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05 Sep 2024, 01:30
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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:
51% (01:59) correct
49%
(01:44)
wrong
based on 281
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Not Attempted Yet
A social networking website reported x% higher profit this year compared to last year. Is x greater than 10? (They made a profit in both years)
(1) The website has reported an increase of 5% in expenses.
(2) The website reported an increase of 10% in revenue.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) The website has reported an increase of 5% in expenses.
(2) The website reported an increase of 10% in revenue.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
08 Sep 2024, 10:04
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Previous year: \(Revenues_1 - Expenses_1 = Profit_1\)
Current year: \(Revenues_2 - Expenses_2 = Profit_2 \)
Rewriting taking into account both statements 1) and 2):
Current year: \(1,1Revenues_1 - 1,05Expenses_1 = (1+x\%)*Profit_1\)
The yearly change in percentage is thus: \(x\%= \frac{1,1Revenues_1 - 1,05Expenses_1 - (Revenues_1 - Expenses_1)}{Revenues_1 - Expenses_1}*100\)
Which is equivalent to: \(x\% = \frac{0,1Revenues_1 - 0,05 Expenses_1}{Revenues_1 - Expenses_1}*100 \). It's useful to rewrite this as: \(x\% = \frac{0,1(Revenues_1 - Expenses_1) + 0,05Expenses_1}{Revenues_1 - Expenses_1}*100 \).
We can simplify further: \(x\% = 10+ \frac{0,05Expenses_1}{Revenues_1 - Expenses_1}*100\). Examining this last equation we can see how, given that Profit last year (or \(Revenues_1 - Expenses_1 > 0\)) and \(Expenses_1 \geq{0}\), \(x\%\geq{10}\).
Thus answer is E, both statements taken together are not sufficient. Where did I do wrong? I guess a possible explanation would be that if an increase in expenses is mentioned it would be naive to think they were 0?
Current year: \(Revenues_2 - Expenses_2 = Profit_2 \)
Rewriting taking into account both statements 1) and 2):
Current year: \(1,1Revenues_1 - 1,05Expenses_1 = (1+x\%)*Profit_1\)
The yearly change in percentage is thus: \(x\%= \frac{1,1Revenues_1 - 1,05Expenses_1 - (Revenues_1 - Expenses_1)}{Revenues_1 - Expenses_1}*100\)
Which is equivalent to: \(x\% = \frac{0,1Revenues_1 - 0,05 Expenses_1}{Revenues_1 - Expenses_1}*100 \). It's useful to rewrite this as: \(x\% = \frac{0,1(Revenues_1 - Expenses_1) + 0,05Expenses_1}{Revenues_1 - Expenses_1}*100 \).
We can simplify further: \(x\% = 10+ \frac{0,05Expenses_1}{Revenues_1 - Expenses_1}*100\). Examining this last equation we can see how, given that Profit last year (or \(Revenues_1 - Expenses_1 > 0\)) and \(Expenses_1 \geq{0}\), \(x\%\geq{10}\).
Thus answer is E, both statements taken together are not sufficient. Where did I do wrong? I guess a possible explanation would be that if an increase in expenses is mentioned it would be naive to think they were 0?
09 Sep 2024, 05:55
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let's pose P2 = profit of the year and P1= profit of the year before
P1=R1-C1
P2=R2-C2
then P2=((100+x)/100)P1
statement 1 only : C2=(105/100)C1 not sufficient to solve the problem.
statement 2 only : R2=(110/100)R1 net sufficient either
both statements: P2=R2-C2=(110/100)R1-(105/100)C1=[1/100](110R1-105C1+5C1-5C1)=[1/100](110P1+5C1)
we already know P2=((100+x)/100)P1 so ((100+x)/100)P1=[1/100](110P1+5C1)
Rearrange : 100+x-110=110+(5C1/P1)
because 5C1/P1>0 we get : 100+x-110>0 ie x>10
P1=R1-C1
P2=R2-C2
then P2=((100+x)/100)P1
statement 1 only : C2=(105/100)C1 not sufficient to solve the problem.
statement 2 only : R2=(110/100)R1 net sufficient either
both statements: P2=R2-C2=(110/100)R1-(105/100)C1=[1/100](110R1-105C1+5C1-5C1)=[1/100](110P1+5C1)
we already know P2=((100+x)/100)P1 so ((100+x)/100)P1=[1/100](110P1+5C1)
Rearrange : 100+x-110=110+(5C1/P1)
because 5C1/P1>0 we get : 100+x-110>0 ie x>10
19 Nov 2024, 01:14
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Explanation please? I believe it should be less than 10% since expenses have gone up and revenue is up 10% so we will net lesser profit
