Question 1

Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the given question.  What will be th…

Accepted Answer

Concept & Logic To find the sum of two numbers, we need to determine the exact values of both numbers. This requires two distinct linear equations representing their relationship. Let the bigger number be x and the smaller number be y. We need to find x + y. Step-by-Step Solution • Analyze Statement I: The bigger number is greater by 6. Equation: x - y = 6. • Analyze Statement II: 40% of smaller = 30% of bigger. • Equation for II: 0.40y = 0.30x \implies 4y = 3x \implies x/y = 4/3. • Analyze Statement III: Ratio between half of bigger and one-third of smaller is 2:1. • Equation for III: (x/2) / (y/3) = 2/1 \implies (3x)/(2y) = 2 \implies 3x = 4y \implies x/y = 4/3. • Notice that Statement II and Statement III yield the exact same ratio (x/y = 4/3). They are mathematically identical. • To find the exact values, we must combine the difference from Statement I with the ratio from either Statement II or Statement III. • Using I and II (or I and III): x = 4k, y = 3k \implies 4k - 3k = 6 \implies k=6. The numbers are 24 and 18, and their sum is 42. • Thus, we need "Statement I and either Statement II or Statement III" to answer the question. Since this option is not available, we must select "None of these". Exam Strategy & Shortcut Ratios, percentages, and fractions often express the exact same relationship disguised in different formats. Instantly simplify percentage relationships (40% and 30%) into simple ratios (4:3) and do the same for fraction relationships. If they match, you know the statements are redundant, saving you from calculating the final answer. Common Pitfall Many test-takers assume "Any two of the three" is correct because they see three distinct text strings. However, if you combine Statement II and Statement III, you only get the ratio 4:3 without any absolute value (like the difference of 6), leaving the exact numbers unknown. Final Answer Therefore, the correct answer is None of these.

Question 2

Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the given question.  What is the two…

Accepted Answer

Concept & Logic To uniquely identify a two-digit number, we need two independent linear equations to solve for the two variables (the individual digits). Original Number = 10x + y Step-by-Step Solution • Analyze Statement I: The difference between the number and its reverse is 27. • Calculation for I: |(10x+y) - (10y+x)| = 27 \implies 9|x-y| = 27 \implies |x-y| = 3. (Insufficient alone) • Analyze Statement II: The absolute difference between the digits is 3. So, |x-y| = 3. This is mathematically identical to Statement I. (Insufficient alone) • Analyze Statement III: The unit's digit is less than the ten's digit by 3. This gives us the exact order: x - y = 3. (Insufficient alone) • Test Combinations: All three statements essentially provide the same core piece of information: the difference between the digits is 3. We are completely missing a crucial second independent equation (such as the sum or product of the digits). • Because we only know x - y = 3, the number could easily be 41, 52, 63, 74, 85, or 96. Exam Strategy & Shortcut Realize immediately that "difference of digits" and "difference between a number and its reversed form" are the exact same mathematical property in disguise. If no statement provides an independent metric like a sum, product, or ratio, finding the exact unique number is impossible. Common Pitfall Test-takers often assume that a single linear equation is sufficient if the variables are restricted to single digits (0-9). While the digit restriction limits the possibilities, it rarely narrows it down to a single unique answer unless the sum or product is explicitly provided. Final Answer Therefore, the correct answer is Even with all I, II and III, answer cannot be given.

Question 3

Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the given question.  What is the two…

Accepted Answer

Concept & Logic We test each statement to find a unique two-digit number. The digits must be integers between 0 and 9, and the leading ten's digit cannot be 0. Original Number = 10x + y Step-by-Step Solution • Analyze Statement I: The ten's digit (x) is 4 × Unit's digit (y). The only valid single-digit integer pairs for (x, y) are (4,1) and (8,2). The number could be 41 or 82. (Insufficient) • Analyze Statement II: The digits are unequal, x 
eq y. (Insufficient) • Analyze Statement III: The ten's digit is the cube of the unit's digit, x = y^3. Since x is a single non-zero digit, y can only be 1 or 2. The possible pairs are (1,1) or (8,2). The number is 11 or 82. (Insufficient) • Test Combo I & III: Both statements are satisfied only by the unique number 82. (Sufficient) • Test Combo II & III: Statement III gives 11 or 82. Statement II says digits are unequal, thereby eliminating 11. The unique number is 82. (Sufficient) • Therefore, Statement III combined with either I or II is sufficient. • Since the option "III and either I or II" is not available among (a) to (d), we must choose "None of these". Exam Strategy & Shortcut Test discrete integer properties quickly. Cubes of digits 0-9 that result in single digits are extremely limited (just 0, 1, and 8). This severely restricts the possibilities, making checking statement combinations incredibly fast and visual. Common Pitfall A frequent mistake is forgetting that 11 is a valid two-digit number where the ten's digit (1) is indeed the cube of the unit's digit (1^3 = 1). Without remembering 11, you might falsely conclude that Statement III alone is sufficient to find 82. Final Answer Therefore, the correct answer is None of these.

Question 4

4/7th of the boys and 6/11th of girls of a school participated in marathon. If the number of participating students is 208 out of which 124 are boys, what is the total, number of students in the school? [NICL—AAO Exam, 2015]

Accepted Answer

Concept & Algebraic Manipulation: We can find the total number of individuals in a specific group if we know the fractional amount that represents a participating subset of that group. Total Group = Specific Part × \frac{Denominator}{Numerator} Step-by-Step Solution: 1. Identify the given values for participants: - Total participating students = 208 - Participating boys = 124 2. Calculate the number of participating girls: - Participating girls = Total participants - Participating boys - Participating girls = 208 - 124 = 84 3. Calculate the total number of boys in the school: - We are given that (4/7) of the total boys participated. - Let total boys be B. So, (4/7) × B = 124. - B = (124 × 7/4) = 31 × 7 = 217. 4. Calculate the total number of girls in the school: - We are given that (6/11) of the total girls participated. - Let total girls be G. So, (6/11) × G = 84. - G = (84 × 11/6) = 14 × 11 = 154. 5. Determine the total number of students in the school: - Total students = Total boys + Total girls - Total students = 217 + 154 = 371. Exam Strategy & Shortcut: Solve for the subgroups independently using reciprocal fractions. For boys: 124 × ((7/4)) = 217. The remaining participants are girls: 208 - 124 = 84. For girls: 84 × ((11/6)) = 154. Add them together: 217 + 154 = 371. Common Pitfall: A typical error is applying the total participant number (208) to the fractions directly or cross-mixing the fractions, ignoring the explicit breakdown of boys and girls which have completely different fractional participation rates. Final Answer: Therefore, the correct answer is 371.

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