Lesson: Variables in the Answer Choices

Comment on Variables in the Answer Choices

Hey Brent,
Just a question:

https://gmatclub.com/forum/last-sunday-a-certain-store-sold-copies-of-newspaper-a-for-101739.html

Would you consider the following question a good one to guess on?
I really struggled at this question until I solved this question using various other ways which I could think of and which other people came up with. Even then gives me the chills thinking about how I would go about solving such a question in the real test.
gmat-admin's picture

Question link: https://gmatclub.com/forum/last-sunday-a-certain-store-sold-copies-of-ne...

This is a great candidate to guess on if you're running behind at all (see the following video on when it's a good time to look for questions to guess on: https://www.gmatprepnow.com/module/general-gmat-strategies/video/1244

For this particular question, I suggest a way to quickly narrow down your guessing options here: https://gmatclub.com/forum/last-sunday-a-certain-store-sold-copies-of-ne...

This year, a woman has a lucrative one-year position. During this year, she will give a fraction f of her salary to her husband, a private investor, to invest and they will live this year on the remainder. Through investments, her husband can turn each dollar she gives him into 1 + r, which will be deposited in a bank account. Their goal is to save & invest enough money so they can live off this money for two years following the end of the wife'sLet position. Toward this end, they want to choose f such that the amount in the account at the end of the year is twice what they lived off this year. In terms of r, what should f be?


A. 1/(r+1)

B. 2/(r+2)

C. 2/(2r+1)

D. 2/(r+3)

E. 2/(2r+3)

For this question, I do not understand how you came up with the below reasoning:

If the husband is given 1 dollar, then he will turn that into 1 + r dollars
If the husband is given 2 dollars, then he will turn that into 2 + 2r dollars
If the husband is given 3 dollars, then he will turn that into 3 + 3r dollars
So, If the husband is given fT dollars, then he will turn that into fT + fTr dollars

I would have assumed fT + r dollars instead
gmat-admin's picture

Here's my full solution: https://gmatclub.com/forum/this-year-a-woman-has-a-lucrative-one-year-po...

We have the following pattern:
If the husband is given 1 dollar, then he will turn that into 1 + r dollars
If the husband is given 2 dollars, then he will turn that into 2 + 2r dollars
If the husband is given 3 dollars, then he will turn that into 3 + 3r dollars
If the husband is given 4 dollars, then he will turn that into 4 + 4r dollars
If the husband is given 5 dollars, then he will turn that into 5 + 5r dollars
.
.
.

So, if the husband is given Q dollars, then he will turn that into Q + Qr dollars
And, if the husband is given (something) dollars, then he will turn that into (something) + (something)r dollars

From here, of the husband is given fT dollars, we just replace (something) with fT.
We get: If the husband is given fT dollars, then he will turn that into fT + fTr dollars

Does that help?

Cheers,
Brent

Understood. I was assuming 100 + r, whereas the correct logic is 100 + 100r for getting percentage increases.

Hi Brent,

Don't know where to post this type of question, but need your help in this one:

https://gmatclub.com/forum/if-20-swiss-francs-is-enough-to-buy-9-notebooks-and-89226.html


Jonah drove the first half of a 100-mile trip in x hours and the second half in y hours. Which of the following is equal to Jonah’s average speed, in miles per hour, for the entire trip?

A. 50/(x + y)
B. 100/(x + y)
C. 25/x + 25/y
D. 50/x + 50/y
E. 100/x + 100/y


Whats wrong with my solution?

Total distance 100 mile
x=10 hrs
y= 20 hrs

Total Time

50/10=5 miles an hour
50/20= 5/2 miles an hour

Total speed

100/(5+5/2) = 200/15

Please suggest where i'm going wrong.

Thanks!
gmat-admin's picture

In your solution, you have a section called Total TIME
However, your calculations suggest that you are finding the average SPEED for each part of the trip.

Once you let x = 10 hrs and y = 20 hrs, you can apply the formula:
Average speed = (total distance)/(total travel time)
= 100/(10 hrs + 20 hrs)
= 100/30

Then, when you check each answer choice, you'll find that B yields an OUTPUT of 100/30 when x = 10 and y = 20

Does that help?

Cheers,
Brent

https://gmatclub.com/forum/last-sunday-a-certain-store-sold-copies-of-newspaper-a-for-101739.html
This question is very confusing.
I got these two equations:
(100)(1a)/(1a + 1.25b) = r
(100)(a)/(a+b) = p


gmat-admin's picture

You're on the right track. The only problem is that, from this point, the algebra is a total pain.

Hint: Solve either equation for a or b so you can plug that expression into the other equation (and eliminate one of those variables)

That said, you might already recognize that the algebraic approach is probably slower than the INPUT-OUTPUT approach. So, if ti encountered this question on test day, you should consider changing strategies at this point.

If you get stuck, see Bunuel's calculations here: https://gmatclub.com/forum/last-sunday-a-certain-store-sold-copies-of-ne...

https://gmatclub.com/forum/last-sunday-a-certain-store-sold-copies-of-newspaper-a-for-101739.html

For the following your solutions usings the picking # approach, but from an algebra standpoint could you advise?. The following post by user 'brainlab' ............A..... B
Price:.... 1.... 1,25
Amount:. P.... 100-P
------------------------------
Revenue: P+1,25*(100-p) ---> P + 125 - 1,25P= 125 - 0,25P

---> Revenue of A / Total Revenue: P / 125 - 0,25P = P/ ((500-p)/4)) = 4P/500-P
---> r/100 = 4P/500-P --> r = 400P / 500-P ...................Correct Answer is (D)

seems logical, however how do you know to solve for rev A/Total revenue?
gmat-admin's picture

Question link: https://gmatclub.com/forum/last-sunday-a-certain-store-sold-copies-of-ne...

We know that the revenue from Newspaper A = p dollars (if we say 100 papers were sold that day)
We also know that the TOTAL revenue = 125 - 0.25p
We also know that r percent of the store’s revenues from newspaper sales was from Newspaper A

In other words: (revenue from Newspaper A)/(TOTAL revenue) = r%
Rewrite as: (revenue from Newspaper A)/(TOTAL revenue) = r/100

Substitute values to get: p/(125 - 0.25p) = r/100
Then solve for r

Does that help?

Cheers,
Brent

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