A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh. If the panchayat funds the park and the road repair, on which of the following could it spend the rest of the money?

the bus shelter. The park and road repair cost ₹65 lakh, leaving exactly ₹5 lakh, which is the bus shelter. Every other the correct optionosts more than ₹5 lakh.

the water tank and the bus shelter

the school library and the bus shelter

A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh. If neither the park nor the community hall is funded, which of the following must be funded?

the street lights. Without the park or hall, the only full ₹70 lakh plans are health + street lights + water tank + library, or road + street lights + water tank + library + bus shelter. The street lights are in both.

A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh. If the street lights are funded, which of the following CANNOT also be funded?

the park. Street lights (₹20) + park (₹40) = ₹60 leaves ₹10 lakh, and no project or pair costs exactly ₹10 lakh. Each of the other projects appears in some full ₹70 lakh plan with the street lights.

A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh. If the health sub-centre and the community hall are funded, which is the only single other project that can complete the budget?

the road repair. ₹30 + ₹15 = ₹45 lakh leaves exactly ₹25 lakh, and the only project costing ₹25 lakh is the road repair.

A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh. If the panchayat funds the health sub-centre and the community hall, which two other projects could it fund?

the street lights and the bus shelter. ₹30 + ₹15 = ₹45 lakh leaves ₹25 lakh for two projects, and only street lights (₹20) + bus shelter (₹5) make exactly ₹25. Water tank + library is ₹20 and would still leave ₹5 unspent.

the water tank and the school library

the road repair and the bus shelter

the school library and the street lights

the water tank and the bus shelter

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Logical Reasoning · Arrangements & Puzzles

Logical Games — Questions & Answers

Logical games set out a group, a few rules, and ask which arrangement or selection is possible. Test each option against every rule; one broken rule rules the option out.

5 solved questions
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Read all the rules, then test each option against them. An option "could be true" if at least one complete arrangement obeys every rule and the option. The rules are repeated in each question.
Find all the arrangements that obey the rules (and any extra condition in the question). The answer is the statement that holds in every one of them.
Test each option: try to build one arrangement that obeys every rule and the option. The option for which no arrangement works is the answer.
An extra condition fixes part of the arrangement. Follow the rules step by step from that condition until the asked item is forced.

5 solved Logical Games questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh.
If the panchayat funds the park and the road repair, on which of the following could it spend the rest of the money?
4 steps · reveal one at a time
1. Step 1: Calculate Initial Spend
  First, let's find out how much money the panchayat has already decided to spend. They are funding the park (₹40 lakh) and road repair (₹25 lakh). Add these costs together.
2. Step 2: Find Remaining Budget
  The total cost for the park and road repair is $40 + 25 = 65$ lakh. The panchayat has a total budget of ₹70 lakh. To find out how much money is left, subtract the spent amount from the total budget: $70 - 65 = 5$ lakh.
3. Step 3: Identify Matching Project
  The panchayat has exactly ₹5 lakh remaining. Now, look at the list of available projects and their costs to see which one matches this remaining amount. We need a project that costs exactly ₹5 lakh.
4. Step 4: The answer
  So the answer is (C) the bus shelter. The bus shelter costs ₹5 lakh, which perfectly matches the remaining budget after funding the park and road repair.
02
A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh.
If neither the park nor the community hall is funded, which of the following must be funded?
5 steps · reveal one at a time
1. Step 1: Understand the Goal
  The village panchayat has $70$ lakh to spend. We need to find a combination of projects that sums to exactly $70$ lakh, given certain exclusions. We must identify a project that is part of all possible combinations.
2. Step 2: Exclude Projects
  The problem states that neither the park ( $40$ lakh) nor the community hall ( $15$ lakh) is funded. This means we remove these two projects from our list of available options for funding.
3. Step 3: List Remaining Projects
  Our available projects and their costs are: Road repair ( $25$ lakh), Water tank ( $12$ lakh), School library ( $8$ lakh), Street lights ( $20$ lakh), Health sub-centre ( $30$ lakh), and Bus shelter ( $5$ lakh).
4. Step 4: Find Funding Combinations
  We need to find combinations of these remaining projects that sum to exactly $70$ lakh. There are two such combinations: \n1. Health sub-centre ( $30$ ) + Street lights ( $20$ ) + Water tank ( $12$ ) + School library ( $8$ ) = $70$ . \n2. Road repair ( $25$ ) + Street lights ( $20$ ) + Water tank ( $12$ ) + School library ( $8$ ) + Bus shelter ( $5$ ) = $70$ .
5. Step 5: The answer
  So the answer is (C) the street lights. Both valid combinations that sum to $70$ lakh include the street lights, meaning it must be funded.
03
A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh.
If the street lights are funded, which of the following CANNOT also be funded?
5 steps · reveal one at a time
1. Step 1: Understand the budget
  The village panchayat has a total budget of \₹70 lakh. We must spend this full amount. Each project is either fully funded or not funded at all.
2. Step 2: Calculate remaining funds
  We are told the street lights project is funded. This costs \₹20 lakh. So, the remaining amount to spend on other projects is $70 - 20 = 50$ lakh.
3. Step 3: Test the park project
  Let's assume the park project is also funded. It costs \₹40 lakh. If both street lights and the park are funded, $20 + 40 = 60$ lakh is spent. This leaves $70 - 60 = 10$ lakh.
4. Step 4: Find projects for remaining funds
  With \₹10 lakh remaining, we need to find other projects that sum to exactly \₹10 lakh. The available projects are: road repair (\₹25), water tank (\₹12), school library (\₹8), community hall (\₹15), health sub-centre (\₹30), bus shelter (\₹5). No single project or combination of these sums to exactly \₹10 lakh.
5. Step 5: The answer
  So the answer is (B) the park. If the street lights and the park are funded, \₹10 lakh remains, which cannot be exactly covered by any other project or combination of projects.
04
A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh.
If the health sub-centre and the community hall are funded, which is the only single other project that can complete the budget?
4 steps · reveal one at a time
1. Step 1: Calculate Initial Spend
  The problem states that the health sub-centre and the community hall are funded. Their respective costs are $\text{Rs}\,30$ lakh and $\text{Rs}\,15$ lakh. Let's find their combined cost.
2. Step 2: Determine Remaining Budget
  Add the costs of the two funded projects: $\text{Rs}\,30 \text{ lakh} + \text{Rs}\,15 \text{ lakh} = \text{Rs}\,45 \text{ lakh}$ . The total budget is $\text{Rs}\,70$ lakh. Subtract the spent amount to find the remaining budget: $\text{Rs}\,70 \text{ lakh} - \text{Rs}\,45 \text{ lakh} = \text{Rs}\,25 \text{ lakh}$ .
3. Step 3: Identify Final Project
  We need to find a single project from the list that costs exactly $\text{Rs}\,25$ lakh to spend the full amount. Looking at the project costs, the road repair project costs $\text{Rs}\,25$ lakh.
4. Step 4: The answer
  So the answer is (C) the road repair. This project costs exactly $\text{Rs}\,25$ lakh, which is the remaining amount needed to complete the budget.
05
A village panchayat has ₹70 lakh to spend on development projects. It must spend the full amount, with nothing left over, and each project is either fully funded or not funded at all. Costs: road repair ₹25 lakh; water tank ₹12 lakh; school library ₹8 lakh; community hall ₹15 lakh; street lights ₹20 lakh; health sub-centre ₹30 lakh; bus shelter ₹5 lakh; park ₹40 lakh.
If the panchayat funds the health sub-centre and the community hall, which two other projects could it fund?
4 steps · reveal one at a time
1. Step 1: Calculate Initial Spend
  First, find the total cost of the projects already funded: the health sub-centre at ₹30 lakh and the community hall at ₹15 lakh. This sums to $30 + 15 = 45$ lakh.
2. Step 2: Find Remaining Budget
  The total budget is ₹70 lakh. Subtract the amount already spent to find the remaining funds: $70 - 45 = 25$ lakh. This is the exact amount left to spend.
3. Step 3: Identify Matching Projects
  Now, we need to find two other projects from the list that add up to exactly ₹25 lakh. Look at the costs: road repair (₹25), water tank (₹12), school library (₹8), street lights (₹20), bus shelter (₹5).
4. Step 4: The answer
  So the answer is (A) the street lights and the bus shelter. The street lights cost ₹20 lakh and the bus shelter costs ₹5 lakh, which perfectly adds up to the remaining ₹25 lakh ( $20 + 5 = 25$ ). Other combinations do not match.

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