An arboretum wishes to plant three new groves of four trees each. Each

Question

An arboretum wishes to plant three new groves of four trees each. Each grove is to contain two different conifers and two different flowering trees. At least one grove must contain both a hemlock and a crabapple. No two groves may contain more than one of the same type of tree, and no one type of tree may be planted in all three groves. Three trees in each grove have already been chosen:

Grove 1 
 
 hemlock (conifer) 
 spruce (conifer) 
 magnolia (flowering)

Grove 2 
 
 crabapple (flowering) 
 dogwood (flowering) 
 larch (conifer)

Grove 3 
 
 cherry (flowering) 
 crape myrtle (flowering) 
 hemlock (conifer)

Select a tree that must be added to one of the groves. Then select a tree that cannot be added to any grove. Make only two selections, one for each column.

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=86402 Restrictions: Each grove must have 2 conifers and 2 flowering trees. At least one grove must contain both a hemlock and a crabapple. No two groves may share more than one tree type. No tree type may appear in all three groves. Hemlock already appears in Grove 1 and Grove 3, so adding it to any other grove would make it appear in all three, violating the fourth restriction. Therefore, hemlock cannot be added to any grove. To satisfy the condition that at least one grove must contain both hemlock and crabapple, we must add crabapple to a grove that already has hemlock. Grove 3 cannot take crabapple (flowering) because it already has two flowering trees. Grove 1, however, has hemlock, spruce (conifers), and magnolia (flowering), leaving one flowering slot open. Adding crabapple there gives Grove 1 two conifers and two flowering trees, meeting all conditions. Therefore, crabapple must be added to Grove 1. GMAT-Club-Forum-6c19uw3n.png

GmatTest2026 · Answer

Solution:

As mentioned in the question stem:

1. Plant three new groves of four trees each.

2. Each grove contains two different conifers and two different flowering trees.

3. At least one grove must contain both a hemlock and a crabapple.

4. No two groves may contain more than one of the same type of tree, and no one type of tree may be planted on all three groves.

Based on the given information, the only answer choice that matches a tree that must be added to one of the groves is  Crabapple , and for a tree that cannot be added to any grove is  Hemlock.

SwethaReddyL · Answer

Hi  Bismuth83  could you please share the official explanation for this question? I picked b and c and the answer is c and b. Would really love to know the explanation

BongBideshini · Answer

An arboretum wishes to plant three new groves of four trees each. Each grove is to contain two different conifers and two different flowering trees. At least one grove must contain both a hemlock and a crabapple. No two groves may contain more than one of the same type of tree, and no one type of tree may be planted in all three groves.

Cannot be added     to any grove:    Only hemlock is present in two out of three groves. Because "each grove is to contain two different conifers", hemlock can not be added in Grove 1 and Grove 3. 
 And, because " no one type of tree may be planted in all three groves", we can not have "hemlock" in all three Groves. So, "hemlock" can not be added in Grove 2.

Must be added to one of the groves: " At least one grove must contain both a hemlock and a crabapple."    From the previous discussion, we know that we can not add Hemlock in Grove 2. To fulfill the quoted statement, we must also add Crabapple in Grove 1.

SwethaReddyL · Answer

Hi  bb , can you please explain this question

cheshire · Answer

Each grove: 4 trees → 2 conifers + 2 flowering 
 At least one grove must have both hemlock (conifer) and crabapple (flowering) together. 
 No grove can have more than one of the same tree. 
 No tree can appear in all three groves.  
Current groves:
   Grove 1 
 Grove 2 
 Grove 3 
 
  Hemlock (C) 
 Crabapple (F) 
 Cherry (F) 
 
  Spruce (C) 
 Dogwood (F) 
 Crape Myrtle (F) 
 
  Magnolia (F) 
 Larch (C) 
 Hemlock (C) 
 
   ? + ?  
  ? + ?  
  ? + ?

Each grove still needs one conifer and one flowering.

2.  Why Crabapple must be used 
 
 Only Grove 2 already has Crabapple. A second grove would need it if we’re to satisfy “ some  grove has both Hemlock & Crabapple.” 
 Hemlock currently appears in Grove 1 and Grove 3. The only way to get Hemlock + Crabapple together in a single grove is to put Crabapple into Grove 1 or Grove 3 (since those are the only groves with Hemlock). 
 You can’t move Hemlock (it’s already planted), so the only way to pair it with Crabapple is to plant Crabapple again. 
 Therefore, Crabapple must be added to one of Grove 1 or Grove 3.  
3.  Why Hemlock cannot be used at all 
 
 Hemlock is already in two groves (1 and 3). 
 Planting a third Hemlock would violate “no tree may be planted in all three groves.” 
 Thus, Hemlock is now “off the table” for any new planting.  
4.  C  hecking the other options 
 
 Could we instead satisfy the Hemlock + Crabapple requirement by adding Hemlock to Grove 2?
 
 No, Grove 2 already has Larch (C); and that would be a second conifer, allowed only if we remove Larch, which we can’t.

Other flowering tree? Doesn’t help the “must have Crabapple with Hemlock” rule. 
 Other conifer? Doesn’t affect the critical Hemlock + Crabapple pairing, and you still need to place Crabapple somewhere.

The two forced choices are: 
 
 Must be added → Crabapple 
 Cannot be added → Hemlock

Bismuth83 · Answer

1. Given a selection of trees to plant, we are asked to  find the trees that are must and cannot be added to the groves .

2. Here are the following restrictions:

- Each grove is to contain two different conifers and two different flowering trees. 
 - At least one grove must contain both a hemlock and a crabapple. 
 - No two groves may contain more than one of the same type of tree.
 - No one type of tree may be planted in all three groves.

3. Second, let's review each of the groves in a step by step basis.

4. Grove 1: Rule 1 tells us that the fourth tree must be a different flowering tree, and only the Crabapple works, which means it must be planted there.

5. Grove 2: Rule 1 says that the fourth tree is a different conifer, Rule 2 is already satisfied by grove 1, Rule 3 tell us that it can't be a Hemlock (if we were to compare groves 1 and 2), and Rule 4 says that a Spruce possibly won't work (depends on if it's planted in grove 3).

6. Grove 3: Rule 1 says that the fourth tree is a different conifer and this restricts it from being a Hemlock, Rule 2 is already satisfied by grove 1, Rule 3 tell us that it can't be a Spruce (if we were to compare groves 1 and 3), and Rule 4 doesn't restrict us.

7. To sum up the restrictions on the trees, Crabapple must be planted in grove 1 and Hemlock can't be in any grove. The rest are either not in the options or can be placed anywhere in groves 2 and 3.

8. Our answer will be:   Must be added to one of the groves - Crabapple (flowering) and Cannot be added to any grove - Hemlock (conifer)  .

svsivakrishna · Answer

Hi,

Given:

Grove 1

hemlock (conifer)  
  spruce (conifer)  
  magnolia (flowering)

Grove 2

crabapple (flowering)  
  dogwood (flowering)  
  larch (conifer)

Grove 3

cherry (flowering)  
  crape myrtle (flowering)  
  hemlock (conifer)

4 conditions/ restrictions are stated: 
 a) Each grove is to contain two different conifers and two different flowering trees.  
 b) At least one grove must contain both a hemlock and a crabapple.  
 c) No two groves may contain more than one of the same type of tree, and  
 d) no one type of tree may be planted in all three groves.

Must be added/ Cannot be added :  As per condition (b) atleast 1 grove must contain both hemlock and crab apple, but as per the given data , either hemlock can be added to grove 2 or crab apple can be added to grove 1 or 3, but if hemlock is added to grove 3, all 3 groves will contain hemlock which contradicts condition 4.  
 Further if crab apple is added to grove 1 or 3, it satisfies conditions (a) and (c) also.

Therefore crab apple must be added and hemlock cannot be added.

Robo_123 · Answer

This took me a lot of time. How should I go about it to do it faster?

hr1212 · Answer

One way here is to jot down the details quickly and then work around the conditions -

Grove 1

hemlock (conifer)  
  spruce (conifer)  
  magnolia (flowering)

Grove 2

crabapple (flowering)  
  dogwood (flowering)  
  larch (conifer)

Grove 3

cherry (flowering)  
  crape myrtle (flowering)  
  hemlock (conifer)

Conditions => 
 
  Each grove is to contain two different conifers and two different flowering trees.   
  At least one grove must contain both a hemlock and a crabapple.   
  No two groves may contain more than one of the same type of tree, and no one type of tree may be planted in all three groves.

Question:

Must be added to one of the groves?   - Go through the conditions which will allow you to get to this answer quickly (Doesn't condition 2 seem a bit unique?). Do you see any grove containing hemlock and crabapple? So the answer to this question should be "Crabapple"

Cannot be added to any grove?   - Skim through grove data... Did you observe anything? Hemlock is already being used by Grove 1 and Grove 3. Now let's go back to the conditions, "no one type of tree may be planted in all three groves" (condition 3). So "Hemlock" cannot be used in Grove 2 for sure and the other two already have it.

Idea here is to get to the answers without trying out all combinations and instead focusing on the data given and how you can leverage the conditions to your advantage without getting lost in the data.

mkeshri185 · Answer

Well i have one doubt. It says 'No two groves may contain more than one of the same type of trees' so according to this if we place 'crabapple' in G1 then G1 and G2 will contain 2 crabapple which is not allowed. If we add crabapple in G2 then it will have 3 flowering which is also not allowed. If we place crabapple in G3 then G2 and G3 will contain more then 1 crabapple. then how can crabapple be placed in any one?

Bunuel · Answer

That rule doesn’t mean the same tree type can appear only once overall. It means that if you compare any  two  groves, they can share  only one  tree type in common.

So if you add crabapple to Grove 1:

Grove 1 and Grove 2 would share  only crabapple  (one common tree). 
 Grove 1 and Grove 3 would share  only hemlock  (one common tree).

No pair shares more than one tree type, so the rule is not violated. That’s why adding crabapple to Grove 1 is valid.

Check complete solution  HERE .

An arboretum wishes to plant three new groves of four trees each. Each

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

Must be added to one of the groves	Cannot be added to any grove
		Cedar (conifer)
		Hemlock (conifer)
		Crabapple (flowering)
		Cypress (conifer)
		Fir (conifer)
		Pine (conifer)

Grove 1	Grove 2	Grove 3
Hemlock (C)	Crabapple (F)	Cherry (F)
Spruce (C)	Dogwood (F)	Crape Myrtle (F)
Magnolia (F)	Larch (C)	Hemlock (C)
? + ?	? + ?	? + ?

GMAT Two-part Analysis (TPA) Questions

An arboretum wishes to plant three new groves of four trees each. Each

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