word problem

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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 amFollowed by: 2 members; Thanked: 1 times

by sud21 » Wed Jan 25, 2012 7:29 pm

A guy sent an order of sofas and loveseats, if the total cost was $3800, how many sofas did he buy?
1) One sofa costs $800 and one loveseat costs $300.
2) There was more than one sofa in the order.

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Source: Beat The GMAT — Data Sufficiency | Wed Jan 25, 2012 7:29 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jan 25, 2012 9:03 pm

sud21 wrote:A guy sent an order of sofas and loveseats, if the total cost was $3800, how many sofas did he buy?
1) One sofa costs $800 and one loveseat costs $300.
2) There was more than one sofa in the order.

Let assume he bought x sofas and y loveseats.

Statement 1: 800x + 300y = 3800 --> 8x + 3y = 38
As x and y must be integer, either (x = 1 and y = 10) or (x = 4 and y = 2)

Not sufficient

Statement 2: We don't know the cost of sofas or loveseats.

Not sufficient

1 & 2 together: x > 1
Hence, x = 4 and y = 2

Sufficient

The correct answer is C.

Last edited by Anurag@Gurome on Fri Jan 27, 2012 11:15 pm, edited 1 time in total.

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kprabhala.mba: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sat Apr 10, 2010 3:07 pm

by kprabhala.mba » Fri Jan 27, 2012 11:12 pm

x = 2 and y = 4 is not a solution to 8x + 3y = 38.

Hence when statements 1 & 2 are taken together, there is only
one solution: x = 4 and y = 2.

Sufficient.

The correct answer should be C.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Jan 27, 2012 11:16 pm

kprabhala.mba wrote:x = 2 and y = 4 is not a solution to 8x + 3y = 38

Thanks for pointing it out.
Edited the reply.

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