An ice-cream stand sells two sizes of cones, Generous and Colossal. Ho

Let number of Colossal cones sold = c
and number of Generous cones sold = g
price per unit of Colossal cone = x
price per unit of Generous cone = y
We need to find c
(1) The total sales were $209.15
cx + gy = 209.15
Not sufficient
(2) Generous cones sold for 75 cents, and Colossal cones sold for $1.25
y=.75
x=1.25
Not sufficient

Combining 1 and 2 ,
Not sufficient
1.25c + .75g = 209.15

Answer E
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

An ice-cream stand sells two sizes of cones, Generous and Colossal. How many Colossal cones were sold one day?

(1) The total sales were $209.15.
(2) Generous cones sold for 75 cents, and Colossal cones sold for $1.25.


When you look at the original condition, this is a frequently given question, which is "2 by 2" que like a table below.

On the table above, there are 4 variables(a,b,c,d), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), they become 0.75a+1.25b=209.15, which is not unique and not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

HI Bunuel,
Info in statements 1 and 2 do not correlate to each other..
Given individual values of cones in statement 2, the total value can never be 209.15....
both 75 cents and $1.25 are multiples of 25 cents, so their total too should be a multiple of 25
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It's like some mathwiz know the answer b4 solving.
Are u guys saying that 125(x) + 75(y) can never equal 20915?
I don't think so.

or that y & x will have many solutions?
If so, evidence please.

Hi,
I will take the equation that you have written..
125(x) + 75(y)...
1) here x and y have to be integer, as cones can't be purchased as a fraction of totall..
2) 125x+75y= 25(5x+3y)...
what does this tell us ...
5x +3y has to be some integer and that integer is multiplied by 25....
so our answer has to be a multiple of 25..

lets see 20915...
how do you know whether a number is a multiple of 25..
its last two digits should be divisible by 25...
so last two digits should be 25, 50, 75, or 00..
this is not the case with 20915..

that is why i said 125x+75y \(\neq{20915}\)..
i hope it makes sense now..
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75G + 125 C = 20915
which can be written as:
5 (3G + 5C) = 4123

4123 is not a multiple of 5 so there is no solution whereby G and C are both integers

Statement 1 just gives us the total sales clearly insufficient
Statement 2 gives us individual pricing for both cones but we don't know how much cones
even after combining we don't get the answer as we need the total number of cones to solve the problem
correct answer - E