JKSSB Reasoning MCQs

Explanation

Step 1: Identify the Given Data

• Total Students ($N$): 80

• Math ($M$): 40

• Science ($S$): 35

• English ($E$): 30

• Math and Science ($M \cap S$): 15

• Math and English ($M \cap E$): 12

• Science and English ($S \cap E$): 10

• All Three ($M \cap S \cap E$): 5

Step 2: Calculate the Union of All Sets

The formula to find the number of students who like at least one subject ($M \cup S \cup E$) is:

$$n(M \cup S \cup E) = n(M) + n(S) + n(E) - [n(M \cap S) + n(M \cap E) + n(S \cap E)] + n(M \cap S \cap E)$$

Substituting the values:

$$n(M \cup S \cup E) = 40 + 35 + 30 - [15 + 12 + 10] + 5$$

$$n(M \cup S \cup E) = 105 - 37 + 5$$

$$n(M \cup S \cup E) = 68 + 5 = 73$$

This means 73 students like at least one of the three subjects.

Step 3: Calculate "None of the Subjects"

To find the students who like none, we subtract the number of students who like at least one subject from the total number of students in the class.

$$\text{None} = \text{Total Students} - n(M \cup S \cup E)$$

$$\text{None} = 80 - 73 = 7$$

Explanation

Step 1: Analyze the Overlaps

The given intersections (Mathematics and Science, etc.) include the 5 students who like all three subjects. We must first isolate those who like exactly two subjects involving Mathematics.

• Total liking Mathematics (M): 40

• Liking M and Science (S): 15 (includes those who like English too)

• Liking M and English (E): 12 (includes those who like Science too)

• Liking all three (M, S, and E): 5

Step 2: Calculate "Mathematics only"

To get the "Mathematics only" group, we subtract everyone who likes Mathematics plus at least one other subject.

1. Students liking M and S (but not E): $15 - 5 = 10$

2. Students liking M and E (but not S): $12 - 5 = 7$

3. Students liking all three: $5$

Formula for Mathematics only:

$$M_{\text{only}} = n(M) - [(\text{M and S only}) + (\text{M and E only}) + (\text{All three})]$$

$$M_{\text{only}} = 40 - [10 + 7 + 5]$$

$$M_{\text{only}} = 40 - 22 = 18$$

Explanation

Step 1: Define the Sets and Intersections

Let $M$ be Mathematics, $S$ be Science, and $E$ be English.

• Total Students (N): 80

• Total liking M: $n(M) = 40$

• Total liking S: $n(S) = 35$

• Total liking E: $n(E) = 30$

• Liking M and S: $n(M \cap S) = 15$

• Liking M and E: $n(M \cap E) = 12$

• Liking S and E: $n(S \cap E) = 10$

• Liking all three: $n(M \cap S \cap E) = 5$

Step 2: Calculate "Exactly Two"

The intersections provided (like $n(M \cap S) = 15$) include the students who like all three subjects. To find those who like exactly two, we must subtract the "all three" group from each dual intersection.

1. Exactly M and S (only): $15 - 5 = \mathbf{10}$

2. Exactly M and E (only): $12 - 5 = \mathbf{7}$

3. Exactly S and E (only): $10 - 5 = \mathbf{5}$

Step 3: Final Calculation

To find the total number of students who like exactly two subjects, we add these three specific groups together:

$$10 + 7 + 5 = 22$$

Explanation

Figure 2

Explanation

North-West

Explanation

10 m East

Explanation

• Step 1: Starts at Point A.

• Step 2: Walks 10 m North to Point B.

  • Position relative to A: 10 m North.

• Step 3: Turns Right (East) and walks 8 m to Point C.

  • Position relative to A: 10 m North and 8 m East.

• Step 4: Turns Left (North) and walks 12 m to Point D.

  • Position relative to A: 22 m North (10 + 12) and 8 m East.

• Step 5: Turns Left (West) and walks 5 m to Point E.

  • Position relative to A: 22 m North and 3 m East (8 - 5).

Explanation

• In a standard compass, the directions are ordered clockwise as: North $\rightarrow$ East $\rightarrow$ South $\rightarrow$ West.

• The problem describes a 90° anti-clockwise rotation:

  • North moves to West (90° ACW)

  • West moves to South (90° ACW)

  • South moves to East (90° ACW)

• Following this same pattern, the original East will rotate 90° anti-clockwise to become North.

Explanation

• 35: $3 + 5 = \mathbf{8}$ (Even)

• 77: $7 + 7 = \mathbf{14}$ (Even)

• 91: $9 + 1 = \mathbf{10}$ (Even)

• 133: $1 + 3 + 3 = \mathbf{7}$ (Odd)

Explanation

The most definitive pattern is that three of the numbers are perfect squares ($15^2, 25^2, 27^2$), while one is only a perfect cube ($7^3$).

Explanation

B: 54 as per provisional answer key

Explanation

Figure-IV

Explanation

Grandfather

Explanation

Mother

Explanation

P is Q's cousin

Explanation

🔹 Statement 1 (A to B):

“Your mother’s father’s only daughter is my wife.”

• B’s mother’s father = B’s maternal grandfather

• His only daughter = B’s mother

• So A’s wife = B’s mother

👉 This means A is B’s father

🔹 Statement 2 (B to A):

“Then your father must be the only son of my grandmother.”

• B’s grandmother = mother of B’s mother = A’s mother-in-law

• Her only son = B’s maternal uncle

• So A’s father = B’s maternal uncle

👉 This is consistent if A married his maternal uncle’s sister (i.e., B’s mother), which is valid under the given condition (no same-generation marriage).

✅ Final Conclusion:

A is B’s father

Explanation

• The relationship is based on Instrument : Physical Quantity Measured.

• A Clock is a device specifically designed to measure and indicate Time.

• Similarly, a Barometer is a scientific instrument used to measure Atmospheric Pressure (also known as barometric pressure). It is a key tool in weather forecasting to help predict changes in weather patterns.

Explanation

• The relationship is based on Isolated Feature : Surrounding Environment.

• An Island is a piece of land completely surrounded by the Ocean.

• Similarly, an Oasis is a fertile area with water and vegetation completely surrounded by a Desert.

Explanation

• This analogy explores the relationship between a Political System and its Source of Power.

• In a Democracy, the primary source of power and decision-making is the people, exercised through the Vote.

• In an Oligarchy, power is concentrated in the hands of a small, influential Elite group (often distinguished by wealth, family ties, military control, or religious status).

Explanation

• The relationship is based on Instrument : Quantity Measured.

• A Thermometer is used to measure Temperature.

• Similarly, an Anemometer is a device used for measuring Wind Speed and direction. It is a common instrument used in weather stations.

Explanation

1. Divide the total investment ($Rs. 12,00,000$) into Projects A, B, and C based on the ratio $2:3:5$:

The sum of the ratio parts is $2 + 3 + 5 = 10$.

• Project A: $\frac{2}{10} \times 12,00,000 = Rs. 2,40,000$

• Project B: $\frac{3}{10} \times 12,00,000 = Rs. 3,60,000$

• Project C: $\frac{5}{10} \times 12,00,000 = Rs. 6,00,000$

2. Calculate the individual profit or loss for each project:

• Project A (10% profit): $10\% \text{ of } 2,40,000 = +Rs. 24,000$

• Project B (20% profit): $20\% \text{ of } 3,60,000 = +Rs. 72,000$

• Project C (10% loss): $10\% \text{ of } 6,00,000 = -Rs. 60,000$

3. Calculate the total net profit or loss:

$$\text{Net Profit/Loss} = 24,000 + 72,000 - 60,000 = \mathbf{+Rs. 36,000} \text{ (Profit)}$$

4. Calculate the overall percentage gain:

$$\text{Overall Percentage Gain} = \frac{\text{Net Profit}}{\text{Total Investment}} \times 100$$

$$\text{Overall Percentage Gain} = \frac{36,000}{12,00,000} \times 100 = \mathbf{3\%}$$

Explanation

The value is calculated by taking the sum of the numerical positions of each letter in the alphabet ($A=1, B=2, \dots, Z=26$) and then adding the square of the number of letters in the word.

Formula:

$$\text{Total Value} = (\text{Sum of Alphabetical Positions}) + (\text{Number of Letters})^2$$

Calculations

1. SMART = 96

   • Sum of positions: $S(19) + M(13) + A(1) + R(18) + T(20) = 71$

   • Number of letters: 5 ($5^2 = 25$)

   • $71 + 25 = 96$

2. MIND = 56

   • Sum of positions: $M(13) + I(9) + N(14) + D(4) = 40$

   • Number of letters: 4 ($4^2 = 16$)

   • $40 + 16 = 56$

3. PRO = ?

   • Sum of positions: $P(16) + R(18) + O(15) = 49$

   • Number of letters: 3 ($3^2 = 9$)

   • $49 + 9 = \mathbf{58}$