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

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Math Expert
Joined: 02 Sep 2009
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At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon  [#permalink]

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25 May 2018, 02:34
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Difficulty:

25% (medium)

Question Stats:

77% (01:36) correct 23% (01:43) wrong based on 103 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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At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon  [#permalink]

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25 May 2018, 02:55
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]

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

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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]

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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]

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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]

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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
_________________
behind your feelings there is nothing, but behind every principle is a promise. "Eric"
I used a lot of LSAT CR. At the same time it was important to switch back to GMAT CR before exam
because reasoning is different and you need to adjust your CR skills to GMAT .
https://gmatclub.com/forum/bunuel-signature-collection-the-next-generation-170062.html
Re: At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon   [#permalink] 11 Aug 2019, 02:14
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