During a 7-year period the profits of Midas, Inc. changed by

This increase is the actual increase not increase in %.

The OA is C.
Combining the two statements, Let P be the Profit in the third year and x be the increase in profit which is constant. Thus profit in the 6th year = P+3x
and Profit in the 7th year = P+4x
Also from statement 1 Profit in 7th year =1.5 times profit in 3rd year
thus P+4x = 1.5P
thus x=P/8

Hence the percentage increase of 7th year over 6th can now be known.

Hope this is clear.

Good question Ankit

Damn... I was caught in the trap.

Is this a relatively high level question or not?

No its a simple question. which reinstates the fact that one needs to be really careful, alert and consider all possibilities.

This is an interesting old question,But I think needs expert opinion.

we need to know the profits of 6th and 7th year in order to answer this question.

(1) The profits of Midas, Inc. during the seventh year were 50 percent greater than the profits during the third year.
Nothing about the sixth year so Insufficient

(2) The increase in the profits of Midas, Inc. was the same for each year during the 7-year period.

Initially I thought this was sufficient as profits of 6 and 7 year seemed to be same, but that is not so.

The original profits of 6 and 7 year may be different but increase may be same, hence we do not know that actual 6 and 7 year profits.

1+2
from 1
Let 3 year profit be x and 7 year profit is 1.5x still we know nothing about 6 year

from 2 : increase in profits were the same each year , so let the increase in profits be y each year

year ---- profit
3 ------- x
4 ------- x+y
5 ------- x+y+y = x+2y
6 ------- x+3y
7 ------- x+4y

Now we know 6 year profit is x+3y and 7 year profit is x+4y

also we know x+4y=1.5x ( 7 year profit is 1.5 times 3 year profit, we have taken 3 year profit to be x)
on solving x+4y=1.5x we get x= 8y

now 6 year profit is 11y ( from chart above )and 7 year profit is 12y
so profit % increase from 6 to 7 year \(\frac{12y-11y}{11y}*100 =\frac{100}{11} = 9.09\)

We know C is is the answer, but can any one tell me if I have arrived at the correct percentage change in profit?
Thanks

Yes, the actual increase is 100/11%.

mikemcgarry

Hi Mike, I need your help here...

I think that you explain thing really well, so you might help me a lot

I can't understand what is happening here.. How can we add percents?? Aren't we supposed to multiply the starting value by the percent to get the percent change? Why are we summing percents???

Omg I am so lost with this topic and it's so important on the test. Plus I am running out of questions and I just cant seem to grab the fundamentals. I am 100% sure I understand all the basics but I keep getting these Qs wrong all the time.. Please help!

Dear iliavko,

My friend, thank you for your kind words. I am happy to respond.

The first thing I'll say is that when we have a series of percent changes, one after the other---say a 40%, then a 30% increase on that, then a 20% decrease--never think addition. Think multiplication.

In fact, for any percent increase or decrease, you should be thinking about these in terms of multiplication. Read this thoroughly:
Understanding Percents on the GMAT

Thus, to accomplish the proposed series of percent changes above, we would find the multipliers for each and multiply them together (I used a calculator to get the product--that's beyond what the GMAT would expect you compute in your head!)
(1.4)*(1.3)*(0.80) = 1.456
Thus, if we have an initial amount, and we increase by 40%, then increase by 30%, then decrease by 20%, that's equivalent to a 45.6% increase over the initial amount.

Now, if you read the blog thoroughly and understand all that, we can look at this problem:
During a 7-year period the profits of Midas, Inc. changed by what percent from the sixth year to the seventh year?
(1) The profits of Midas, Inc. during the seventh year were 50 percent greater than the profits during the third year.
(2) The increase in the profits of Midas, Inc. was the same for each year during the 7-year period.

The individual statements are not sufficient. Let's deal with the combined statements. Let's say that x is the percent change from year to year, written as a decimal. Thus, x would be the answer to the prompt question, because the change from year 6 to year 7 would be the same as the change from any other year.

The multiplier for a change from one year to the next is (1 + x). Let P3 be profit in the third year, P4, profit in the 4th year, etc. We know

P4 = P3*(1 + x)
P5 = P4*(1 + x) = P3*(1 + x)^2
P6 = P5*(1 + x) = P3*(1 + x)^3
P7 = P6*(1 + x) = P3*(1 + x)^4

Now, since we also know that P7 = 1.5*P3, that allows us to set up an equation:

1.5 = (1 + x)^4

We'd need a calculator to solve for the exact value, but that doesn't matter. This is DS, it's enough to know that we could solve for the exact value of x and answer the prompt question. Both statements together are sufficient. Answer = (C).

BTW, x = .10668192..., about 10.67%

Does all this make sense?
Mike

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