Was Store K's profit last month at least 10 percent greater than its

Target question: Was Store K's profit last month at least 10 percent greater than its profit the previous month?

IMPORTANT: Profit = Revenue - Expenses

Statement 1: Store K's expenses last month were 5 percent greater than its expenses the previous month.
Since we have no information about revenue, there is no way to compare profits.
Statement 1 is NOT SUFFICIENT

Statement 2: Store K's revenues last month were 10 percent greater than its revenues the previous month.
Since we have no information about expenses, there is no way to compare profits.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Important concepts: If X is 5% greater than Y, then X = 1.05Y, and if X is 10% greater than Y, then X = 1.10Y.
If we let R = the revenue from the previous month, then (from statement 2), 1.1R = the revenue from last month.
If we let E = the expenses from the previous month, then (from statement 1), 1.05E = the expenses from last month.

The target question asks Was Store K's profit last month at least 10 percent greater than its profit the previous month?
In other words, Was Store K's profit last month greater than or equal to a value that's 10 percent greater than its profit the previous month?
In other words: Is 1.10R - 1.05E ≥ 1.10(R - E)?
Expand the right side to get: Is 1.10R - 1.05E ≥ 1.10R - 1.10E?
Add 1.10E to both sides of the inequality to get: Is 1.10R + 0.05E ≥ 1.10R?
Subtract 1.10R from both sides to get: Is 0.05E ≥ 0?
The answer to this rephrased target question is a definite YES (since we can assume E ≥ 0, which means 0.05E ≥ 0)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

STRAIGHT to POINT: Profit(P)=revenue(R)-expense(E)
' is used for last month and no numenation :plain E,P,R for previous month


1)E'=1.05E>>Insufficient
2)R'=1.10R >>Insufficient

Now combined(C): R'-E'=1.10R-1.05E----->>> difference between last month and now-->>P'-P=(R'-E')-(R-E)=.10R-.05E

Now is .10R-.05E>.10(R-E) ?
YES IT is using some sense
.10R-.05E>.10R-.10E
since substracting small number>>> greater value>>> LHS>RHS in above equation

Therefore C

HOPE THIS HELPS

THANKS

We can pick easy numbers here.

AS we know Profit=Revenue-Expense

Suppose, Previous Month Revenue=200 , Expense = 100 ; Profit=100

Statement1: Expense=100*1.05=105; no information about the revenue, so not sufficient.
Statement1: Last Month Revenue=200*1.10=220, no information about the expense, so not sufficient

Combine both statements, Profit=115

last month at least 10 percent greater than its profit the previous month

as, 115-100/100*100 =15%

Let's Say, First Expenses= E, then new expenses= 1.05E

First Revenue = R, then new revenue= 1.1R

So, First Profit= R- E and, new profit = 1.1R - 1.05E = 1.1R - 1.1E +0.05 E = 1.1 (first profit) + 0.05E

So, minimum 10% profit increases.

So, Both stats are not individually sufficient. Both combined stats are sufficient. So, option C.

Still a bit unsure about the reasoning behind C. Can't profit also be negative (net loss)?

For example, if Revenue was $100 and Expenses was $300. This would be a negative profit of -$200.

Taking both 1 + 2 into the next month gives us a Revenue of $110 and Expenses of $315. Giving a negative profit of -$205. This is then less.

Let me know what I am doing wrong.

mryan01867

Profit can't be negative. So, you can try with another set of example, Option C holds true.

This is really one of the questions that you dont even have to spend time solving. If you dont have revenue AD are not sufficient. if you don't have expenses B is not sufficient pick C

BrentGMATPrepNow

I don't see how this is correct. We do not know the relationship between Revenue & Expenses. For example: what if expenses in the previous month were $1,000,000 put Revenue was $1 (an extreme example). A 5% increase in expenses would result in significantly less profit than the previous month while if we reversed the amounts profit would significantly increase. The question forces the taker to assume the company is profitable which cannot be inferred. Should I just always assume a company is profitable in GMAT questions...very poor test question from the makers of the GMAT.

Please elaborate on the logic.

Great question!

The main idea here is that:
- if expenses are less than revenue, we have a profit.
- if expenses are greater than revenue, we have a loss.

Since the question uses the word profit , we can conclude that revenue exceeded expenses in both months.

Statement 1: Not Sufficient, Since we don't have any info about revenue. So, A and D are out.
Statement 2: Not Sufficient, Since we don't have any inform about expense. So, B is out.
Now we need to check whether both statements together are sufficient.
Let's,
Previous month's revenue = $200
Previous month's expenses = $100
Profit = $200- $100 = $100
So,
Last month revenue = $200*1.1 = $220
Last month expense = $100*1.05 = $105
Profit = $220-$105 = $115
As we can compare the profits between two periods, we can say both statements together are sufficient even if the profit is 10% higher or not.
Just to check,
The profits increased = ($115-$100)/$100 = 15%.
Answer: C

Is this a correct approach? Please

Statement 1 and 2 are not sufficient on their own. Let's directly jump to 1+2,

Let Store K previous Month Revenue (R1)= 100 and Expense (E1)= 90. Hence, Profit(P1) = 10 (Profit = Revenue- Expense)

Now, Store K last month Revenue will be = 10% of R1 i.e. 110.

And Expense will be = 5% of E1 i.e. 94.5. Hence, the profit(P2) for last month will be (110-94.5) = 15.5.

We have profit values of both the months and can find if profit last month at least 10 percent greater than its profit the previous month.

No need to solve further.

Option 'C' is the right answer.

avigutman

To follow-up, you mentioned in this video (https://www.youtube.com/watch?v=x6lQeAPoGuQ) that knowing the difference between two tick marks on the number line does not enable you to find their ratio.

However, in a problem like this, if you know the percentage difference between variables, you are able to find their ratio, correct?

Do you have a general rule for percentage differences? Thanks again!

Excellent question, woohoo921!
A percentage difference isn't really a difference at all. It's a ratio.
For example, a 20% increase means multiplying by 6/5. The ratio of the increased quantity to the original quantity is 120:100, or 6:5.
When people say "add 20%" it makes us imagine that we're dealing with an additive operation - that the 20% is a difference between two numbers. But, it's not, and we shouldn't say that we're adding 20%. Rather, we're increasing the original number by 20% (of itself).
This is why I split my book into two main sections, named Additive Reasoning and Multiplicative Reasoning (and, percent change lives entirely in the second section).