A wildlife conservation organization is conducting a study on

Question

A wildlife conservation organization is conducting a study on a population of birds. In this study, pairs of birds are tagged and released into designated habitats. Each pair consists of exactly two birds, and no bird is part of more than one pair.   The study begins with 1024 birds being tagged and released into the habitats. After each week, half of the pairs of birds in the habitats remain in the study, while the other half are removed from the habitats and returned to a safe environment.

Select for  Weeks  the number of weeks since the birds were released into the habitats, and select for  Pairs  the number of pairs of birds still in the habitats after that number of weeks that would be jointly consistent with the given information. Make only two selections, one in each column.

Bunuel · Accepted Answer

Official Solution:

The study begins with 1024 birds, which means 1024/2 = 512 pairs.
 
After each week, half of the pairs remain in the habitats:
 
• Week 1: 512/2 = 256 pairs

• Week 2: 256/2 = 128 pairs

• Week 3: 128/2 = 64 pairs

• Week 4: 64/2 = 32 pairs

• Week 5: 32/2 = 16 pairs

• Week 6: 16/2 = 8 pairs

...
 
We need to look for the number of weeks and the corresponding number of pairs from this list that are present in the options.
 
We have 6 weeks and 8 pairs — both values are in the options.

Correct answer:

Weeks  "6"

Pairs  "8"

siddhantvarma · Answer

We have 1024 birds in the beginning => 512 pairs of tagged birds.  This is crucial, if you start with 1024 you'll get the wrong answer.  
After each week, half birds are released and the other half remains.

After Week 1, 256 birds are released, 256 pairs remain.
After Week 2, 128 birds are released, 128 pairs remain.
After Week 3, 64 birds are released, 64 pairs remain.
After Week 4, 32 birds are released, 32 pairs remain.
After Week 5, 16 birds are released, 16 pairs remain.
After Week 6, 8 birds are released, 8 pairs remain.

Therefore, Weeks Completed = 6, pairs remaining = 8.

catinabox · Answer

This is the right solution!

Here is the official solution:

The study begins with 1024 birds being tagged and released, and since each pair consists of exactly two birds, this means there are initially:

1024 birds / 2 = 512 pairs

After each week, half of the remaining pairs of birds continue in the study, while the other half are returned to a safe environment. We are asked to determine how many weeks must have passed and how many pairs of birds remain after that number of weeks.

Step-by-step reduction in the number of pairs:

Week 0:  512 pairs of birds (no weeks have been completed yet) 
  Week 1:  Half of the 512 pairs remain, so:
512 / 2 = 256 pairs 
  Week 2:  Half of the 256 pairs remain, so:
256 / 2 = 128 pairs 
  Week 3:  Half of the 128 pairs remain, so:
128 / 2 = 64 pairs 
  Week 4:  Half of the 64 pairs remain, so:
64 / 2 = 32 pairs 
  Week 5:  Half of the 32 pairs remain, so:
32 / 2 = 16 pairs 
  Week 6:  Half of the 16 pairs remain, so:
16 / 2 = 8 pairs

Thus, after 6 weeks, 8 pairs of birds remain.

The number of weeks completed is 6, and the number of pairs remaining is 8. Therefore, the correct selections are:

Weeks Completed:  6 
 Pairs Remaining:  8

Note that if we contintue into week 7, 4 pairs remain. However, none of the option choices have 7,4.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

A wildlife conservation organization is conducting a study on

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

GMAT Two-part Analysis (TPA) Questions

A wildlife conservation organization is conducting a study on

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