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Bunuel
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Price of a Belgian chocobar has increased by x percent but the number 05 Nov 2024, 01:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

47% (02:29) correct 53% (02:23) wrong based on 176 sessions

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Price of a Belgian chocobar has increased by x percent but the number of units sold is decreased by y percent. Was the revenue collected at new price more than the revenue collected at original price?

(1) x = y.

(2) 100x − 100y − xy < 0


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D
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ajay405
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Price of a Belgian chocobar has increased by x percent but the number 06 Nov 2024, 16:34
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from the 2nd equation we can't conclude a relation between x and y independently as similar to equation 1. So the answer has to be A.
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stne
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Price of a Belgian chocobar has increased by x percent but the number 06 Nov 2024, 23:23
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Bunuel
Price of a Belgian chocobar has increased by x percent but the number of units sold is decreased by y percent. Was the revenue collected at new price more than the revenue collected at original price?

(1) x = y.

(2) 100x − 100y − xy < 0


­
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Let \(p\) be the price and \(u\) the number of units

We need to know whether \( (\frac{100+x}{100})p * ( \frac{100-y}{100})u >pu \)

or \((\frac{100+x}{100})*( \frac{100-y}{100})>1\)

or \((100+x)*(100-y) >10^4\)

or is \(100x - 100y- xy > 0 ...(i)\)

(1) x = y.

from (i) we have \(-x^2 >0\)

We know \(x \) is not zero, hence \(-x^2 > 0\) is False

We can answer NO to the asked question.

SUFF.

(2) 100x − 100y − xy < 0

This is exactly what we needed to find, according to eqn.(i)

We can answer NO to the asked question.

SUFF.

Ans D

Hope it helped.
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Price of a Belgian chocobar has increased by x percent but the number 24 Jul 2026, 17:23
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Bunuel
Price of a Belgian chocobar has increased by x percent but the number of units sold is decreased by y percent. Was the revenue collected at new price more than the revenue collected at original price?

(1) x = y.

(2) 100x − 100y − xy < 0
Show more

This question tests a couple of things that sometimes come up in percentage and DS problems. First, when a quantity both increases and decreases by the same percentage, the quantity always decreases. Second, when terms in the prompt are similar to those in a statement, you should see if you can make them "match".

The prompt tells us that the price (call it p) is increased by x percent and the units sold (call it u) is decreased by y percent.

The original revenue is therefore p*u and the new revenue is p(1 + x/100)*u(1 - y/100).

Since it doesn't matter in which order you multiply, this is the same as pu(1 + x/100)(1 - y/100). In other words, the total original revenue (pu) is increasing by x percent and decreasing by y percent. If (1 + x/100)(1 - y/100) > 1, then the revenue will go up, so we can restate the question as:
Is (1 + x/100)(1 - y/100) > 1?

Then, simplifying further:
Is 1 + x/100 - y/100 - xy/10,000 > 1?
Is x/100 - y/100 - xy/10,000 > 0?

(1) x = y
If x = y, you are increasing and decreasing the revenue by the same percentage. Whenever you increase and decrease a quantity by the same nonzero percentage, the new quantity will be lower than the original quantity.

For example, if the original revenue was $100 and x = y = 10, then the 10% increase is $110 and the 10% decrease yields a final result of $99. Again, the order doesn't matter, so if you took the 10% decrease first, you'd have $90, and the 10% increase would again result in $99.

Thus, the answer is a definite NO and the statement is sufficient.

(2) 100x − 100y − xy < 0
It may be hard to see how to apply this statement, but note that it's an inequality. Let's see if we can match it to the inequality we found in the question prompt.

If we divide Statement 2 by 100 we get:
x - y - xy/100 < 0

Then divided by 100 again:
x/100 - y/100 - xy/10,000 < 0

This matches the restated question ("Is x/100 - y/100 - xy/10,000 > 0?") and gives a definite answer of NO. (We're multiplying the original revenue by something less than 1; the revenue must go down.) Sufficient.

The answer is D.

You might wonder, "What if I didn't restate the question at the beginning of the problem?" You could still handle this question by matching Statement 2 to the question. Note that the question asks whether the new revenue is "more than" the original revenue. The "more than" language implies an inequality, and you could then work with the question and Statement 2 to see if they match, as shown above.

The takeaways:
1. On DS, look for ways to match terms between the question and the statements. You can do this by manipulating / restating the question or by working with the statement (or both).
2. Remember that a when a quantity is increased and decreased by the same percentage (or vice versa), the result will be lower than the original.
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