Five coffee-chicory blends - J, K, L, M, and N - are all priced

Question

Five coffee–chicory blends—J, K, L, M, and N—are all priced differently. The blends are such that the greater the proportion of coffee, the more expensive the blend—and the greater the proportion of chicory, the stronger the flavor of the blend. If the five blends were ranked in order of cost per kilogram, which would fall in the middle?

(1) Blend L has a higher proportion of coffee than the other blends except for Blend M.

(2) Blend K and Blend N both have a stronger flavor than Blend J.

(1) Blend L has a higher proportion of coffee than the other blends except for Blend M.

(2) Blend K and Blend N both have a stronger flavor than Blend J.

MT1302 · Accepted Answer

The key thing which you have to look for in this question is how Gmat is using  Hyphen(-)  and  Dash(--)  to signify something.

Five coffee–chicory blends—J, K, L, M, and N—are all priced differently. 
Between Coffee and Chicory , a  Hyphen  is provided i.e. it is interlinking the 2 words . So, Increase in coffee means Decrease in Chicory or vice versa. This is what this statement is implying.

After Chicory Blends , a  Dash  is provided which is sharing with us information wrt to types of Coffee-Chicory blends.

Statement 1  :  Not Sufficient

Reason :

In terms of Cost : M>L > (Rest of the three) . We don't know the order of other three. So nothing can be said about the middle term.

Statement 2  :  Not Sufficient

Reason : 
 
In terms of Flavour : K & N > J . But we cannot say between K & N which one is first . Also, we have no info wrt to M & L.

Either it can be K>N>J>M>L . So, J is in the middle.

or, it can be M>L>N>K>J . So, N is in the middle .

or, there can be number of ways which you can think of to arrange these types of coffee-chicory blends.

Combining Statement 1 & 2  :  Suffcient

Reason :

M > L in terms of cost.
And the question is informing us Greater the cost, Greater the Coffee proportion.
So, it means Chicory concentration is least in M and second least in L.

K & N > J in terms of Flavour. And the question is informing us Greater the chicory concentration, stronger is the flavour. 
So it means, K & N have more chicory than J and as they have more chicory, it implies there coffee concentration is less. Therefore , there cost will be less than J.

Hence, if you rank them as per  cost  : M>L>J>(K or N). So, no matter which order you put for K or N,   J will always be in the middle  .
Hence, By combining , statement is sufficient.

Therefore , Answer is  C .

Hope it helps.

Rebaz · Answer

I didnot know that higher proportion of chicory meant lower proportion of coffee=lower costs.

Maybe this has to do with my knowledge about coffee and i thought this is a DS question, so a iam not allowed to make assumptions.

Apparently it is common knowledge that higher proportion of chicory means lower proportion of coffee, which translates to lower costs. In this case then indeed the correct answer is  C

GMATCoachBen · Answer

Video solution here:

https://www.youtube.com/watch?v=IEEGVyANV5k

ShilpiAgnihotrii · Answer

Hey  Rebaz,  its given in the question statement "greater the proportion of coffee, the more expensive the blend" so it obviously means that higher the chicory lower the cost because the blend has only Coffee + chicory. No assumptions required.

CWC · Answer

It also helped me to think about it outside of coffee... for instance, imagine if the problem was talking about red-white piant blends to make pink paint and it told you that red paint cost more than white. You would be able to infer (without assumption) that the the more of a red hue the pink had, the more that paint would cost to make. Hope this helps. I konw it is frustrating when a question seems difficult due to the conceptual workding and not the "math of it"

egmat · Answer

Here is a  detailed video solution  for this interesting question.
See how this question can be solved in the test environment using " Owning the Dataset " approach.

https://www.youtube.com/watch?v=sR1TyQHHpWs

Let us know if you have any questions.

Gemmie · Answer

Statement (1):

Blend L has a higher proportion of coffee than the other blends except for Blend M.

In terms of proportion of coffee, M > L

==> In terms of price, M > L
==> Do not know about the 3rd position (can be K, N, J)
==> NOT sufficient

Statement (2):

Blend K and Blend N both have a stronger flavor than Blend J.

Since the greater the proportion of chicory, the stronger the flavor, we can infer:

==> Blend J has a lower proportion of chicory than both Blend K and Blend N.
==> Blend J has a higher proportion of coffee​​​​​​ than both Blend K and Blend N
==> In terms of price, J > both K & N.
==> J can be 1st, 2nd or 3rd position
==> NOT sufficient

Combining Statements (1) and (2):  J is the 3rd most expensive
==> Sufficient

GMATBusters · Answer

There is no need to know about coffee to say "  higher proportion of chicory meant a lower proportion of coffee"

Whenever we have a mixture of 2 components, a higher proportion of one means a lower composition of other.

let's the mixture is composed of x and y

proportion of x in the mixture = x/(x+y)

proportion of y in the mixture = y/(x+y)

if x> y , proportion of x is more which is same as proportion of y is less and vice versa

goaltop30mba · Answer

From the question stem, we have below information:

Each of the 5 blends is a combination of Coffee and Chicory. So, what does that mean? It means that some Coffee to Chicory ratio exists, in terms of weight, in each of the 5 blends.

Coffee proportion = k1 * price of the blend

Chicory proportion = k2 * strength of flavor

Now, pause for a moment, and think whether there is something we can infer from all the information given to us in the question stem.

Notice: Greater the strength of flavor, greater the proportion of Chicory in a blend - Greater the proportion of Chicory in a blend, lesser the proportion of Coffee in a blend - Lesser the proportion of coffee in a blend, lesser the price of a blend. So, clearly, there is an inverse logical relationship between the Coffee proportion and strength of flavor and direct logical relationship between Coffee proportion and price.

So, we have "Coffee proportion = K * (1/strength of flavor) * (price)"

OR

Coffee proportion = K * (price/strength of flavor)

Statement 1:

So, we have, as per this statement.

_ < _ <_ < L< M

Notice that we don't have any information on J, K, and N - either of the 3 can be in the middle at the 3rd spot. Hence, statement 1 is not sufficient.

Statement 2:

From the combined logical relationship we have inferred from the question stem, which is "Coffee proportion = K * (price/strength of flavor)", we can clearly see that J is greater in terms of price than both K and N because it is the least in terms of strength of flavor out of J, K and N, which means least Chicory proportion, which means most Coffee proportion out of J, K, and N, which means "most" price when compared to both K and N.

So, one possibility is this: K < N < J < L < M

Another possibility is this : M < L < K < N < J

So, we have one possibility where J is the middle term, and we have another possibility where J is not the middle term or K is the middle term. Also, there are multiple other arrangements possible. Hence, statement 2 is not sufficient as well.

Now, what do we finally have from question stem, statement 1, and statement 2?

"K < N < J < L < M" OR "K < N < J < L < M"

Either way, J will always be the middle term as per all the information we have from question stem, statement 1, and statement 2.

Final answer: C

Five coffee-chicory blends - J, K, L, M, and N - are all priced

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Five coffee-chicory blends - J, K, L, M, and N - are all priced