Mathematics

Diophantus wrote:Three sets of beans x, y and z are sold for $5.00, $15.00 and $17.50 respectively per kg. If they are mixed in the ratio 1:3:2, what is the cost per kg of the mixture?

You're missing the 5 answer choices.

Cheers,
Brent

Diophantus wrote:Three sets of beans x, y and z are sold for $5.00, $15.00 and $17.50 respectively per kg. If they are mixed in the ratio 1:3:2, what is the cost per kg of the mixture?

Nevertheless, here's one approach:

Let's combine 1 kg of the X Beans, 3 kg of the Y Beans and 2 kg of the Z Beans
This allows us to have the desired 1:3:2 ratio

COST of 1 kg of the X Beans = $5.00
COST of 3 kg of the Y Beans = (3)($15.00) = $45.00
COST of 2 kg of the Z Beans = (2)($17.50) $35.00

TOTAL cost = $5.00 + $45.00 + $35.00 = $85
TOTAL weight = 1 kg + 3 kg + 2 kg = 6 kg

Cost per kg = $85/6 kg = 14 1/6 dollars per kg
≈ $14.17 per kg

Cheers,
Brent

Hi Diophantus ,

Brent's explanation is spot-on, so I won't rehash any of that here. Instead, I want to point out that including the 5 answer choices is important. On a variety of questions, the answer choices are designed to give you a 'hint' as how you might approach the prompt or provide a 'shortcut' so that you don't have to take a long, math-heavy approach to get the correct answer. By not including the answers here, we're essentially forced to do math.

Given the 'weights' of the three values in this question, the average would have to be a little less than $15 (since the two $17.50s won't "offset" the one $5). If the answer choices are 'spread out' to a certain degree, then you might not need to do much math at all to get the correct answer.

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

Hi Diophantus,

Great explanations by the experts. Something for you to work...

I modified the question as follows. Pl. attempt this one.

Three sets of beans x, y and z are sold for $4.37, $14.37 and $19.37, respectively per kg. If they are mixed in the ratio 1:3:2, what is the cost per kg of the mixture?

-Jay
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