Pretty Pink Bonnet

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Tue Feb 23, 2010 6:18 am

My brother, Chris, is a little simple. I recently asked him to buy me some ribbon for my daughter's pretty bonnet. He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches. When I measured the resulting ribbon I only had 5/8 of the length I required. How much ribbon did I originally ask for?

a) 66 inches

b) 77 inches

c) 88 inches

d) 176 inches

e) 55 inches

[spoiler]OA :C[/spoiler]

Last edited by ajith on Fri Feb 26, 2010 3:32 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Tue Feb 23, 2010 6:18 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Tue Feb 23, 2010 6:20 am

ajith wrote:My brother, Chris, is a little simple. I recently asked him to buy me some ribbon for my daughter's pretty bonnet. He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches. When I measured the resulting ribbon I only had 5/8 of the length I required. How much ribbon did I originally ask for?

a) 66 inches = 5ft 6inches

b) 77 inches = 6feet 5 inches

c) 88 inches = 7feet 4inches

d) 176 inches = 14feet 8inches

e) 55 inches

= 4feet 7inches

Woah!A question posted by ajith.Now this is rare to find.

Let me give a try if I can solve it .
Let it be a feet and b inches
Total = 12 x a + b
=12a + b
Now Chris bought 12b + a

12b + a = 5/8(12a + b)
52a = 91b
So a = 91/52 b =7/4b
or 4a =7b
or 4 x (no. of feet) = 7(no. of inches)

Checking the option choices,I find C.

The trap is b/w C and E i suppose.

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Tue Feb 23, 2010 7:08 am

IMO C.
But the method I use was not elegant.
Ribbon I ordered is 12x + y, but got 12y + x
12x+y/12y+x = 5/8
using componendo / divinendo

11(x-y)/13(x+y) = 3/13
11(x-y) = 3(x+y)

so x-y = 3 and x+y = 11

It is easier to compare the answers.

Last edited by kstv on Fri Feb 26, 2010 6:07 am, edited 2 times in total.

anki_jain: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Jul 20, 2009 9:22 am; Location: Hyderabad

by anki_jain » Fri Feb 26, 2010 3:30 am

original lenth would be 8/5x.

check with options:

8/5x=88 => x=55
i.e. 33 short or 3/8 short from original length. IMO C

kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Fri Feb 26, 2010 6:08 am

sorry I have been chastened by ajith for not rechecking.
I edited my post.

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