SSC CGL Tier 1 2012 General Intelligence & Reasoning Questions with Solutions

Explanation

To find the current day, we first determine the reference day mentioned in the problem. Three days after Saturday is calculated by counting forward: Saturday + 1 day is Sunday, Saturday + 2 days is Monday, and Saturday + 3 days is Tuesday.

The phrase the day before the day before yesterday represents a specific count of days relative to today. If we let today be T, then yesterday is T - 1, the day before yesterday is T - 2, and the day before the day before yesterday is T - 3. According to the problem, T - 3 is Tuesday. To find today, we add three days back to Tuesday: Tuesday + 1 day is Wednesday, Tuesday + 2 days is Thursday, and Tuesday + 3 days is Friday.

Explanation

The word TAMPER can be constructed using the letters found in RAPPROCHEMENT. By analyzing the letter composition of the source word, we find that it contains the letters T, A, M, P, E, and R, which are the exact components required to form TAMPER. Specifically, RAPPROCHEMENT provides one T, one A, one M, two Ps, two Es, and two Rs. Since each letter in TAMPER appears in the source word in sufficient quantity, it can be successfully formed.

Explanation

The final direction can be determined by calculating the net rotation. We treat anticlockwise (ACW) turns as positive and clockwise (CW) turns as negative. Using the starting position of East as the reference point:

Net Rotation = (90° + 180°) - 45° = 225° ACW

Starting from East, we move 225° in the anticlockwise direction. A 90° ACW turn from East points North, a 180° ACW turn points West, and an additional 45° ACW turn from West (moving toward South) results in the Southwest direction. Alternatively, the same result is achieved by observing that 225° ACW is equivalent to 135° CW (360° - 225° = 135°). A 90° CW turn from East points South, and an additional 45° CW turn from South points Southwest.

Explanation

In Chennai, the sea (Bay of Bengal) is to the East. Since the house faces the sea, the person is facing East when starting. Turning to the left from an Eastward orientation means he is now facing North. He walks 50 metres North, then turns to the right, which brings him back to facing East. Walking 50 metres East from that point places him 50 metres North and 50 metres East of his original position. Therefore, his friend's house is in the North-East direction from his own house.

Explanation

Based on the logical structure of the problem and the provided answer key, the letter-coded operations are as follows: A stands for addition (+), D stands for subtraction (-), V stands for division (÷), G stands for "greater than" (>), L stands for "less than" (<), and E stands for "equal to" (=).

First, calculate the value of the target expression: 20 A 4 = 20 + 4 = 24

Now, substitute the symbols in option (c) to evaluate the logical statement: Expression: 24 G (21 V 3) Substitute V with ÷ and G with >: 24 > (21 ÷ 3) 24 > 7

Since 24 is greater than 7, the statement is mathematically correct. Evaluating other options using the same symbol assignments: a) 24 < (21 - 3) ⟹ 24 < 18 (False) b) 24 > (30 - 3) ⟹ 24 > 27 (False) d) 24 = (15 × 2) ⟹ 24 = 30 (False)

Explanation

The total quantity of numbers in the inclusive range from 4 to 55 is calculated as 55 - 4 + 1 = 52. To find the numbers left after removal, we first identify the set of numbers to be removed based on two criteria. First, the numbers divisible by 3 in this range are 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, which totals 17 numbers. Second, the numbers that contain the digit 3 are 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, totaling 14 numbers. To avoid double-counting, we identify the numbers common to both sets, which are 30, 33, 36, 39. Since there are 4 such overlapping numbers, the total unique numbers removed is calculated using the inclusion-exclusion principle as 17 + 14 - 4 = 27. Subtracting these removed values from the initial count gives 52 - 27 = 25.

Explanation

Let the two consecutive positive numbers be n and n + 1. The problem states that the sum of their squares is 1861, which gives the equation n² + (n + 1)² = 1861. Expanding the term (n + 1)², we get n² + n² + 2n + 1 = 1861. Combining like terms results in 2n² + 2n - 1860 = 0. Dividing the entire equation by 2 simplifies it to n² + n - 930 = 0.

To find the value of n, we can factor this quadratic equation. We look for two numbers that multiply to -930 and add up to 1. These numbers are 31 and -30. Thus, the equation becomes (n + 31)(n - 30) = 0. Since the problem specifies that the numbers are positive, we discard n = -31 and take n = 30. The two consecutive numbers are n = 30 and n + 1 = 31. We can verify this by calculating 30² + 31², which equals 900 + 961 = 1861.

Explanation

Statement I establishes that the entire group of educated persons follows public rules, which can be represented as E ⊆ P, where E is the set of educated persons and P is the set of people who follow public rules. Statement II indicates that some educated persons follow Government rules, meaning there is a non-empty intersection between educated persons and Government rule followers (E ∩ G ≠ ∅). Since any educated person who follows Government rules is first and foremost an educated person, they must also follow public rules according to the first statement (E ∩ G ⊆ E ⊆ P). This confirms that Conclusion I logically follows. Conclusion II is not supported because the premises do not provide evidence that any educated persons exist who do not follow Government rules; the assertion that some follow a rule does not logically necessitate that others do not follow it. Therefore, only Conclusion I is a necessary consequence of the provided statements.

Explanation

The logical validity of the conclusion is determined using the transitive property of sets. Statement II establishes that there is an intersection between the set of women and the set of lawyers. Statement I establishes that the entire set of lawyers is a subset of the set of liars. Because the specific group of women who are lawyers belongs to the lawyer set, they must also belong to the liar set by necessity of the first statement. Therefore, it is logically certain that some women are liars. The premises do not provide sufficient distribution of terms to support the second conclusion, as being a liar does not require being a lawyer or a woman based on the given information. Thus, only conclusion I is a direct logical consequence of the premises.

Explanation

The system follows a logic where the result is the sum of the first two numbers added to the product of the last two numbers. For an expression in the form a + b + c + d, the pattern is (a + b) + (c × d).

Applying this to the provided equations: (3 + 8) + (5 × 5) = 11 + 25 = 36 (6 + 2) + (8 × 1) = 8 + 8 = 16 (8 + 5) + (9 × 5) = 13 + 45 = 58

For the unsolved equation 7 + 4 + 3 + 8: (7 + 4) + (3 × 8) = 11 + 24 = 35

Explanation

Let the three consecutive even numbers be represented as x-2, x, and x+2. According to the problem, the sum of their squares is 116, which gives the equation (x-2)² + x² + (x+2)² = 116. Expanding the squares using the algebraic identity (a ± b)² = a² ± 2ab + b², the equation becomes (x² - 4x + 4) + x² + (x² + 4x + 4) = 116. Simplifying by combining like terms, the linear terms -4x and +4x cancel out, leaving 3x² + 8 = 116. Solving for x, we subtract 8 from both sides to get 3x² = 108, then divide by 3 to find x² = 36, which gives x = 6. The three consecutive even numbers are therefore 6-2=4, 6, and 6+2=8. Verification shows that 4² + 6² + 8² = 16 + 36 + 64 = 116, confirming these values satisfy the condition.

Explanation

Substituting the given symbols with their respective mathematical operators, where A denotes +, B denotes -, and C denotes ×, the expression 8 A 8 B 8 C 8 is rewritten as:

8 + 8 - 8 × 8

Following the BODMAS order of operations, the multiplication is solved first:

8 × 8 = 64

Substituting this back into the expression gives:

8 + 8 - 64

Performing the addition:

16 - 64

Performing the final subtraction:

-48

The calculation confirms that the result of the expression matches the value given in the statement.

Explanation

The coding logic is based on the reverse alphabetical position of each letter. The numerical value for each letter is calculated using the formula 27 - rank, where rank is the standard forward position of the letter in the alphabet (A=1, B=2, ..., Z=26). For the word GREEN, the letter positions are G(7), R(18), E(5), E(5), and N(14). Applying the formula gives 27-7=20, 27-18=9, 27-5=22, 27-5=22, and 27-14=13, matching the provided code.

For the word YALLOW, the forward positions are Y(25), A(1), L(12), L(12), O(15), and W(23). Calculating the reverse ranks yields 27-25=2 for Y, 27-1=26 for A, 27-12=15 for L, 27-12=15 for L, 27-15=12 for O, and 27-23=4 for W. This results in the sequence 2, 26, 15, 15, 12, 4.