Julian bought 6 kilograms of cheese from each of Deli A and Deli B. At

This is an interesting question. It's a min/max question disguised as a ratio question (you still need both though!) At first I did the brute force method by figuring out the ratios bought of each etc ... but took too long. So I redid the question using 2 methods: 1) Educated Guessing (about 1 min) and 2) Easier Brute Force (about 2:15). So let's get started.

1) Educated Guessing
The idea here is to look at the product that is most bought and compare to the range of the other Deli
S1) Provolone was the largest quantity purchased at B: 7 * $18 = $126
The range at A will be [7 * $15 = $105, 7 * $19 = $133]
Since $126 falls between this, it might be possible for A to be greater than B

S2) American was the largest quantity purchased at A: 6 * $15 = $90
The range at B will be [6 * $16 = $96, 6 * $20 = $120]
Since $90 is less than $96, B will always be greater than A

2) Easier Brute Force
The idea here is to ignore the 6 kg and use the ratios given. The reason for this is because the 6 will complicate the calculations.
S1) The total bought is 2+7+2 = 11. So instead of buying 6kg, let's say he bought 11kg.
2*$16 + 7*$18 + 2*$20 = $32 + $126 + $40 = $198
Now the range can be calculated by using 11kg at Deli A: [11 * $15 = $165, 11 * $19 = $209]
Since $198 falls between this, we cannot conclude where more was spent.

S2) The total bought is 6+2+1 = 9. So instead of buying 6kg, let's say he bought 9kg.
6*$15 + 2*$17 + 1*$19 = $90+ $34 + $19 = $143
Now the range can be calculated by using 11kg at Deli A: [9 * $16 = $144, 9 * $20 = $180]
Since $143 is less than the minimum ($144), that means less was spent at A than B.



Let me know if there is something wrong with my logic.

Thanks,
sunz3000

I would go with C as
Stmt 1: we can find out how much he spent at Deli B but we have no idea about the spending distribution at Deli A....so insufficient

Stmt 2: we can find out how much he spent at Deli A but we have no idea about the spending distribution at Deli B....so insufficient

Stmt 1 + Stmt 2 : sufficient

Statement 1 : 6kg paneer from deliB in 2:7;2 ration will cost = (2x16 +7x18 +20x2)6/11= 108
From Deli A minimum cost for 6kg shall be 15x6=90 and maximum shall be 19X6=114 for any ratio from deli A cost vary from 90 to 108 hence without knowing ration for Deli A can not determine spend , hence unsufficient
Statement 2: 6kg paneer from deliB in 6:2;1 ration will cost = (6x15 +17x2 +19x1)6/9= 95.3 around
From Deli B minimum cost for 6kg shall be 16x6=96 and maximum shall be 20X6=120 for any ratio from deli A cost vary from 96 to 120 ,minimum cost from deli B is more than the 95.3 hence money spend from deliB shall be more ,hence sufficient
correct Ans is B

I agree. I don't think you have to even bother solving. the question stem tells us he bought 6 kg of 3 different cheeses at different prices in each store. we just need to know the amount of each type of cheese from each store. I & II together gives us that info.

if you wanted to work it out you would start by:

I: 6 kg divided amoung 11 parts

american is 2/11*6kg = 1 1/11kg of american * $16

etc.. etc..

but going through all of that would waste you at least a minute and a half if not more..you have the information to answer that he either spent more money at A, more money at B, or the same amount at both deli's... the answer itself is irrelevant.

hope that helps

anonymousegmat, hello

I disagree with you about the need to solve the question - let's assume that you did solve, and found out that in deli A he spend 102 dollar on six kilo of cheese.

Now let's assume that deli B has the following cheese prices:

American - 18
Provolone - 19
Swiss - 20

Julian bought 6 kilo from deli B - so the least he could buy from deli B is 6*18 = 108

That implies the answer is (A) and not (C). doesn't it ?

Yeah, this is right. It's B, not C. It's also not so hard because the ratios in statement 2 are all out of 9, and we're multiplying by 6 pounds, so everything cancels nicely. At that ratio, there's no way to spend as much as if he just purchased 6 pounds of $16 cheese at deli B.

Have you noticed that all the prices at Deli A are lower than the corresponding prices at Deli B and (2) says a lot of the 15 dollar cheese is being bought?

great question !!! certainly 750+ level.

What if he buys 5989 grams at deli A with ratio 6-2-1 and 11 grams at deli B with ratio 2-7-2?

In this case he would spend slightly more at deli A.

I don't think it's forbidden to buy fractional amounts as the question is worded. L

In my opinion the right answer is E.

Posted from my mobile device

You can check the correct answer under the spoiler in the original post and it's B, not E.

Regarding your doubt: you misinterpreted the question. The question says that Julian bought 6 kilograms of cheese from each of Deli A and Deli B, not that he bough total of 6 kilograms in A and B.

Hope it helps.

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