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At the bakery, Lew spent a total of $6.00 for one kind of [#permalink]

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07 Apr 2009, 10:57

3

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00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

56% (02:14) correct
44% (01:17) wrong based on 63 sessions

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At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy?

(1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes. (2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35.

Re: At the bakery, Lew spent a total of $6.00 for one kind of [#permalink]

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25 Jan 2010, 20:51

Looking into the question it seems as if one kind of cup cake and one kind of donut refers to 1 cup cake and 1 Donut. In that case we would get 1C+1D=6.

How is it by the wording we can be sure that one kind of cup cake refers to more than one cup cake.

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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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?

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. Answer (E)

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.

Re: At the bakery Lew spent a total of 6$ for one kind of [#permalink]

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03 Mar 2015, 06:19

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Re: At the bakery Lew spent a total of 6$ for one kind of [#permalink]

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29 Mar 2016, 12:18

Hello from the GMAT Club BumpBot!

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Re: At the bakery, Lew spent a total of $6.00 for one kind of [#permalink]

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14 Oct 2016, 10:06

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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