1. Anu is taller than Bala. 2. Chitra is shorter than Bala. 3. Anu is taller than Chitra. Assuming the first two statements are true, is the third statement true, false or uncertain?

True. True: Anu > Bala > Chitra in height, so Anu is taller than Chitra.

1. Gita is younger than Esha. 2. Deepa is older than Esha. 3. Deepa is older than Gita. Assuming the last two statements are true, the first statement is:

Uncertain. Uncertain: Deepa is older than both Esha and Gita, but Esha and Gita are never compared.

Facts: 1. Asha is taller than Bina. 2. Chandra is taller than Asha. Which of these must be true?

Chandra is the tallest of the three.. Chandra > Asha > Bina in height, so Chandra is the tallest. Bina is the shortest, so the other two statements are false.

Asha is the shortest of the three.

Facts: 1. Pala is faster than Qadir. 2. Rani is slower than Qadir. 3. Siva is faster than Rani. Which of these statements is uncertain, neither definitely true nor definitely false?

Siva is faster than Qadir.. Siva is faster than Rani, but Siva and Qadir are never compared, so that is uncertain. Pala > Qadir > Rani makes "Pala is faster than Rani" true and "Rani is the fastest" false.

Rani is the fastest of the four.

1. The mango costs more than the guava. 2. The guava costs more than the banana. 3. The banana costs more than the mango. Given that statements 1 and 2 are true, the third statement is:

False. False: mango > guava > banana in price, so the banana costs the least, not more than the mango.

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Logical Reasoning · Arrangements & Puzzles

Logical Problems — Questions & Answers

Logical problems give two statements comparing people or things, and ask whether a third statement is true, false or uncertain. Put the facts in one order and check the third statement against it.

5 solved questions
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Turn the first two statements into one line in order (for example Anu > Bala > Chitra). If the third statement always holds on that line it is true; if it never can, it is false; if the two facts never connect the people it mentions, it is uncertain.
Picture the groups as circles. "All A are B" puts circle A inside B; "some A are B" means the circles overlap; "no A are B" keeps them apart. Test the third statement against every way the circles could be drawn.
This time the last two statements are the facts. Combine them first, then check the first statement against every arrangement they allow.
Combine the facts into an order or a picture of the groups, then test each option. Exactly one option holds in every arrangement the facts allow.

5 solved Logical Problems questions

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

01
Anu is taller than Bala.

Chitra is shorter than Bala.

Anu is taller than Chitra.
Assuming the first two statements are true, is the third statement true, false or uncertain?

4 steps · reveal one at a time
1. Step 1: Interpret the facts
  First, let's turn the given statements into simple inequalities. Statement 1 says Anu is taller than Bala, which we can write as $A > B$ . Statement 2 says Chitra is shorter than Bala, which means $C < B$ .
2. Step 2: Combine the statements
  Now, let's combine these two facts. We know $A > B$ . We also know $C < B$ , which is the same as saying $B > C$ . Putting these together, we get a clear order: $A > B > C$ . This means Anu is taller than Bala, and Bala is taller than Chitra.
3. Step 3: Evaluate the conclusion
  The third statement asks if Anu is taller than Chitra. From our combined order $A > B > C$ , it is clear that Anu is indeed taller than Chitra. There is no ambiguity.
4. Step 4: The answer
  So the answer is (A) True. Based on the first two statements, Anu's height is greater than Bala's, which is greater than Chitra's, making Anu taller than Chitra.
02
Gita is younger than Esha.

Deepa is older than Esha.

Deepa is older than Gita.
Assuming the last two statements are true, the first statement is:

5 steps · reveal one at a time
1. Step 1: Identify true statements
  We are told to assume that the last two statements are true. These are: "Deepa is older than Esha" (Deepa > Esha) and "Deepa is older than Gita" (Deepa > Gita).
2. Step 2: Combine true statements
  From these two true statements, we know that Deepa is older than both Esha and Gita. We can represent this as Deepa > Esha and Deepa > Gita.
3. Step 3: Evaluate the first statement
  The first statement is "Gita is younger than Esha" (Gita < Esha). Our true statements establish Deepa's age relative to Esha and Gita, but they do not compare Esha and Gita directly.
4. Step 4: Consider possibilities
  It's possible that Gita is younger than Esha, or that Esha is younger than Gita, or that they are the same age. The given information doesn't specify their relationship.
5. Step 5: The answer
  So the answer is (C) Uncertain. Deepa is older than both Esha and Gita, but Esha and Gita are never compared, making their relationship unknown.
03
Facts:

Asha is taller than Bina.

Chandra is taller than Asha.
Which of these must be true?

4 steps · reveal one at a time
1. Step 1: Read the facts
  We have two facts about the heights of Asha, Bina, and Chandra. Let's write them as inequalities.\nFact 1: Asha is taller than Bina. This means $Asha > Bina$ .\nFact 2: Chandra is taller than Asha. This means $Chandra > Asha$ .
2. Step 2: Combine relationships
  Now, let's put these two facts together. We know that Chandra is taller than Asha ( $Chandra > Asha$ ). We also know that Asha is taller than Bina ( $Asha > Bina$ ). We can link these two statements.
3. Step 3: Determine height order
  By combining $Chandra > Asha$ and $Asha > Bina$ , we get a complete order of their heights: $Chandra > Asha > Bina$ . This chain clearly shows the relative height of each person.
4. Step 4: The answer
  So the answer is (C) Chandra is the tallest of the three. Our combined order $Chandra > Asha > Bina$ directly shows that Chandra is indeed the tallest person among them.
04
Facts:

Pala is faster than Qadir.

Rani is slower than Qadir.

Siva is faster than Rani.
Which of these statements is uncertain, neither definitely true nor definitely false?

4 steps · reveal one at a time
1. Step 1: List the facts
  First, let's write down the speed relationships given in the facts. We can use the symbol ' $>$ ' to mean 'is faster than'.
  
  Pala $>$ Qadir
  
  Qadir $>$ Rani
  
  Siva $>$ Rani
2. Step 2: Combine relationships
  We can combine the first two facts to create a longer chain: Pala $>$ Qadir $>$ Rani. This tells us the relative speeds of Pala, Qadir, and Rani. The third fact, Siva $>$ Rani, tells us Siva is faster than Rani, but doesn't place Siva relative to Pala or Qadir.
3. Step 3: Evaluate certainty
  Let's check each statement. From Pala $>$ Qadir $>$ Rani, 'Pala is faster than Rani' is definitely true, and 'Rani is the fastest' is definitely false. However, Siva is faster than Rani, but we have no information comparing Siva and Qadir directly. Siva could be faster or slower than Qadir.
4. Step 4: The answer
  So the answer is (C) Siva is faster than Qadir. This statement is uncertain because the given facts do not provide enough information to determine if Siva is faster or slower than Qadir.
05
The mango costs more than the guava.

The guava costs more than the banana.

The banana costs more than the mango.
Given that statements 1 and 2 are true, the third statement is:

4 steps · reveal one at a time
1. Step 1: Understand true statements
  We are given two true statements about the costs of fruits. First, the mango costs more than the guava. Second, the guava costs more than the banana. Let's represent this with inequality signs.
2. Step 2: Combine the statements
  From the first statement, we know that $\text{Mango} > \text{Guava}$ . From the second, we know that $\text{Guava} > \text{Banana}$ . We can combine these two facts to get a clear order: $\text{Mango} > \text{Guava} > \text{Banana}$ .
3. Step 3: Evaluate the third statement
  Our combined order shows that the mango is the most expensive fruit and the banana is the least expensive. Now, let's look at the third statement: 'The banana costs more than the mango' or $\text{Banana} > \text{Mango}$ .
4. Step 4: The answer
  So the answer is (B) False. Since the mango costs more than the guava, and the guava costs more than the banana, the mango must cost more than the banana. Therefore, the statement that the banana costs more than the mango is false.

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