Doctors have advised Rita, a chocolate freak, not to consume more than

Question

Doctors have advised Rita, a chocolate freak, not to consume more than 20 chocolates in one day. When she went to the market to buy her daily quota, she found that if she were to buy chocolates from the market-complex, she would have to pay $3 more for the same number of chocolates than she would have spent had she bought them from her uncle Scrooge’s shop, getting two chocolates fewer per dollar at the market complex than at uncle Scrooge’s shop. She finally decided to get them from uncle Scrooge’s shop paying only in one-dollar bills.

Choose for 1 the number of chocolates Rita bought and for 2 the amount she would have paid if she had purchased the chocolates from the market complex. Make only two selections, one in each column.

Choose for 1 the number of chocolates Rita bought and for 2 the amount she would have paid if she had purchased the chocolates from the market complex. Make only two selections, one in each column.

callingTardis · Answer

Let n be the number of chocolates bought.
Let c be number of chocolates per dollar at uncle's.
Let u be number of dollars paid at uncle's.

number of chocolates per dollar * number of dollars paid = number of chocolates bought
for uncle: c*u = n
for market, c-2 * u+3 = n

Try values for n, maybe start with larger values like 18,15,12 etc 
12 seems most diverse in the sense that it may contain divisors within a difference of +-3 or +-2

12 = 4*3 = 2*6 is consistent!
hence, n = 12 and u+3 = 6 works!

Bismuth83 · Answer

1. Let's look at the deals at both shops:

- Scrooge's shop: for  c  dollars you can buy  n  chocolates (quota).
 - Market-complex: for  c+3  dollars you can buy  n  chocolates (quota).

2. The number of chocolates, n, has to be a whole number. Since Rita bought the chocolates using one-dollar bills, then c and c+3 must be whole numbers too.

3. The market-complex has a deal that gives 2 chocolates fewer per dollar compared to Scrooge's shop. So,  \frac{n}{c} - \frac{n}{c + 3} = 2 .

4.  \frac{n}{c} - \frac{n}{c + 3} = 2 = n(\frac{3}{c(c + 3)}) \rightarrow n = \frac{2}{3} * c(c + 3) . Since n is whole, the right hand side must be whole too and that means c(c + 3) is divisible by 3. This is only possible if c is divisible by 3.

5. Now let's look at some possible cases:

- c = 3.  n = \frac{2}{3} * 3 * (3 + 3) = 12 . This works.
 - c = 6.  n = \frac{2}{3} * 6 * (6 + 3) = 36 . n must be no more than 20.
 - Larger c will also not work since n will then be larger than 20.

6. The deals will now look like:

- Scrooge's shop: for 3 dollars you can buy 12 chocolates.
 - Market-complex: for 6 dollars you can buy 12 chocolates.

7. That means Rita bought 12 chocolates and would've payed 6 dollars at the market-complex.

8. Our answer will be:   1 - 12 and 2 - 6  .

Rickooreoisb · Answer

Bunuel  - what is the question type, can this form part of Data Insight ? or this is Integrated reasoning and need not be looked into

Carcass · Answer

The former Integrated reasoning then changed into Data Insight. Essentially they are the same. Your question is trivial

DishaAgarwal12 · Answer

I did hit and trial

I assumed that in uncle's store you can buy 4 chocolates for 1 dollar, therefore in 3 dollars you can get 12. While at market complex for 3 dollar you will get 6. To get 12 chocolates you will have to spend 6 dollars.

Is this a good enough method?

Bunuel · Answer

Not really, because you assumed “4 chocolates per dollar” without justification. Your specific trial picked a rate (4 per dollar) that happens to fit the final answer, but it is not guaranteed by the prompt, so it is not a sound method by itself.

crimson_noise · Answer

IMG_0166.jpeg I solved with quadratic

Doctors have advised Rita, a chocolate freak, not to consume more than

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Two-part Analysis (TPA) Questions

Doctors have advised Rita, a chocolate freak, not to consume more than

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards