An inventory of a neighborhood's trees found that 32 percent were

Question

An inventory of a neighborhood's trees found that 32 percent were conifers and most of the rest were deciduous. Among the conifers were 258 spruces and 112 pines, along with some cedars and other species. Most of the deciduous trees were oaks, but one in eight was a maple. Of the oaks, 65 percent were red oaks and 25 percent were white oaks. Of the maples, 20 percent were Japanese maples.

Select for  A  and for  B  two types of trees such that the ratio of the number of trees of the type selected for  A  to the number of trees of the type selected for  B  can be determined and is less than 1. Make only two selections, one in each column.

egmat · Accepted Answer

This is a question that has layers of complexity as listed below:
 
 Sheer volume of information in the dataset that needs to be translated and visualized as a tree diagram with 4 layers of branches. 
 Imprecise information about the quantity of the nodes. For some nodes, exact number is given, for some ratios are given, for some range is given. 
 The question statement is not a straight forward one and hence needs translation to understand what is being asked. 
 The processing of the choices utilizing the tree structure that is created requires skilled processing.

All in all, an amazing question that highlights the importance of ‘owning the dataset’, processing the information as we are reading by drawing inferences. It also showcases how with solid understanding of the dataset one can comfortably answer the question that is asked.

https://www.youtube.com/watch?v=5RmOYGVfzoc

Tell me which layer(s) of complexity made this question difficult for you.
Happy learning!
Payal

KarishmaB · Answer

Make a tree diagram of the trees to understand the relations. 
To know the relation between the number of two types of trees, either both should be exact numbers available to us such as Spruces and Pines or their number should be in terms of the same variable such as Red Oaks (65% of Oaks) and White Oaks (25% of Oaks).

Of the given options, number of cedars is unknown so ignore. Ignore Coniferous and Deciduous for the time being because they will likely be the denominator in the ratio (since ratio is less than 1). Let's look for the smaller numerator first.

Japanese maples are 20% of 1/8th of Deciduous.

Japanese = \frac{1}{40} * Deciduous

\frac{Japanese}{Deciduous} = \frac{1}{40}   ANSWER

This ratio we have.

chetan2u · Answer

Again a great question. can be done in exactly 30 seconds if understood well.

The question wants us to find a ratio that is determinable, so let us see each statement. Working on options directly would be a faster way.

An inventory of a neighborhood's trees found that 32 percent were conifers and most of the rest were deciduous.  
We can just say that deciduous are anything greater than (100-32)/2 or >34 and  \leq 100-32 
Thus, no ratios can be found between conifers or its subpart and deciduous or its parts.

Among the conifers were 258 spruces and 112 pines, along with some cedars and other species.  
We can find ratio  between spruces and pines  but nothing with total conifers or any other of its subparts.

Most of the deciduous trees were oaks, but one in eight was a maple.  
Again use of 'most' restricts anyratio between deciduous and oaks or its sub parts. However ratio  between deciduous and maple  is given as 8:1.

Of the oaks, 65 percent were red oaks and 25 percent were white oaks. Of the maples, 20 percent were Japanese maples. 
Ratio  between Red oaks and white oaks  is given but this cannot be connected to any other parts.
Also,  Ratio between Japenese maples and total maples  is given as 1:5

The ratios known are given in bold above
between spruces and pines.......   Spruce is given in option but pine is not. 
between deciduous and maple......   Deciduous is given but maple is not 
between Red oaks and white oaks.....  Red Oaks is given but White oaks is not given in the option 
between Japenese maples and total maples.......  Japenese maples is given but total maples is not given in the option

However, deciduous is related to maples, which is further related to japenese maples.
D:M = 8:1 and J:M = 1:5
D:M = 8:1 = 40:5 and J:M = 1:5. Hence D:M:J = 40:5:1 or  D:J = 40:1

Elite097 · Answer

chetan2u  why cant it be japanese/conifers?

chetan2u · Answer

Japanese maples were 20% of maples, which were 1/8 of oaks, so Japanese maples = 1/5 * 1/8 * x, where x is number of deciduous trees. 
Next conifer are 32% of total, so t* 32/100

But do we have a relation between t and x? 
No, had the trees been only deciduous and conifers, then x would be t*68/100, and we would get a relation between Japanese maples and conifers. But most of the rest are deciduous does not give the exact percentage of deciduous. 40% or 50% or 60% would give different answers every time.

qingyuuu · Answer

Why can't we choose A: Cedar & B:Conifer? The number of Cedar is less than Conifer.

KarishmaB · Answer

Question stem: Select for A and for B two types of trees such that the ratio of the number of trees of the type selected for A to the number of trees of the type selected for B  can be determined  and is less than 1

We need to be able to "determine" the ratio which means we need its exact value. We don't know how many cedars there are. The ratio will be less than 1 but what will it be exactly, we cannot say.

We can only determine the ratio of Japanese maples to Deciduous trees in the given options.

johnpepe · Answer

Why cant I choose A: japanese maple B: Red oaks? Since the ratio of oak and maple was known,red oaks contain 65% of total oak. Please tell me why I am wrong, thank.

chetan2u · Answer

Red oaks are related numerically to Oaks, but oaks is not linked to Deciduous. We just know most deciduous are oaks, but numerically or a ratio..NO.
Further, JM is linked to maples , which is further linked to deciduous.

But, Oaks and Maples are not linked anywhere. The ration between JM and RO may be less than 1, but the exact ratio cannot be determined.

Gemmie · Answer

32%: Conifers   
   258 Spruces
   112 Pines
   Cedars
   Others species

Most of the rest: Decidious
   Most: Oaks       
        65%: Red
        25%: White
   1/8: Maples
        20%: Japanese

==> We only know the ratio of Japanese maples to Decidious trees

Ratio = 20% *   \frac{1}{8}    < 1

DonBosco7 · Answer

Conifers = 32% of ALL TREES = 258 spruce + 112 pines + some cedars & others
Deciduous = 68% of ALL TRESS
Oaks > 50% of Deciduous (i.e. 50% of 68% of ALL TREES)
Maple = 1/8 of Deciduous = 12.5% of Deciduous = 12.5% of 68% of ALL TREES
Red Oaks = 65% of oaks
White Oaks = 25% of oaks
Japanese Maples = 20% of Maples = 20% of 12.5% of 68% of ALL TRESS

From the above data if we take some numerical figure for ALL TRESS we can say confidently that we can determine A & B and A < B only for  Deciduous trees and Japanese Maple , because all the others are unknown quantity and cannot be determined.

A = Japanese Maple
B = Deciduous trees

anushkatew · Answer

why can't we choose a) conifers and b) deciduous ??

cheshire · Answer

Because we do not know the exact number of deciduous and cannot create a ratio.

UditA1 · Answer

Let Total Trees = 100x 
 
 Conifers = 32x
 → Spruces = 258
 → Pines = 112
 → Cedars = p (unknown)
 → Others = q (unknown) 
 Rest of trees = 68x
→ Deciduous trees = y
→ Others = 68x-y

For Deciduous trees = y :-   
 • Oaks = 100z (unknown)
 → Red Oaks = 65% of Oaks = 65z
 → White Oaks = 25% of Oaks = 25z
 → Others = 10% of Oaks = 10z
 • Maples = y/8
 → Japanese Maples = 20% of Maples (1/5)= y/40

We have to choose A&B in such a way that A/B <1
Options :- 
Cedar : p
Confiners : 32x
Deciduous : y
Japanese Maples : y/40
Red Oaks : 65z
Spruces : 258

Only Possible options: y and y/40, so A= y/40 (smaller quantity), B = y. A/B = 1/40. 
A = Japanese Maples, B = Deciduous.

Rickooreoisb · Answer

I am confused about why Japanese maples cannot be compared with conifers in this question.

From the chart, conifers are 32% of all trees, so the remaining 68% are non-conifers. Since most non-conifers are deciduous in the diagram, I treated the 68% as the largest possible pool from which maples could come.

Since Japanese maples are 8.5% of all maples (1/8 of decidious), even if I assume the entire 1/8 * 68% consists of maples, Japanese maples would be at most 25% *1/8 × 68% ≈ 1.8%, which is still much smaller than conifers (32%).

My intuition is: by taking the largest possible denominator, I am maximizing Japanese maples, so if even then they are smaller than conifers, they should always be smaller.

Can someone explain why this “maximum base” reasoning is invalid here?

guddo · Answer

I think your question was replied  here , at least partially. Also, I'd say that you treated “most of the rest were deciduous” as “all of the rest were deciduous.” Not sure, that this is allowed.

We do know conifers are exactly 32 percent, but we do not know deciduous is exactly 68 percent, so we cannot determine how many maples or Japanese maples there are. Therefore Japanese maples/conifers is not a determinable ratio, even though it is definitely less than 1.

Puranjaysapra · Answer

Why not spruces and confers?

guddo · Answer

Because you do not know the total number of conifers.

You only know that spruces = 258 and pines = 112, plus “some cedars and other species.” That means total conifers = 258 + 112 + (cedars and others), but that extra part is unknown. So 258 divided by (total conifers) cannot be determined.

Puranjaysapra · Answer

Thanks for responding. If I was to use the same logic, I also don't know the exact % of D trees as it says most of it implying that it could be anything less than 68%. I can determine that conifers will be more than spruces

An inventory of a neighborhood's trees found that 32 percent were

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A	B
		Cedars
		Conifers
		Deciduous trees
		Japanese maples
		Red oaks
		Spruces

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An inventory of a neighborhood's trees found that 32 percent were

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