John buys only chocolates and cookies from the market. Was the total

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.

John buys only chocolates and cookies from the market. Was the total money spent by him on cookies and chocolates equal to 375.20?

1) The cost of one chocolate is 2.25 and one cookie is 1.75.
2) John purchased 50 chocolates and 100 cookies.


When you modify the original condition and the question, this question is frequently given on GMAT Math, which is "2 by 2" question like the 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 2.25(50)+1.75(100)=287.5, which is no and sufficient. However, this is an integer question, which is one of the key questions and apply the mistake type 4(A).
Then, for 1), 2.25a+1.75b=375.20 -> a=b=positive integer -> Such a and b don’t exist, which is no and sufficient.
Thus, the answer is A.


 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% 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 C 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, D or E.

I didn't do any algebra, i looked at the statement 1 and thought: well it would take me a long time but i bet i can test number to find if the total money for chocolates and cookies could be $375.20.

Statement 2 is simply not enough because it doesn't give any price of the items.

x - number of cookies, y - no of chocs

Statement 1:
Assume 2.25 x + 1.75 y = 375.2
(9/4) x + (7/4) y = 375.2
9 x + 7 y = (375.2 * 4)
as x, y are integers , LHS will be integer, but RHS (375.2 * 4) wont be integer. So assumpution is false => 2.25 x + 1.75 y != 375.2
Sufficient

Statement 2:
Let a - price of cookie, b - price of choc
50 a + 100 b = 375.2 ? Maybe or maybe not, unlike statement1, a and b need not be integers => Not sufficient

Answer (A)

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