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# Eggs in Loach s Grocery can only be bought individually

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Eggs in Loach s Grocery can only be bought individually [#permalink]  04 Jul 2006, 07:36
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Eggs in Loachâ€™s Grocery can only be bought individually ($0.16 each), by the half-dozen ($0.60 each carton of 6 eggs), or by the dozen ($1.00 each carton of 12 eggs). The eggs that Larry bought at LoachÂ´s last year cost$15.00. How many cartons of eggs did Larry buy last year?

(1) He bought a total of 150 eggs, some but not all individually.
(2) He bought 30 eggs individually and 9 cartons of 12 eggs.

Last edited by kevincan on 04 Jul 2006, 12:11, edited 1 time in total.
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[#permalink]  04 Jul 2006, 07:48
without solving and by just looking at it i go for D.
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[#permalink]  04 Jul 2006, 08:00
B.

(1) is insufficient because he could have bought 25 cartons of 6 eggs or 15 cartons of 12 eggs.

(2) is sufficient because if he bought 30 single eggs and 9 cartons of 12 eggs he would have spent:

30(0.16) + 9(1) = 13.80
15-13.80 = 1.20 --> 2 cartons of 6 eggs
2 cartons of 6 eggs + 9 cartons of 12 eggs = 11 cartons
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[#permalink]  04 Jul 2006, 08:17
'B' it is.

1) insufficient
2) sufficient
30 individually = $4.80 9 cartons of 12 eggss each$1 = $9 2 cartons of 6 eggs each$0.60 = $1.20 TOTAL$15.00 - 11 Cartons.
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[#permalink]  04 Jul 2006, 12:08
Notice that the average price paid is exactly the price of a carton of 6. How can this happen? (clue)
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[#permalink]  04 Jul 2006, 14:27
amartin6165 wrote:
B.

(1) is insufficient because he could have bought 25 cartons of 6 eggs or 15 cartons of 12 eggs 15 x12 = 180 .

(2) is sufficient because if he bought 30 single eggs and 9 cartons of 12 eggs he would have spent:

30(0.16) + 9(1) = 13.80
15-13.80 = 1.20 --> 2 cartons of 6 eggs
2 cartons of 6 eggs + 9 cartons of 12 eggs = 11 cartons

These are the deadly ones

how does one go about it and conclude unique soln for state 1 -

Shampoo,

can you please shed some light on this ?
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[#permalink]  04 Jul 2006, 16:50
I know B gives the answer but not sure about A.

Somehow I feel A will give the answer like 30 individual, 3 cartons of 6 and 9 cartons of 12.

So I go for D.
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[#permalink]  05 Jul 2006, 01:15
ps_dahiya wrote:
I know B gives the answer but not sure about A.

Somehow I feel A will give the answer like 30 individual, 3 cartons of 6 and 9 cartons of 12.

So I go for D.

Very true.

B does give the answer. But trying to find out A will be very long.

Gut feeling in these cases is that the answer should be D
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[#permalink]  05 Jul 2006, 12:00
ps_dahiya wrote:
I know B gives the answer but not sure about A.

Somehow I feel A will give the answer like 30 individual, 3 cartons of 6 and 9 cartons of 12.

So I go for D.

Exactly my feelings too! Somehow after solving numerous problems of various difficulty I am starting to get a sixth sense on these traps. I hope that my gut feeling would not let me down on the exam date...

So, anybody knows how to show that (A) is sufficient too?
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can [#permalink]  05 Jul 2006, 12:26
can we have the official answer, i'd go with D, i dont see how any other way A will yield 150.
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[#permalink]  05 Jul 2006, 13:17
v1rok wrote:
ps_dahiya wrote:
I know B gives the answer but not sure about A.

Somehow I feel A will give the answer like 30 individual, 3 cartons of 6 and 9 cartons of 12.

So I go for D.

Exactly my feelings too! Somehow after solving numerous problems of various difficulty I am starting to get a sixth sense on these traps. I hope that my gut feeling would not let me down on the exam date...

So, anybody knows how to show that (A) is sufficient too?

A mathematical approach to solve this would be:

x = No of dozens
y = No of half-dozens
z = No of individual eggs

From the stem,
x + 0.6y+0.16z = 15 --(A)

From 2:
x = 9
z = 30

We can find y (as everyone here has found) and only one such y exists. And hence SUFF.

Condition #1.
Given
x + 0.6y+0.16z = 15 --(A)
12x+6y+z = 150 --(B)

(From #2) x = 9, y = 2 and z = 30 is defenitely one of the solutions. We are looking for alternate solution

(A)*10 - (B) gives
10x = 3z

We ALREADY KNOW that
x = 9, z = 30 --> y = 2 is a valid solution
Try to find other integer solutions for ths:
x = 3, z = 10 --> y = 104/6 Not an integer. Invalid solution
x = 6, z = 20 --> y = 58/6 Not an integer. Invalid solution
x = 12, z = 40 --> y becomes -ve. No neeto to check further

#1. is also sufficient. Hence D.

But as everyone here mentioned, all of this analysis takes a hell lot of time. It is not worth spending more than 3 minutes.
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[#permalink]  05 Jul 2006, 14:35
It pays to be observant. From (1), the average price of the eggs was $0.10, which means that the average price of the eggs bought individually or by the dozen was also$0.10

As an equation,
(0.16x+ y)/(x+12y)=0.1 x=no. of ind. eggs, y=no. of dozens

so 3x=10y (x,y) could be (0,0),(10,3),(20,6) or (30,9)

But no. of eggs sold in 6 packs must be multiple of 6

Thus 150-x-12y must be a multiple of 6

Thus x must be 0 or a multiple of 6
Thus x must be either 0 or 30, but x cannot be 0 since x+y must be greater than 0
Thus x=30, y=9 and no. of 6 packs must be 2

Therefore (1) is sufficient, as is (2) OA: D
A friend of mine did the GMAT last week and this was similar to the last question
[#permalink] 05 Jul 2006, 14:35
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# Eggs in Loach s Grocery can only be bought individually

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