Lets assume 1 gallon of Brand X antifreeze costs=x and 1 quarts of Brand Y antifreeze costs=y , Thus we need to find: \(x+y= ?\)
(1)==> \(6x+10y=58\)==>\(3x+5y=29\)......a .......... cannot be reduced any further/no specific info.......... Thus insufficient
(2)==> \(4x+12y=44\)==>\(x+3y=11\).......b ............. cannot be reduced any further/no specific info.......... Thus insufficient
(1)+(2)==> \(a-b\) ==>\(2x+2y=18\)==>\(x+y=9\)........................................................................... Thus Sufficient
Hence I would go for option C.
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could anyone explain when and why GMAT use one variable and one equation and when 2 variable with one equation ?
because sometimes both are accept and have suffice answer !!!!
6x+10y=58 ......> answer is x=3 and y=4 and i think it is suffice ! and answer can be A.
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09173140521 You posted a valid question and the answer to this lies in the question stem.

When the question stem has certain restrictions, then that should signal us about the usage of 2 variables in 1 equation. Consider the following :-

2x + y = 5, find the value of x

(1) x and y are integers
(2) x > 1

Soln -

(1) x = 1 y = 3 ; x = 2 y = 1 INSUFF
(2) x = 2 y = 1 ; x = 1.4 y = 2.2 INSUFF Please DO NOT forget the decimal values of the given variables.

Combining both we get, x = 2 y = 1 Suff

Now notice despite having 1 eqn with 2 variables we could find the value for x and y given the restrictions posted in the question

takeaway -
1) Always consider the 2 statements individually before combining. Had we ignored the decimal values of x and y we would have chosen (B) as our answer
2) It is not always true that 1 equation with 2 variables is insufficient

The missing punctuation before Excluding is confusing. I thought the total cost was Price+ sales tax

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Is total cost, including sales tax, to be found? That will get an answer, different from OA, E
Can anyone confirm that.

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Hoozan thanks but I find at last. the best approach is <<<<<<we use 6x+10y=58 paraphrase to 5y=29-3x and find all answer .....clearly insufficient ....we got 2 answer .....we do not need Diophantine equation
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