ; Boys = B

22B+24G = 160 , B, G integers
22(B+G) +2G = 160 -------------> 11(B+G)+G = 80

Since B, G are integers B+G must also be an integers and the only positive integers which satisfy the equations are 7 and 3

So G = 3 and B= 4

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