Eggs in Loach s Grocery can only be bought individually

Question

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.

shampoo · Answer

without solving and by just looking at it i go for D.

amartin6165 · Answer

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

M8 · Answer

'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.

kevincan · Answer

Notice that the average price paid is  exactly  the price of a carton of 6. How can this happen? (clue)

old_dream_1976 · Answer

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 ?

ps_dahiya · Answer

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.

jaynayak · Answer

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

v1rok · Answer

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?

GMATCUBS21 · Answer

can we have the official answer, i'd go with D, i dont see how any other way A will yield 150.

giddi77 · Answer

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.

kevincan · Answer

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

Eggs in Loach s Grocery can only be bought individually

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