If a candy manufacturer makes a new candy consisting of a core compose

Lets break down the question stub first. New candy (yum!)

Core (W1) => Has 10% chocolate by weight ==> so actual weight of chocolate in the core = 0.1*W1

Outer layer (W2) => Has 40% chocolate by weight. ==> so actual weight of chocolate in the outer layer = 0.4*W2

Entire weight of candy: W1+W2
Chocolate weight: 0.1W1 + 0.2W2

What we need to find: (W1 + W2) / (0.1W1+0.2W2) ==> (W1/W2 + 1) / (0.1*W1/W2 + 0.2)

As you can see what we need to find only depends on the ratio of core to outer layer. Only B has this information. Hence B is sufficient.

No need to actually do the calculation.

Hope this helps.

a) insuff

b)
4/1 = (40-x)/(x-10)

we have one unknown in the equation
Therefore we can find x

If "consisting of a core composed of 10 percent chocolate by weight" and provided weight of chocolate is 250 grams, is the weight of the core not 25 grams? Can someone explain what the wording is saying?

Hi bpdulog,

We're told that a candy manufacturer makes a new candy consisting of a CORE that is composed of 10 percent chocolate by weight, and an OUTER LAYER that is composed of 40 percent chocolate by weight. We're asked for the PERCENT of the ENTIRE candy, by weight, that consists of chocolate. Thus, we have to consider two values: the CORE and the OUTER LAYER. Knowing the overall weight of the candy does NOT tell us the weight of the core. This question can be solved in a couple of different ways, including by TESTing VALUES.

1) The entire candy weighs 250 grams.

Fact 1 tells us the overall weight of the candy, but we don't know the weights of the core and the outer layer.

IF....
Core = 50 grams and outer layer = 200 grams, then...
Core chocolate = (.1)(50) = 5 grams
outer chocolate = (.4)(200) = 80 grams
Total percent that is chocolate = 85/250 = 340/1000 = 34%

Core = 100 grams and outer layer = 150 grams, then...
Core chocolate = (.1)(100) = 10 grams
outer chocolate = (.4)(150) = 60 grams
Total percent that is chocolate = 70/250 = 280/1000 = 28%
Fact 1 is INSUFFICIENT

2) The ratio of the weight of the core to the weight of the outer layer is 4:1

Fact 2 gives us the ratio of the core to the outer layer; this actually IS sufficient (since the ratios do NOT change), but you might need to do a little work to prove it to yourself...

IF....
Core = 40 grams and outer layer = 100 grams, then...
Core chocolate = (.1)(40) = 4 grams
outer chocolate = (.4)(10) = 4 grams
Total percent that is chocolate = 8/50 = 16/100 = 16%

Core = 80 grams and outer layer = 20 grams, then...
Core chocolate = (.1)(80) = 8 grams
outer chocolate = (.4)(20) = 8 grams
Total percent that is chocolate = 16/100 = 16%

As long as the weights are in the ratio of 4:1, changing the weights won't change the percentage
Fact 2 is SUFFICIENT

Final Answer: [spoiler]B[/spoiler]

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

This tests a few things:

It tests whether we know that we don't need hard exact numbers to find percentages and ratios,

it tests number sense in regard to weighted averages.

After reading the question stem, you should realize that you are able to find the total % chocolate of the candy if you know the weighting (or relative sizes) of both the core and outer layer. All you need to answer this question is info about the two components sizes relative to one another (which is a ratio or %).

A) Tells us it's 250 grams. ok so what? Tells us nothing about the relative sizes of the two components. Axe it.

B) Tells us the ratio between the outer and core components. Bingo. This alone is sufficient.