gclub backsolve

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Tue May 24, 2011 10:18 am

In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05, $0.10 and $0.25 each. The total that Brittany paid was $2.05. If Brittany bought twice as many gel pens as ink pens, how many ball pens did she buy?

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oa-B- got this correct by backsolving, but got stuck in trying to form equations-anybody ?
[spoiler]last question for the day-i've had enough :/[/spoiler]

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Source: Beat The GMAT — Problem Solving | Tue May 24, 2011 10:18 am

manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Tue May 24, 2011 10:37 am

bblast wrote:In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05, $0.10 and $0.25 each. The total that Brittany paid was $2.05. If Brittany bought twice as many gel pens as ink pens, how many ball pens did she buy?

4
5
7
8
10

oa-B- got this correct by backsolving, but got stuck in trying to form equations-anybody ?
[spoiler]last question for the day-i've had enough :/[/spoiler]

ball pens=x; gel pens=y, ink pens= z;
0.05x+0.1y+0.25z=2.05;
also y=2z;
0.05x+0.2z+0.25z=2.05;
5x=205-45z;
x= 205-45z/5;
by putting z=4 we get x=5; hence B

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue May 24, 2011 10:38 am

Hi,
Let the number of ball,gel and ink pens be b,g,i.
Given that b+g+i = 17 ---eqn(1)
and (0.05)b+(0.1)g+(0.25)i = 2.05 =>b+2g+5i = 41 ---eqn(2)
Also given that g=2i
So eqn(1) -> b+3i = 17
eqn(2) -> b+9i = 41
Solving, we get 6i=24 =>i=4
So, b= 17-3.4 =5

Hence, answer B

Cheers!

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Wed May 25, 2011 11:14 am

good work frankenstein,
for the sake of it I solved the problem looking directly at the answerS.

5 ball pens means 12 left for ink and gel,AHA 4 and 8,so 5 it is. But such time saving shortcut might not have worked on a more convoluted problem and trickier numbers, so my approach would have been better had this question come after question 30 on the test. However equations are a safer option anyday.

thanks !!!

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sat May 28, 2011 11:14 am

5 ball pens means 12 left for ink and gel,AHA 4 and 8,so 5 it is.

Even option D can be correct in that sense. 8 ball pens => 9 ink + gel pens => 6 gel and 3 ink.
After this equation regarding the total cost should be solved

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Sat May 28, 2011 10:50 pm

yes, i overlooked that, just got lucky, Thanks cans

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