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15 Apr 2012, 22:29
3
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Difficulty:

75% (hard)

Question Stats:

56% (02:46) correct 44% (01:33) wrong based on 108 sessions

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At the bakery Lew spent a total of 6$for one kind of cupcake and one kind of doughnut. How many donuts did he buy? (1) Price of 2 doughty was$.10 less than 3 cupcakes
(2) Average price of 1 doughnut and 1 cupcake was $.035 [Reveal] Spoiler: OA Senior Manager Joined: 13 Mar 2012 Posts: 357 Concentration: Operations, Strategy Re: Word problem: doughnut [#permalink] ### Show Tags 15 Apr 2012, 22:56 2 This post received KUDOS 1 This post was BOOKMARKED Smita04 wrote: At the bakery lew spent a total of 6$ for one kind of cupcake and one kind of doughnut. How many donuts did he buy?
1) price of 2 doughty was $.10 less than 3 cupcakes 2) average price of 1 doughnut and 1 cupcake was$.035

let
cupcakes purchased= x
doughnut purchased= y

price of one cupcake and doughnut be c and d respectively,
then

cx+dy = 6

we need to find y.

statement 1) 2d= 3c - 0.1
INsufficient

statement 2) (c+d)/2 = 0.035
c+d = 0.035*2

Insufficient

1) and 2)

we can have c and d but we have no info about x and y.

Insufficient.

hence E

Hope this helps..!!
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05 Feb 2014, 14:41
Smita04 wrote:
At the bakery lew spent a total of 6$for one kind of cupcake and one kind of doughnut. How many donuts did he buy? 1) price of 2 doughty was$.10 less than 3 cupcakes
2) average price of 1 doughnut and 1 cupcake was $.035 let cupcakes purchased= x doughnut purchased= y price of one cupcake and doughnut be c and d respectively, then cx+dy = 6 we need to find y. statement 1) 2d= 3c - 0.1 INsufficient statement 2) (c+d)/2 = 0.035 c+d = 0.035*2 Insufficient 1) and 2) we can have c and d but we have no info about x and y. Insufficient. hence E Hope this helps..!! But I guess still one has to prove whether 'x' and 'y' could be found using the equation Dx + Cy, remember that x,y standing for the number of Donuts and Cupcakes have to be integers and must satisfy Dx + Cy = 6. Therefore, the next question is, how can we do this in the most efficient way? Experts, any thoughts? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7451 Location: Pune, India Re: At the bakery Lew spent a total of 6$ for one kind of [#permalink]

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05 Feb 2014, 22:54
Expert's post
3
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BOOKMARKED
Smita04 wrote:
At the bakery Lew spent a total of 6$for one kind of cupcake and one kind of doughnut. How many donuts did he buy? (1) Price of 2 doughty was$.10 less than 3 cupcakes
(2) Average price of 1 doughnut and 1 cupcake was $.035 There is an error in this question. "Average price of 1 doughnut and 1 cupcake was$0.35"
It doesn't make sense if the average price is 3.5 cents. The numbers don't work. It must be 35 cents. Convert everything to cents.

Using both statements together, you get
3C - 2D = 10 (C is the price of cupcakes and D is the price of doughnuts)
C + D = 35*2

Solving them simultaneously, you get C = 30, D = 40.

If Nc is number of cupcakes and Nd is number of doughnuts,
30*Nc + 40*Nd = 600
3*Nc + 4*Nd = 60
The first solution I get is Nd = 3, Nc = 16
We will get many more solutions such as Nd = 6, Nc = 12. Also, Nd = 9, Nc = 8 etc
Hence both statements together are not sufficient.

Note that in this equation: 3*Nc + 4*Nd = 60, if instead of 60, the total price were say 18, there would have been only one solution.
3*Nc + 4*Nd = 18
Nc = 2, Nd = 3
Other possible solutions will be Nc = 6, Nd = 0; Or Nc = -2, Nd = 6 etc
Since we cannot buy negative or 0 number of items (she spends money on doughnuts AND cupcakes so she must have bought at least one of each), no other solution works.

Refer to this post for further details on this method: http://www.veritasprep.com/blog/2011/06 ... -of-thumb/
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03 Mar 2015, 06:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: At the bakery Lew spent a total of 6$for one kind of [#permalink] ### Show Tags 29 Mar 2016, 12:18 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: At the bakery Lew spent a total of 6$ for one kind of   [#permalink] 29 Mar 2016, 12:18
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