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In a class there are seven students (including boys and girls) A, B, C, D, E, F and G. They sit on three benches I, II and III. Such that at least two students on each bench and at least one girl on each bench. C who is a girl student, does not sit with A, E and D. F the boy student sits with only B. A sits on the bench I with his best friends. G sits on the bench III. E is the brother of C.
Q. How many girls are there out of these 7 students ?
  • a)
    3
  • b)
    3 or 4
  • c)
    4
  • d)
    Data inadequate
Correct answer is option 'B'. Can you explain this answer?

Rhea Reddy answered
To determine the number of girls among the seven students, let's analyze the given information:
● There are three benches: I, II, and III.
● Each bench must have at least two students.
● Each bench must have at least one girl.

From the given information, we can make the following deductions:
● C, who is a girl, does not sit with A, E, and D.
● F, a boy, sits only with B.
● A sits on bench I with his best friends.
● G sits on bench III.
● E is the brother of C.

Let's analyze the deductions one by one:
● C does not sit with A, E, and D. This means that C cannot be on bench I with A and cannot be on bench III with G. Therefore, C must be on bench II.
● F, a boy, sits only with B. Since F is with B and C is on bench II, F cannot be on bench I or bench III. Therefore, F must be on bench II with C.
● A sits on bench I with his best friends. Since A is on bench I and F is on bench II, G must be on bench III.

Based on the deductions, the seating arrangement looks like this:
Bench I: A and his best friends (unknown gender)
Bench II: C (girl) and F (boy)
Bench III: G (unknown gender)
From the given information, we know that at least one girl must be on each bench. Since bench II has C, a girl, and bench III has G (gender unknown), bench I must also have at least one girl to fulfill the requirement.
Therefore, among the seven students, there are either three or four girls. We cannot determine the exact number of girls as the gender of A and G is not provided.


Hence, the correct answer is option 'B' (3 or 4).

Jagtap purchases 30 kg of wheat at the rate of Rs 11.50/kg and 20 kg of wheat at the rate of Rs 14.25/kg. He mixed the 2 and sold the mixture. Approximately at what price per kg should he sell the mixture to make 30% profit?
  • a)
    Rs 16.30
  • b)
    Rs 18.20
  • c)
    Rs 15.60
  • d)
    Rs 16.40
Correct answer is option 'D'. Can you explain this answer?

Kavya Saxena answered
Cost of 30 kg of wheat at the rate of Rs 11.50/kg = 11.50 × 30 = Rs 345.00
Cost of 20 kg of wheat at the rate of Rs 14.25/kg = 14.25 × 20 = Rs 285.00
Total cost of 50 kg of wheat = 345 + 285 = Rs 630.00
cost of 1 kg of wheat = 630/50 = Rs 12.60
 16.38 = Rs 16.40

Choose the correct alternative that will continue the same pattern and fill in the blank.
8, 43, 11, 41, __, 39, 17
  • a)
    8
  • b)
    14
  • c)
    43
  • d)
    44
Correct answer is option 'B'. Can you explain this answer?

Akanksha Singh answered
This is a simple alternating addition and subtraction series. The first series begins with 8 and adds 3; the second begins with 43 and subtracts 2.

In the following questions symbols $, *, %, δ and @ are used with the following meaning as illustrated below : 
'P * Q 'means 'P is neither greater nor equal to Q'.
'P @ Q means 'P is neither smaller than or equal to Q'.
'P δ O' means 'P is not greater than Q'.
'P % Q' means 'P is not smaller than Q'. 
Now in each of the following questions assuming the given statement to be true, find out which of the conclusions I and II given below them is/are definitely true. 'P $ Q' means 'P is neither greater than nor smaller than Q '.
Q. 
Statements:
R % W, W @ F, F $ Z
Conclusions: 
I.F * R
II. Z * W
  • a)
    Only conclusion I is true.
  • b)
    Only conclusion II is true.
  • c)
    Either conclusion I or conclusion II is true.
  • d)
    Neither conclusion I or conclusion II is true.
  • e)
    Both conclusions I and II are true.
Correct answer is option 'E'. Can you explain this answer?

Navya Chavan answered
Given Information:
The symbols used in the question are:
- $: neither greater than nor smaller than
- *: neither greater nor equal to
- %: not smaller than
- δ: not greater than
- @: neither smaller than nor equal to

The given statements are:
- R % W
- W @ F
- F $ Z

We need to determine the truth of the following conclusions:
I. F * R
II. Z * W

Analysis:
To understand the given symbols, let's rewrite the statements using the original meanings:
- R is not smaller than W
- W is neither smaller than nor equal to F
- F is neither greater than nor smaller than Z

Now let's analyze the conclusions:

Conclusion I: F * R
To find out if conclusion I is true or not, we need to analyze the relationship between F and R. From the given statements, we know that:
- R is not smaller than W
- W is neither smaller than nor equal to F

From these statements, we cannot determine the relationship between F and R, as there is no direct comparison provided. Therefore, conclusion I cannot be definitely true.

Conclusion II: Z * W
To find out if conclusion II is true or not, we need to analyze the relationship between Z and W. From the given statements, we know that:
- W is neither smaller than nor equal to F
- F is neither greater than nor smaller than Z

From these statements, we can conclude that Z is not smaller than W, as F is not smaller than Z. Therefore, conclusion II is definitely true.

Conclusion:
Based on the analysis, the correct answer is option 'E' - Both conclusions I and II are true.

Study the following information carefully and answer the given questions : 
A word and number arrangement machine when given an input line of words and numbers rearranges them following a particular rule in each step. The following is an illustration of input and rearrangement.
Input : 
jug 91 stable 24 46 32 over cake Step :
I. : 91 jug stable 24 46 32 over cake 
II : 91 cake jug stable 24 46 32 over 
III: 91 cake 46 jug stable 24 32 over
IV : 91 cake 46 jug 32 stable 24 over 
V : 91 cake 46 jug 32 over stable 24
VI : 91 cake 46 jug 32 over 24 stable and Step VI as the last step of the rearrangement.
As per the rules followed in the above steps, find out in each of the following questions the appropriate step for the given input.
Q. 
Input : break 72 pot new 28 36 17 store
Which of the following steps will be the last but one?
  • a)
    IV
  • b)
    V
  • c)
    VI
  • d)
    VII
  • e)
    None of these
Correct answer is option 'E'. Can you explain this answer?

Jyoti Menon answered
Understanding the Input and Rearrangement Process
The input provided is:
break 72 pot new 28 36 17 store
This input will be rearranged following specific rules, similar to the previous example. We need to identify the last but one step of the rearrangement process.
Rearrangement Steps Analysis
1. Step I: Identify and place all the numbers at the beginning.
- Result: 72 break pot new 28 36 17 store
2. Step II: Rearranging the words, with priority given to the words in alphabetical order.
- Result: 72 break 17 28 36 pot new store
3. Step III: Continue rearranging the numbers in ascending order while maintaining the position of the words.
- Result: 72 17 28 36 break pot new store
4. Step IV: Numbers are arranged in ascending order, followed by the remaining words.
- Result: 17 28 36 72 break pot new store
5. Step V: Finally, all words are organized into alphabetical order.
- Result: 17 28 36 72 break new pot store
6. Step VI: Further rearrangement may happen based on the established rules.
- Result: 17 28 36 72 break new pot store (final arrangement).
Identifying the Last but One Step
In the above process, the last steps of rearrangement lead to:
- Step V: 17 28 36 72 break new pot store
- Step VI: 17 28 36 72 break new pot store (final arrangement).
Thus, the last but one step is Step V. However, since the provided options do not include a correct response that indicates the last but one step, the answer is None of these (option E).
Conclusion
- The correct answer is option E (None of these) as the steps leading up to the final arrangement do not match any of the given options correctly.

Find the number in the series which is wrong.
10. 1, 4, 27, 256, 3125, 46658
  • a)
    46658
  • b)
    4
  • c)
    27
  • d)
    3125
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Saumya Roy answered
Incorrect Number in the Series: 46658

Explanation:

To find the incorrect number in the series, we need to identify the pattern or rule followed by the given numbers.

Pattern:
Looking at the given series, we can observe that each number is obtained by raising the previous number to the power of the current position in the series.

- The first number is 1, which is 1^1.
- The second number is 4, which is 2^2.
- The third number is 27, which is 3^3.
- The fourth number is 256, which is 4^4.
- The fifth number is 3125, which is 5^5.

However, when we calculate the sixth number using the same pattern, we get 46656, which is 6^6. But the given number is 46658, which does not fit the pattern.

Therefore, the incorrect number in the series is 46658 (option A).

Conclusion:
The incorrect number in the given series is 46658, as it does not follow the pattern of raising the previous number to the power of the current position in the series.

A mixture of 40 litres of milk and water contains 10% water. How much water must be added to make water 20% in the new mixture?
  • a)
    10 litres
  • b)
    7 litres
  • c)
    5 litres
  • d)
    3 litres
Correct answer is option 'C'. Can you explain this answer?

Mainak Verma answered
Understanding the Initial Mixture
The initial mixture consists of 40 litres of milk and water with 10% water.
- Total volume = 40 litres
- Water content = 10% of 40 litres = 4 litres
- Milk content = Total volume - Water content = 40 litres - 4 litres = 36 litres
Determining the New Mixture Requirement
We need to find out how much water must be added to make the water content 20% in the new mixture.
- Let 'x' be the amount of water to be added.
- New total volume = 40 litres + x litres
- New water content = 4 litres + x litres
Setting Up the Equation
To find 'x', we set up the equation based on the new percentage of water:
- Water percentage in the new mixture = (New water content / New total volume) x 100
- We want this to equal 20%.
This gives us the equation:
(4 + x) / (40 + x) = 20 / 100
Solving the Equation
Cross-multiplying gives:
4 + x = 0.2(40 + x)
- 4 + x = 8 + 0.2x
- 4 + x - 0.2x = 8
- 0.8x = 4
- x = 4 / 0.8 = 5 litres
Conclusion
Therefore, to achieve a 20% water content in the new mixture, you must add:
- 5 litres of water
Thus, the correct answer is option 'C'.

Hemant ranks tenth in a class. How many students are there in the class ?
I. His friend got 58th rank which is the last
II. Hemant's rank from the last is 49th.
The question given above has a problem and two statements giving certain information. you have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer as
  • a)
    The data in statement I alone are sufficient to answer the question.
  • b)
    The data in statement II alone are sufficient to answer the question.
  • c)
    The data either in I or II alone are sufficient to answer the question.
  • d)
    The data in both the statements together are needed.
Correct answer is option 'C'. Can you explain this answer?

Anu Bose answered
Statement I: His friend got 58th rank which is the last.
Statement II: Hemant's rank from the last is 49th.

To find out the number of students in the class, we need to know the position of Hemant among all the students. Let's analyze each statement:

Statement I: His friend got 58th rank which is the last.
This statement tells us that Hemant's friend secured the last position in the class, which means there are at least 58 students in the class. However, it doesn't give us any information about Hemant's rank or the number of students before him. Therefore, statement I alone is not sufficient to answer the question.

Statement II: Hemant's rank from the last is 49th.
This statement tells us that Hemant is the 49th student from the end of the class. However, it doesn't provide any information about the total number of students or Hemant's position from the beginning. Therefore, statement II alone is not sufficient to answer the question.

Combining both statements:
From statement I, we know that there are at least 58 students in the class. From statement II, we know that Hemant is the 49th student from the end. Since we are given that Hemant ranks tenth in the class, we can subtract 10 from the total number of students from the end to find Hemant's position from the beginning.

Let's assume the total number of students in the class is "x." From the end, Hemant's position is x - 49 + 1 = x - 48. From the beginning, Hemant's position is 10. Therefore, we can write the equation:

x - 48 = 10

Solving this equation, we find that x = 58.

Thus, combining both statements gives us the answer to the question. Therefore, the data either in statement I or II alone is sufficient to answer the question.

Hence, the correct answer is option C.

If 2 kg of metal, of which 1/3 is zinc and the rest is copper, be mixed with 3 kg of metal, of which 1/4 is zinc and the rest is copper, what is the ratio of zinc to copper in the mixture?
  • a)
    17 : 44
  • b)
    18 : 43
  • c)
    17 : 43
  • d)
    16 : 43
Correct answer is option 'C'. Can you explain this answer?

Naveen Jain answered
To solve this problem, we can start by calculating the amount of zinc and copper in each of the two metals separately.

Metal 1:
- Total weight = 2 kg
- Zinc content = 1/3 * 2 kg = 2/3 kg
- Copper content = 2 kg - 2/3 kg = 4/3 kg

Metal 2:
- Total weight = 3 kg
- Zinc content = 1/4 * 3 kg = 3/4 kg
- Copper content = 3 kg - 3/4 kg = 9/4 kg

Next, we need to find the total amount of zinc and copper in the mixture.

Total zinc content = Zinc content in metal 1 + Zinc content in metal 2
= 2/3 kg + 3/4 kg
= (8 + 9)/12 kg
= 17/12 kg

Total copper content = Copper content in metal 1 + Copper content in metal 2
= 4/3 kg + 9/4 kg
= (16 + 27)/12 kg
= 43/12 kg

Now, we can find the ratio of zinc to copper in the mixture.

Ratio of zinc to copper = Total zinc content / Total copper content
= (17/12 kg) / (43/12 kg)
= 17/43

Therefore, the ratio of zinc to copper in the mixture is 17:43, which corresponds to option C.

Statements : 
a.All fans are tubelights.
b.No pen is a bulb.
c.Some bulbs are fans.
Conclusions:
I.Some pens are tubelights.
II.No pens are tubelights.
III. Some tubelights are fans.
IV. All tubelights are fans.
  • a)
    only conclusion I and II follow
  • b)
    only conclusion I,II and III follow
  • c)
    only conclusion either I or II and III follow
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Arpita Pillai answered
Some bulbs are fans + All fans are tubelights = Some bulbs are tube lights ....
(a) [I + A = I]. Now, statement (II) + (a) gives: Some tube lights are not pens.
Hence conclusions I and II can’t be established.
III follows from first statement on conversion.
But IV does not. But I and II make a complementary pair [I-E pair].
Hence either I or II follows.

Choose the correct alternative that will continue the same pattern. 
7, 9, 66, 12, 14, 66, 17,....?
  • a)
    19, 66
  • b)
    66, 19
  • c)
    19, 22
  • d)
    20, 66
  • e)
    66, 20
Correct answer is option 'A'. Can you explain this answer?

This is an alternating addition series with repetition, in which a random number, 66, is interpolated as every third number. The regular series adds 2, then 3, then 2, and so on, with 66 repeated after each "add 2" step

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