Distribution Amount

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nlpfollower: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Tue Dec 29, 2009 11:03 pm

Distribution Amount

by nlpfollower » Wed Mar 17, 2010 2:14 am

A certain amount was to be divided among A, B and C in the ratio of 4:5:6 but, by mistake, it was divided in such a manner that 4 times of A's share was equal to 5 times of B's share and 6 times of C's share. As a result, 'A' got $154 more than the expected amount. What was the amount that was divided among them?

A. $370
B. $450
C. $560
D. $1000
E. $1110

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Source: Beat The GMAT — Problem Solving | Wed Mar 17, 2010 2:14 am

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

by kstv » Wed Mar 17, 2010 2:24 am

The initial ratio 4:5:6 A's share was 4/15 (4+5+6)
To find the errorneous ratio let's assume A's share is x/4 B's share is x/5 C's share is x/6
Ratio will be 15: 12 : 10 A's share 15/37(15+12+10)

(15/37 - 4/15) of the total amount is = 154
solve for x, x = 1110.

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nlpfollower: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Tue Dec 29, 2009 11:03 pm

by nlpfollower » Wed Mar 17, 2010 2:36 am

sorry, i have not been able to understand your explanation.

how did you arrive at the new ratio of 15:112:10?

And what is x defined as?

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

by kstv » Wed Mar 17, 2010 5:07 am

Is the answer correct otherwise what's the point.

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nlpfollower: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Tue Dec 29, 2009 11:03 pm

by nlpfollower » Wed Mar 17, 2010 5:10 am

OA is E

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

by kstv » Wed Mar 17, 2010 5:45 am

The initial ratio 4:5:6 A's share was 4/15 15 is (4+5+6)
To find the errorneous ratio let's assume A's share is x/4 B's share is x/5 C's share is x/6
4 times A's share = 5 times B's share
A's share is x/4 (not choosing x as the calc will get complicated) four times x/4 is x
but that is 5 times B's share so B's share 1/5 x C's share x/6
A:B:C x/4 : x/5 : x/6 LCM of 4,5 & 6 = 4*5*3 = 60 so multiply by 60 to get integers
A:B:C 15x:12x:10x so now remove x we get 15:12:10
Ratio will be 15: 12 : 10 A's share in the new (errorneous) ratio is 15/37 37 is (15+12+10)

given (15/37 - 4/15) of the total amount is = 154
I assumed the total amount again as x but did not clearly mention it , assume Tot amt =y
(15/37 - 4/15) y = 154 solve for y
The calc. are a wee bit tedious which should not be as GMAT tests application of concepts not rigourous maths skill per se.

Last edited by kstv on Wed Mar 17, 2010 6:30 am, edited 1 time in total.

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Wed Mar 17, 2010 6:19 am

nlpfollower wrote:A certain amount was to be divided among A, B and C in the ratio of 4:5:6 but, by mistake, it was divided in such a manner that 4 times of A's share was equal to 5 times of B's share and 6 times of C's share. As a result, 'A' got $154 more than the expected amount. What was the amount that was divided among them?

A. $370
B. $450
C. $560
D. $1000
E. $1110

According to the initial plan, A should have gotten 4/15 of the total amount (let it be T) or A= (4/15) * T

But, due to the error, B got 4/5* A OR B=(4/5)*A
and .......................... C got 4/6 *A OR C=(4/6)*A

but the total amount, T, is the same
Hence, T= A + B + C = A + (4/5)*A + (4/6)*A
OR T = (74/30) * A or A = ( 30/74) * T ---------------don't simplify right now

the question says, difference in these two amounts is 154.

Hence, (30/74) * T - (4/15) * T = 154

OR [ 30*15 - 74 * 4 ]/ (74 * 15) * T = 154

OR [450 - 296]/(74 * 15) * T = 154

OR 154 / (74 * 15) * T = 154

OR T = (74 * 15) = 1110