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At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon

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Bunuel
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At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink] New post   25 May 2018, 02:34
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85% (01:37) correct 15% (01:45) wrong based on 441 sessions
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At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon and Brand Y motor oil is sold by the quart. Excluding sales tax, what is the total cost for 1 gallon of Brand X antifreeze and 1 quart of Brand Y motor oil?

(1) Excluding sales tax, the total cost for 6 gallons of Brand X antifreeze and 10 quarts of Brand Y motor oil is $58. (There is no quantity discount.)

(2) Excluding sales tax, the total cost for 4 gallons of Brand X antifreeze and 12 quarts of Brand Y motor oil is $44. (There is no quantity discount.)
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u1983
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Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink] New post   25 May 2018, 02:55
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Bunuel wrote:
At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon and Brand Y motor oil is sold by the quart Excluding sales tax, what is the total cost for 1 gallon of Brand X antifreeze and 1 quart of Brand Y motor oil?

(1) Excluding sales tax, the total cost for 6 gallons of Brand X antifreeze and 10 quarts of Brand Y motor oil is $58. (There is no quantity discount.)

(2) Excluding sales tax, the total cost for 4 gallons of Brand X antifreeze and 12 quarts of Brand Y motor oil is $44. (There is no quantity discount.)


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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Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink] New post   22 Jun 2019, 23:49
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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Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink] New post   10 Aug 2019, 23:22
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
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Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink] New post   10 Aug 2019, 23:38
Bunuel wrote:
At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon and Brand Y motor oil is sold by the quart Excluding sales tax, what is the total cost for 1 gallon of Brand X antifreeze and 1 quart of Brand Y motor oil?

(1) Excluding sales tax, the total cost for 6 gallons of Brand X antifreeze and 10 quarts of Brand Y motor oil is $58. (There is no quantity discount.)

(2) Excluding sales tax, the total cost for 4 gallons of Brand X antifreeze and 12 quarts of Brand Y motor oil is $44. (There is no quantity discount.)


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

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Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink] New post   11 Aug 2019, 00:27
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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Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink] New post   11 Aug 2019, 02:14
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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Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink] New post   04 Dec 2022, 03:15
Hello from the GMAT Club BumpBot!

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Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon [#permalink]
04 Dec 2022, 03:15
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