cost of antifreeze

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EricKryk: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Tue Mar 31, 2009 11:03 am; Thanked: 3 times

by EricKryk » Tue Jan 28, 2014 7:03 am

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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Source: Beat The GMAT — Data Sufficiency | Tue Jan 28, 2014 7:03 am

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Tue Jan 28, 2014 7:19 am

don't worry about trying to convert gallons to quarts. just think of x as the price of one unit of antifreeze X, and think of y as the price of one unit of motor oil Y. We just want to find the value of x+y.

The full solution below is taken from the GMATFix App.

-Patrick

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To prep my students I use this tool >> (screenshots, video)

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Jan 28, 2014 2:46 pm

Hi EricKryk,

This question is built on "system math" and comes with a great shortcut, once you recognize what you're looking at.

The question asks us for the cost of 1 gallon of X and 1 quart of Y. I'm going to write that as "what is X + Y?"

Fact 1: 6X + 10Y = 58

This can be simplified to 3X + 5Y = 29. Unfortunately, there's no way to deduce what X + Y totals.
Fact 1 is INSUFFICIENT

Fact 2: 4X + 12Y = 44

This can be simplified to X + 3Y = 11. We can't figure out the value of X + Y from this either.
Fact 2 is INSUFFICIENT

Combined, we have...
3X + 5Y = 29
X + 3Y = 11
2 variables and 2 unique equations, which means we CAN solve it (and there we be just one answer), but we don't have to.
Combined, SUFFICIENT

Final Answer: C

A final note about GMAT DS questions that LOOK LIKE "system" questions; they're usually NOT system questions, so the answer is usually not C.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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