Critical Reasoning

Many gardeners believe that the variety of clematis vine that is most popular among gardeners in North America is jackmanii. This belief is apparently correct since, of the one million clematis plants sold per year by the largest clematis nursery in North America, ten percent are jackmanii.

Which of the following is an assumption on which the argument depends?

a.The nursery sells more than 10 different varieties of clematis
b.the largest clematis nursery in North America sells nothing but clematis plants
c.some of the jackmanii sold by the nursery are sold to gardeners outside North America
d.most North American gardeners grow clematis in their gardens
e.For all nurseries in North America that specialize in clematis, at least 10% of the clematis plants they sell are jackmanii.

OA:A

For this question, I believe the best way is to use the negation technique. After applying this technique, I found that OA is not airtight, yet I understand that the OA must be correct, then it must be me falling into some logical fallacy.

If we negate the first answer choice,it will become "the nursery sells 10 or less varieties of clematis". Now let's suppose the nursery sells ten varieties of that including jackmanii, each type contributes to 10%, the argument still holds water as jackmanii would still be the best-selling clematis.

Can anyone explain this to me? I would really appreciate it.

allenh wrote:Many gardeners believe that the variety of clematis vine that is most popular among gardeners in North America is jackmanii. This belief is apparently correct since, of the one million clematis plants sold per year by the largest clematis nursery in North America, ten percent are jackmanii.

Which of the following is an assumption on which the argument depends?

a.The nursery sells more than 10 different varieties of clematis
b.the largest clematis nursery in North America sells nothing but clematis plants
c.some of the jackmanii sold by the nursery are sold to gardeners outside North America
d.most North American gardeners grow clematis in their gardens
e.For all nurseries in North America that specialize in clematis, at least 10% of the clematis plants they sell are jackmanii.

Premise: Of the one million clematis plants sold per year by the largest clematis nursery in North America, ten percent are jackmanii.
Conclusion: The variety of clematis vine that is most popular among gardeners in North America is jackmanii.

Assumption: The 10% of sales attributed to jackmanjii is the HIGHEST percentage attributed to any variety of clematis.

Answer choice A, negated:
The nursery does not sell more than 10 different varieties of clematis.
Let the total number of varieties = 10.
Let the 10 varieties be A, B, C, D, E, F, G, H, I and J.
Since J=10%, the remaining 90% of sales must be distributed among A, B, C, D, E, F, G, H and I.

Case 1: A=10%, B=10%, C=10%, D=10%, E=10%, F=10%, G=10%, H=10%, I=10%.
Here, each variety accounts for 10% of sales.

Case 2: A=11%, B=9%, C=10%, D=10%, E=10%, F=10%, G=10%, H=10%, I=10%.
Here, A accounts for a HIGHER percentage of sales (11%) than does J (10%).

As Cases 1 and 2 illustrate, it is not possible for J to account for the highest percentage of sales if the nursery sells 10 different varieties of clematis.
Since the negation of A invalidates the conclusion that J is the most popular variety of clematis, A is the assumption: WHAT MUST BE TRUE for the conclusion to be valid.

The correct answer is A.

For Option A nursery sells more than 10 different types
Case 1- each may be less than 10% and has more than 10 different types of clematis.
Case 2- It can be possible that 1 is 20% & rest comprises of 80 % . lets 1 clemati gives 20 % & rest 16 gives 5% each.



I think E is also good candidate of answer.
atleast 10% of plants at jacmannies.

Hello Mitch,


I still could not understand how it would be A.

According to your thoughts:-If there are lets say 11 Varieties(going without negating the statement) then too one of the variety could sell more than Jackmanii. For e.g.)
Let the 11 varieties be A-5%, B-5%, C-10%, D-10%, E-10%, F-10%, G-10%, H-10%, I-9% , J(Jackmanii)-10% and K-11%.

May be I am not understanding your analogy.


Secondly , I thought that the 10% sales from one of the Nurseries represents the complete Sale in North America and this assumption predicted was present in E(Since if it the sales from one nursery do not represent the complete picture then why would the author make such a statement)

. Need some help from your end.


Thanks in Advance.

GMATGuruNY wrote:

allenh wrote:Many gardeners believe that the variety of clematis vine that is most popular among gardeners in North America is jackmanii. This belief is apparently correct since, of the one million clematis plants sold per year by the largest clematis nursery in North America, ten percent are jackmanii.

Which of the following is an assumption on which the argument depends?

a.The nursery sells more than 10 different varieties of clematis
b.the largest clematis nursery in North America sells nothing but clematis plants
c.some of the jackmanii sold by the nursery are sold to gardeners outside North America
d.most North American gardeners grow clematis in their gardens
e.For all nurseries in North America that specialize in clematis, at least 10% of the clematis plants they sell are jackmanii.

Premise: Of the one million clematis plants sold per year by the largest clematis nursery in North America, ten percent are jackmanii.
Conclusion: The variety of clematis vine that is most popular among gardeners in North America is jackmanii.

Assumption: The 10% of sales attributed to jackmanjii is the HIGHEST percentage attributed to any variety of clematis.

Answer choice A, negated:
The nursery does not sell more than 10 different varieties of clematis.
Let the total number of varieties = 10.
Let the 10 varieties be A, B, C, D, E, F, G, H, I and J.
Since J=10%, the remaining 90% of sales must be distributed among A, B, C, D, E, F, G, H and I.

Case 1: A=10%, B=10%, C=10%, D=10%, E=10%, F=10%, G=10%, H=10%, I=10%.
Here, each variety accounts for 10% of sales.

Case 2: A=11%, B=9%, C=10%, D=10%, E=10%, F=10%, G=10%, H=10%, I=10%.
Here, A accounts for a HIGHER percentage of sales (11%) than does J (10%).

As Cases 1 and 2 illustrate, it is not possible for J to account for the highest percentage of sales if the nursery sells 10 different varieties of clematis.
Since the negation of A invalidates the conclusion that J is the most popular variety of clematis, A is the assumption: WHAT MUST BE TRUE for the conclusion to be valid.

The correct answer is A.

Neilsheth2 wrote: I still could not understand how it would be A.

According to your thoughts:-If there are lets say 11 Varieties(going without negating the statement) then too one of the variety could sell more than Jackmanii. For e.g.)
Let the 11 varieties be A-5%, B-5%, C-10%, D-10%, E-10%, F-10%, G-10%, H-10%, I-9% , J(Jackmanii)-10% and K-11%.

May be I am not understanding your analogy.

You are attempting to use the assumption to PROVE the conclusion.
But an assumption is not proof.
An assumption is a PREREQUISITE: something that MUST BE TRUE for the conclusion to be valid.

Here, if not more than 10 varieties of clematis are sold, then it is not possible for jackmanii to account for the greatest percentage of sales.
Consider an extreme case:
If only two varietes of clematis are sold -- A and J -- then J accounts for 10%, while A accounts for the remaining 90%, with the result that jackmanii does NOT account for the greatest percentage of sales.

As shown in my post above, for jackmanii to account for the greatest percentage of sales, IT MUST BE TRUE that more than 10 varieties of clematis are sold.
Hence, A is the correct assumption: WHAT MUST BE TRUE for the conclusion to be valid.

Secondly , I thought that the 10% sales from one of the Nurseries represents the complete Sale in North America and this assumption predicted was present in E(Since if it the sales from one nursery do not represent the complete picture then why would the author make such a statement)

. Need some help from your end.

E: For all nurseries in North America that specialize in clematis, at least 10% of the clematis plants they sell are jackmanii.
Beware extreme language.
If jackmanii account for 10% of sales at 10,000 nurseries but for only 9% of sales at 1 nursery, then the conclusion that jackmanii is the most popular variety of clematis could still be valid.
Since it does not have to be true that the 10% figure holds true for ALL nurseries, eliminate E.

Jacckmanii has 10% so the rest have to equal 90%. If JackManii's share of sales is the greatest, then the share of all other varieties has to be less than 10%. The share of all other varieties willl not equal 90% unless there are at least 10 other varieties. Therefore the share of Jackmanii can be the greatest at 10% ONLY and ONLY if there are at least 10 other varieties. hence the answer is A

Hi Verbal Experts(Dave/Mitch/Ceilidh/others),
Could you please let me know whether the followings would be correct ASSUMPTIONS for this CR -

1. There is a LINK between POPULARITY and SALES. Highest (volume of) sales implies MOST POPULAR variant.

2. 10% should be the HIGHEST amount of clematis variant (jackmanii) sold by the largest clematis nursery.

3. NO other type of clematis is sold @ >=10% by MOST of the clematis nursery in North America.

Am I correct ?

P.S: Also, could there be any other possible ASSUMPTIONS that are IMPORTANT to take note of ?

ceilidh.erickson wrote:

3. NO other type of clematis is sold @ >=10% by MOST of the clematis nursery in North America.

Hm, I'm not sure that this strictly has to be true. We could imagine some number of tiny little shops that happen to sell more of something else, without disrupting the balance of total sold. I would put it this way:

ceilidh.erickson wrote:3. The proportion of clemantis plants sold at the largest nursery is an accurate representation of the aggregate popularity & sales in all of North America.

Absolutely, I agree with your second quote.

However, I guess, what you mentioned in the above FIRST quote is quite similar to what I had mentioned in my adjacent quote through the phrase "by MOST of the clematis nursery in North America" -- doesn't this PHRASE imply that some number of tiny little shops can sell more of something else ?

Quick thoughts please ?