Q: Solve $\left(\frac{18}{4}\right)^2 \times \left(\frac{455}{19}\right) \div \left(\frac{61}{799}\right) = x$

Concept & Logic: This is a classic approximation problem found in banking exams. The numbers are deliberately designed to be slightly off from clean multiples. The strategy is to round the tricky fractions to the nearest whole numbers or simple ratios to execute the calculation quickly. Step-by-Step Solution: • Step 1: Simplify the first term. • (18/4) = 4.5. • (4.5)^2 = 20.25. • Step 2: Approximate the second term. • Notice that 19 \cdot 24 = 456. • Therefore, (455/19) is extremely close to (456/19) = 24. • Step 3: Approximate the third term (the divisor). • Notice that 61 \cdot 13 = 793. So (799/61) is slightly more than 13. • Alternatively, for an easier mental division inversion, (61/799) \approx (60/800) = (3/40). • Let's use the exact inversion: \div ((61/799)) becomes \cdot ((799/61)). • As established, (799/61) \approx 13.1. • Step 4: Multiply the approximated values together. • x \approx 20.25 \cdot 24 \cdot 13.1 • 20.25 \cdot 24 = 486. (Calculated easily as 20 \cdot 24 = 480, and 0.25 \cdot 24 = 6). • 486 \cdot 13.1 \approx 486 \cdot 13 + 486 \cdot 0.1 • 486 \cdot 13 = 6318. • 6318 + 48.6 = 6366.6. • The closest option provided by the exam setter for this approximation is 6350. (If calculated without any rounding, the exact value is roughly 6351.6). Exam Strategy & Shortcut: In approximation questions with options spread 30-50 units apart, immediately replace ugly fractions with their closest clean integers. (455/19) \rightarrow 24. For (799/61), flip it to multiplication: (800/61) \approx 13.1. Then execute 20.25 \cdot 24 \cdot 13.1. Common Pitfall: The biggest mistake is trying to calculate the exact decimal values of (455/19) and (61/799). This will consume minutes of your time and likely lead to an arithmetic error, whereas approximation takes seconds. Final Answer: Therefore, the correct answer is 6350.

Question 1

Solve $2\frac{2}{9} + 4\frac{1}{18} - 1\frac{1}{2} = x$

Accepted Answer

Concept & Formula: When adding or subtracting mixed fractions, the fastest method is to separate the whole numbers from the fractional parts. A(b/c) + D(e/f) = (A + D) + ((b/c) + (e/f)) Step-by-Step Solution: • Given Equation: 2(2/9) + 4(1/18) - 1(1/2) = x • Step 1: Separate Whole Numbers and Fractions Group the integers and the proper fractions separately: x = (2 + 4 - 1) + ((2/9) + (1/18) - (1/2)) • Step 2: Simplify the Whole Numbers 2 + 4 - 1 = 5 • Step 3: Simplify the Fractions Find the Lowest Common Multiple (LCM) of the denominators 9, 18, and 2, which is 18. Convert all fractions to have the denominator 18: (2/9) = (4/18) (1/18) = (1/18) (1/2) = (9/18) Now, evaluate the fraction part: (4/18) + (1/18) - (9/18) = (4 + 1 - 9/18) = (-4/18) = -(2/9) • Step 4: Combine Both Parts x = 5 - (2/9) To subtract the fraction, borrow 1 from 5: x = 4 + 1 - (2/9) = 4 + (9 - 2/9) = 4(7/9) Exam Strategy & Shortcut: Never convert mixed fractions into improper fractions for addition/subtraction (e.g., 20/9 + 73/18 - 3/2). That balloons the numbers and invites calculation errors. Always handle the integers first (2+4-1=5), then quickly balance the fraction denominators mentally. Common Pitfall: Students often convert mixed fractions to improper fractions (like 20/9), which makes finding common denominators and the final division much more tedious and error-prone. Another mistake is improperly handling negative fractional remainders. Final Answer: Therefore, the correct answer is 4(7/9).

Question 2

Solve $\frac{294 \div 14 	imes 5 + 11}{x} = 8^2 \div 5 + 1.7$

Accepted Answer

Concept & Logic: This problem requires strict adherence to the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction). The equation must be simplified by evaluating the numerator on the left and the entire expression on the right before isolating x. Step-by-Step Solution: • Given Equation: (294 \div 14 × 5 + 11/x) = 8^2 \div 5 + 1.7 • Step 1: Simplify the Left-Hand Side (LHS) Numerator According to BODMAS, perform division first, then multiplication, then addition. 294 \div 14 = 21 21 × 5 = 105 105 + 11 = 116 So, the LHS becomes (116/x). • Step 2: Simplify the Right-Hand Side (RHS) Resolve the exponent (order) first, then division, then addition. 8^2 = 64 64 \div 5 = 12.8 12.8 + 1.7 = 14.5 So, the RHS becomes 14.5. • Step 3: Solve for x Equate the simplified sides: (116/x) = 14.5 x = (116/14.5) To remove the decimal, multiply the numerator and denominator by 10: x = (1160/145) Dividing gives: x = 8 Exam Strategy & Shortcut: Simplify expressions in chunks mentally. For LHS: 294/14 = 21; 21 × 5 = 105; 105+11 = 116. For RHS: 64/5 = 12.8; 12.8+1.7 = 14.5. Now you have 116 = 14.5 × x. Instead of long division, check the unit digits or use multiples. 14.5 × 2 = 29. 29 × 4 = 116. Therefore, x = 2 × 4 = 8. Common Pitfall: Failing to follow BODMAS in the numerator is the most common mistake (e.g., multiplying before dividing or adding before multiplying). Also, arithmetic errors frequently happen when dividing by decimals like 14.5. Final Answer: Therefore, the correct answer is 8.

Question 3

Solve $2.5 	imes 4.8 + 7.2 	imes 1.5 - 1.2 	imes 14 = x$

Accepted Answer

Concept & Logic: The problem requires applying the standard order of operations (BODMAS/PEMDAS) to decimal arithmetic. Multiplication must be performed before addition and subtraction. Step-by-Step Solution: • Step 1: Isolate and perform the multiplication operations first. • 2.5 × 4.8 = 12 • 7.2 × 1.5 = 10.8 • 1.2 × 14 = 16.8 • Step 2: Substitute these products back into the original equation. • Equation becomes: 12 + 10.8 - 16.8 • Step 3: Perform addition and subtraction from left to right. • 22.8 - 16.8 = 6 Exam Strategy & Shortcut: To multiply decimals quickly, temporarily ignore the decimal points, perform integer multiplication, and then place the decimal back based on the total decimal places. For example, for 2.5 × 4.8, calculate 25 × 48. An easy way to do 25 × 48 is 100/4 × 48 = 1200. Since there are two decimal places in total (2.5 and 4.8), shift the decimal two spots to the left: 12.00. Common Pitfall: Students often make alignment errors when adding or subtracting the final terms, such as subtracting 16.8 from 10.8 incorrectly or misplacing the decimal point during the initial multiplication steps. Final Answer: Therefore, the correct answer is 6.

Question 4

Solve $\sqrt{197} 	imes 6.99 + 626.96 = x$

Accepted Answer

Concept & Strategy: This is an approximation question, common in banking exams. When you see numbers that are extremely close to integers or perfect squares, round them to the nearest whole number or perfect square to simplify calculations. Step-by-Step Solution: • Step 1: Approximate each term to its nearest workable integer. • \sqrt{197} is very close to \sqrt{196}, which is a perfect square. So, \sqrt{197} \approx 14. • 6.99 is approximately 7. • 626.96 is approximately 627. • Step 2: Substitute the approximated values into the equation. • Equation becomes: 14 × 7 + 627 • Step 3: Apply BODMAS by multiplying first, then adding. • 14 × 7 = 98 • 98 + 627 = 725 Exam Strategy & Shortcut: Never attempt to calculate the exact square root of 197 or multiply exact decimals in approximation sections. Look at the options: they are spaced far apart (e.g., 725, 825, 885). This wide gap is your permission to round aggressively. Common Pitfall: The most common mistake is failing to recognize this as an approximation problem and wasting precious time trying to calculate the exact decimal value of \sqrt{197}, which leads to a massive loss of time and potential calculation errors. Final Answer: Therefore, the correct answer is 725.

Question 5

Which of the following fractions is the largest?  $\frac{3}{2}, \frac{7}{3}, \frac{5}{4}, \frac{7}{2}$

Accepted Answer

Concept & Logic: To compare fractions efficiently, you can convert them into decimal values or compare their numerators and denominators if they share common traits. Since the denominators here are small (2, 3, 4), converting them directly to decimals is the fastest approach. Step-by-Step Solution: • Step 1: Convert each fraction into its decimal equivalent. • (3/2) = 1.5 • (7/3) = 2.33... • (5/4) = 1.25 • (7/2) = 3.5 • Step 2: Compare the resulting decimal values. • The sequence from smallest to largest is: 1.25 < 1.5 < 2.33 < 3.5. • Step 3: Identify the largest decimal and its corresponding fraction. • The largest decimal is 3.5, which corresponds to (7/2). Exam Strategy & Shortcut: You can instantly eliminate (3/2) and (5/4) by observing the numerators and denominators. (7/2) is exactly half of 7, meaning it is larger than 3. The other fractions ((3/2), (7/3), (5/4)) are all clearly smaller than 3. No calculation is needed if you rely on basic estimation. Common Pitfall: Students sometimes resort to finding a common denominator (LCM of 2, 3, 4, 2 is 12) to cross-compare. While technically correct, cross-multiplication or finding LCMs takes much longer than simple decimal conversion or logical elimination for small numbers. Final Answer: Therefore, the correct answer is (7/2).

Question 6

Solve $\left(\frac{18}{4}ight)^2 	imes \left(\frac{455}{19}ight) \div \left(\frac{61}{799}ight) = x$

Accepted Answer

Concept & Logic: This is a classic approximation problem found in banking exams. The numbers are deliberately designed to be slightly off from clean multiples. The strategy is to round the tricky fractions to the nearest whole numbers or simple ratios to execute the calculation quickly. Step-by-Step Solution: • Step 1: Simplify the first term. • (18/4) = 4.5. • (4.5)^2 = 20.25. • Step 2: Approximate the second term. • Notice that 19 \cdot 24 = 456. • Therefore, (455/19) is extremely close to (456/19) = 24. • Step 3: Approximate the third term (the divisor). • Notice that 61 \cdot 13 = 793. So (799/61) is slightly more than 13. • Alternatively, for an easier mental division inversion, (61/799) \approx (60/800) = (3/40). • Let's use the exact inversion: \div ((61/799)) becomes \cdot ((799/61)). • As established, (799/61) \approx 13.1. • Step 4: Multiply the approximated values together. • x \approx 20.25 \cdot 24 \cdot 13.1 • 20.25 \cdot 24 = 486. (Calculated easily as 20 \cdot 24 = 480, and 0.25 \cdot 24 = 6). • 486 \cdot 13.1 \approx 486 \cdot 13 + 486 \cdot 0.1 • 486 \cdot 13 = 6318. • 6318 + 48.6 = 6366.6. • The closest option provided by the exam setter for this approximation is 6350. (If calculated without any rounding, the exact value is roughly 6351.6). Exam Strategy & Shortcut: In approximation questions with options spread 30-50 units apart, immediately replace ugly fractions with their closest clean integers. (455/19) \rightarrow 24. For (799/61), flip it to multiplication: (800/61) \approx 13.1. Then execute 20.25 \cdot 24 \cdot 13.1. Common Pitfall: The biggest mistake is trying to calculate the exact decimal values of (455/19) and (61/799). This will consume minutes of your time and likely lead to an arithmetic error, whereas approximation takes seconds. Final Answer: Therefore, the correct answer is 6350.

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