A candy company conducted market research through a survey and a subse

Dear haardiksharma,

I'm happy to respond. This is a fantastic question!

What do we know for sure? We know 27% of the folks in the survey liked dark chocolate, and this shot up to 60% in the taste test. Now, it could be true that just about everyone swapped around, and almost no one preferred in the taste test what they said they liked on the survey. It's possible for (A) to be false. Keep that in mind.

Suppose we try to keep as many people as possible aligned with their original choice. For started, all 27% that said dark chocolate are still going to prefer it during the taste test. We need another 33% to come from somewhere. Could all of them come from group that preferred the milk chocolate in the survey? Yes, 45% > 33%, so we could fill the rest of this 60% with folks from the milk chocolate survey group and not even touch those that initially preferred white chocolate. Thus, we know it's possible for (B) to be false.

Could all of the rest of that 60% come from group that preferred the white chocolate in the survey? NO! 28% < 33%, so even if all those who initially preferred white chocolate and all of those who initial preferred went into the dark chocolate after the taste test group, that's only 27% + 28% = 55%, not enough. Inevitably, we will have to draw some of the milk chocolate people into the group. In fact, it is impossible to construct a scenario in which none of those who preferred milk chocolate first would wind up in the group preferring dark chocolate in the taste test, because there has to be some overlap between that initial 45% and the final 60%.

The answer has to be (D).

Does this make sense?
Mike
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45% said they preferred milk chocolate. But 40% indicated that they do not prefer dark chocolates after the taste test (as 60% prefer dark chocolates). So there must be some people who earlier said they preferred milk chocolate during the survey and later said they prefer dark chocolates.

Hence, answer D.

VERITAS PREP OFFICIAL SOLUTION:

This inference problem forces you to do some math to determine which answer must be true. You know from the given information that some preferences were different between the survey and the taste test (dark chocolate went from 27% to 60%, from the lowest value to the highest, so some people must have changed their preferences from either milk or white chocolate), but each answer choice will require some analysis to determine whether it "could be true" (incorrect answer) or "must be true" (correct).

Choice A is the qualitative answer and certainly could be true, but isn't necessarily. What if this company simply has lousy white and milk chocolate, but very good dark chocolate? The respondents could have been very accurate in relaying their general preferences, but those preferences just didn't hold in this particular case. So choice A is incorrect.

Choice B is more quantitative. It certainly could be true but doesn't have to be. You know that dark chocolate went from 27% to 60%, so it picked up a net gain of 33%. This could be true if some of that gain came from white and some from milk. But since you do not have the taste test totals from white and milk you can play with different combinations. Suppose all who said dark in the survey said dark in the taste test, and then 33% defected from milk to dark. That would leave white unchanged and still give you 60% dark, just with 28% white and now 12% milk. So choice B is not necessarily true and is therefore incorrect.

Choice C does not have to be true, either. You know that 33% of respondents switched to dark chocolate, but you do not know for certain that anyone switched between white and milk. As you will see with choice D...

Choice D must be true. You need a net gain of 33% moving from either white or milk to dark. And since only 28% preferred white chocolate, you can't get that 33% gain unless at the very least 5% of people changed from milk to dark.

Choice E is incorrect because, again, the minimum change is 33%. All the statements could be true if everyone who liked dark in the survey stuck with dark in the taste test, and then 33% moved to dark from milk. That case satisfies all of the facts but leaves more than half of survey responses intact, thereby invalidating choice E.

Choice D is correct.
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This is much easier when you use some basic numbers, so refer to my image.
The thing that must be 100% absolutely true is that the milk chocolate people (45%) MUST be reduced by 5% to make the math agreeable such that the Dark chocolate group now takes up 60% proportion.

DC- 27
WC- 28
MC- 45

DC+ some MC--> 60 .... so not 'B"

DC+WC--> 55 not enough to make 60..so some from WC-->DC to make it 60.

Clearly D.

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