sandipgumtya wrote:Pl help out in the following DS Prob:
A candy manufacturer decided to decrease the weight of each candy bar, while retaining the price. By how many cents did the per kilogram cost of candy change after the reduction in weight?
(1) The weight of each piece of candy bar reduced by 9 grams.
(2) The weight of each piece of candy bar reduced by 9%
If we know the cost per gram, we can determine the cost per kilogram.
Question stem, rephrased:
By how many cents did the PER GRAM COST change?
Clearly, neither statement on its own is sufficient.
Statements combined:
Let x = the original weight of each bar.
When the statements are combined, we know that a weight reduction of 9 grams is equal to 9% of the original weight:
9 = (9/100)x
x = 100.
Thus:
Original weight = 100 grams.
Reduced weight = 100-9 = 91 grams.
Strategy:
Test different values for the COST, which is the same for each weight.
Case 1: Cost = 9100 cents
In this case:
Original cost per gram = (9100 cents)/(100 grams) = 91 cents per gram.
Cost per gram after weight reduction = (9100 cents)/(91 grams) = 100 cents per gram.
Increase in cost per gram = 100-91 = 9 cents per gram.
Case 2: Cost = 91000 cents
In this case:
Original cost per gram = (91000 cents)/(100 grams) = 910 cents per gram.
Cost per gram after weight reduction = (91000 cents)/(91 grams) = 1000 cents per gram.
Increase in cost per gram = 1000-910 = 90 cents per gram.
Since the increase in cost per gram can be DIFFERENT VALUES, the change in cost per gram cannot be determined.
Thus, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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