In CSC Algebra (Coin / Denomination Problems), a cashier has 30 bills consisting of PHP 50 and PHP 100 bills totaling PHP 2,100. How many PHP 100 bills are there?

12 bills of PHP 100 (and 18 bills of PHP 50). If all 30 bills were PHP 50, the total would be PHP 1,500. The excess PHP 600 (2,100 - 1,500) divided by the PHP 50 difference per bill (100 - 50) gives 600 / 50 = 12 bills of PHP 100.

56 committees. Since order within a committee does not matter, use Combinations: C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = 56.

90. Since Base N = Percentage / Rate = 45 / 0.15 = 300, 30% of 300 = 90 (or directly by proportion: since 30% is double 15%, the result is 2 × 45 = 90).

12 hours. Net filling rate per hour = 1/4 - 1/6 = (3 - 2)/12 = 1/12 of the tank per hour, so total time = 12 hours.

In CSC Fractions, how do you quickly compare which fraction is larger among 5/8, 7/11, and 2/3 without long division?

Use Cross-Multiplication: compare 5/8 vs. 7/11 -> 5×11 = 55 vs. 8×7 = 56, so 7/11 > 5/8. Next compare 7/11 vs. 2/3 -> 7×3 = 21 vs. 11×2 = 22, so 2/3 > 7/11. Thus 2/3 is the largest.

90. Since Base N = Percentage / Rate = 45 / 0.15 = 300, 30% of 300 = 90 (or directly by proportion: since 30% is double 15%, the result is 2 × 45 = 90).

Ana is 12 years old and Maria is 36 years old. Let Ana = x and Maria = 3x. In 12 years: 3x + 12 = 2(x + 12) -> 3x + 12 = 2x + 24 -> x = 12, and 3x = 36.

38. Let the four consecutive even integers be x, x+2, x+4, x+6. Then 4x + 12 = 140 -> 4x = 128 -> x = 32. The largest integer is x + 6 = 38.

In CSC Numerical Reasoning (PEMDAS/GEMDAS), what is the exact value of 48 ÷ 6 × (2 + 2) - 3²?

23. Step 1 (Parentheses & Exponents): 48 ÷ 6 × 4 - 9. Step 2 (Multiplication and Division strictly from LEFT TO RIGHT): (48 ÷ 6) × 4 - 9 = 8 × 4 - 9 = 32 - 9 = 23.

8:03:00 AM. Find the LCM of 12, 18, and 30: 12 = 2²·3, 18 = 2·3², 30 = 2·3·5 -> LCM = 2² × 3² × 5 = 180 seconds = 3 minutes.

215. The pattern is n³ - 1 for n = 1, 2, 3, 4, 5, 6: 1³-1=0, 2³-1=7, 3³-1=26, 4³-1=63, 5³-1=124, and 6³-1 = 216 - 1 = 215.

Maturity value A = P(1 + r)^t = 10,000 × (1.10)² = 10,000 × 1.21 = PHP 12,100. Total compound interest earned = PHP 12,100 - PHP 10,000 = PHP 2,100.

In CSC Motion Word Problems (Catch-Up / Pursuit), a courier leaves Manila at 8:00 AM traveling at 60 km/h. A second courier leaves the same spot at 9:30 AM traveling along the same route at 90 km/h. At what time will the second courier overtake the first?

12:30 PM (after 3 hours of pursuit). In the 1.5-hour head start (8:00 to 9:30 AM), the first courier travels 60 × 1.5 = 90 km. Relative catch-up speed = 90 - 60 = 30 km/h. Catch-up time = 90 km / 30 km/h = 3 hours after 9:30 AM = 12:30 PM.

38. Let the four consecutive even integers be x, x+2, x+4, x+6. Then 4x + 12 = 140 -> 4x = 128 -> x = 32. The largest integer is x + 6 = 38.

23. Step 1 (Parentheses & Exponents): 48 ÷ 6 × 4 - 9. Step 2 (Multiplication and Division strictly from LEFT TO RIGHT): (48 ÷ 6) × 4 - 9 = 8 × 4 - 9 = 32 - 9 = 23.

4 days. In inverse proportion, Workers₁ × Days₁ = Workers₂ × Days₂ -> 6 × 10 = 15 × D₂ -> D₂ = 60 / 15 = 4 days.

In CSC Probability & Combinatorics, how many 3-person committees can be formed from a pool of 8 qualified officers?

56 committees. Since order within a committee does not matter, use Combinations: C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = 56.

By 3: sum of digits is divisible by 3.

63. First-level differences are +4, +8, +12, +16. Second-level differences are constant (+4), so the next first-level difference is +20, giving 43 + 20 = 63.

8 liters. Using the solute balance equation: 0.30(20) + 1.00(x) = 0.50(20 + x) -> 6 + x = 10 + 0.5x -> 0.5x = 4 -> x = 8 liters.

In CSC Geometry, if the length of a rectangle is increased by 20% and its width is increased by 10%, by what percentage does its area increase?

32%. New Area = (1.20 L) × (1.10 W) = 1.32 LW, which is a 32% increase.

13 employees. Since 10 speak neither, 60 - 10 = 50 employees speak at least one language. By the Inclusion-Exclusion Principle, |I ∩ C| = |I| + |C| - |I ∪ C| = 35 + 28 - 50 = 13.

PHP 40,000. A 20% discount means the sale price is 80% (0.80) of the original price: Original Price = 32,000 / 0.80 = PHP 40,000 (do NOT add 20% of 32,000).

3.6 days. In 4 days alone, Alex completes 4 × (1/10) = 4/10 = 2/5 of the work, leaving 3/5 of the work. Their combined rate is 1/10 + 1/15 = 5/30 = 1/6 per day. Time for remaining work = (3/5) ÷ (1/6) =…

In CSC Number Series (Squares/Cubes ± 1), what is the next term in the sequence: 0, 7, 26, 63, 124, ___?

215. The pattern is n³ - 1 for n = 1, 2, 3, 4, 5, 6: 1³-1=0, 2³-1=7, 3³-1=26, 4³-1=63, 5³-1=124, and 6³-1 = 216 - 1 = 215.

3 hours. When moving toward each other (or in opposite directions), relative speed is the sum of their speeds: v_rel = 50 + 70 = 120 km/h. Time = Distance / v_rel = 360 km / 120 km/h = 3 hours.

32%. New Area = (1.20 L) × (1.10 W) = 1.32 LW, which is a 32% increase.

For any two numbers, A × B = GCF(A, B) × LCM(A, B). For 12 (2²·3), 15 (3·5), and 20 (2²·5), take the highest power of each prime: LCM = 2² × 3 × 5 = 60.

In CSC Venn Diagram Word Problems, in an office of 60 employees, 35 speak Ilocano, 28 speak Cebuano, and 10 speak neither language. How many employees speak BOTH Ilocano and Cebuano?

13 employees. Since 10 speak neither, 60 - 10 = 50 employees speak at least one language. By the Inclusion-Exclusion Principle, |I ∩ C| = |I| + |C| - |I ∪ C| = 35 + 28 - 50 = 13.

For any two numbers, A × B = GCF(A, B) × LCM(A, B). For 12 (2²·3), 15 (3·5), and 20 (2²·5), take the highest power of each prime: LCM = 2² × 3 × 5 = 60.

11. Odd positions double each time (2, 4, 8, 16), while even positions decrease by 3 each time (20, 17, 14, 11). The 8th term is an even position: 14 - 3 = 11.

PHP 50,000. Using I = P·r·t, solve for P = I / (r·t) = 9,000 / (0.06 × 3) = 9,000 / 0.18 = PHP 50,000.

In CSC Number Theory, how are the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of two numbers A and B related, and what is the LCM of 12, 15, and 20?

For any two numbers, A × B = GCF(A, B) × LCM(A, B). For 12 (2²·3), 15 (3·5), and 20 (2²·5), take the highest power of each prime: LCM = 2² × 3 × 5 = 60.

PHP 32,000. Total ratio parts = 2 + 3 + 4 = 9 parts. Value of 1 part = PHP 72,000 / 9 = PHP 8,000. Largest share (4 parts) = 4 × PHP 8,000 = PHP 32,000.

3.6 days. In 4 days alone, Alex completes 4 × (1/10) = 4/10 = 2/5 of the work, leaving 3/5 of the work. Their combined rate is 1/10 + 1/15 = 5/30 = 1/6 per day. Time for remaining work = (3/5) ÷ (1/6) =…

280 sq. meters. Since Perimeter = 2(L + W) = 68, L + W = 34. With L = W + 6, we get 2W + 6 = 34 -> W = 14 m and L = 20 m. Area = 20 × 14 = 280 m².

In CSC Percentage Problems (Base, Rate, Percentage), if 45 is 15% of a number N, what is 30% of N?

90. Since Base N = Percentage / Rate = 45 / 0.15 = 300, 30% of 300 = 90 (or directly by proportion: since 30% is double 15%, the result is 2 × 45 = 90).

63. First-level differences are +4, +8, +12, +16. Second-level differences are constant (+4), so the next first-level difference is +20, giving 43 + 20 = 63.

12:30 PM (after 3 hours of pursuit).

86. Required total sum for 5 quizzes = 5 × 86 = 430. Current sum of 4 quizzes = 82 + 85 + 88 + 89 = 344. Required 5th score = 430 - 344 = 86.

In CSC Work Problems with Inlet and Outlet Pipes, Pipe A can fill a tank in 4 hours, while Drain Pipe B can empty the full tank in 6 hours. If both pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank?

12 hours. Net filling rate per hour = 1/4 - 1/6 = (3 - 2)/12 = 1/12 of the tank per hour, so total time = 12 hours.

8 liters. Using the solute balance equation: 0.30(20) + 1.00(x) = 0.50(20 + x) -> 6 + x = 10 + 0.5x -> 0.5x = 4 -> x = 8 liters.

86. Required total sum for 5 quizzes = 5 × 86 = 430. Current sum of 4 quizzes = 82 + 85 + 88 + 89 = 344. Required 5th score = 430 - 344 = 86.

PHP 40,000. A 20% discount means the sale price is 80% (0.80) of the original price: Original Price = 32,000 / 0.80 = PHP 40,000 (do NOT add 20% of 32,000).

In CSC Age Word Problems, 5 years ago, Carlo was 4 times as old as Ben. If the sum of their ages today is 45, how old is Carlo today?

Carlo is 33 years old today. Five years ago, the sum of their ages was 45 - 2(5) = 35. Since their ratio 5 years ago was 4 : 1 (5 parts), Ben was 35/5 = 7 and Carlo was 28 five years ago. Today, Carlo is 28 + 5 = 33 (and Ben is 12).

48 km/h (NOT 50 km/h). For equal distances, Average Speed is the harmonic mean: 2·v₁·v₂ / (v₁ + v₂) = 2(40)(60) / (40 + 60) = 4,800 / 100 = 48 km/h.

12 meters, using the 5-12-13 Pythagorean triple (h = √(13² - 5²) = √(169 - 25) = √144 = 12 m). Common CSC Pythagorean triples to memorize: (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

90. Since Base N = Percentage / Rate = 45 / 0.15 = 300, 30% of 300 = 90 (or directly by proportion: since 30% is double 15%, the result is 2 × 45 = 90).

In CSC Motion Problems (Average Speed for a Round Trip), a driver travels from City A to City B at 40 km/h and returns along the same route at 60 km/h. What is the average speed for the entire round trip?

48 km/h (NOT 50 km/h). For equal distances, Average Speed is the harmonic mean: 2·v₁·v₂ / (v₁ + v₂) = 2(40)(60) / (40 + 60) = 4,800 / 100 = 48 km/h.

12 bills of PHP 100 (and 18 bills of PHP 50).

Use Cross-Multiplication: compare 5/8 vs. 7/11 -> 5×11 = 55 vs. 8×7 = 56, so 7/11 > 5/8. Next compare 7/11 vs. 2/3 -> 7×3 = 21 vs. 11×2 = 22, so 2/3 > 7/11. Thus 2/3 is the largest.

63. First-level differences are +4, +8, +12, +16. Second-level differences are constant (+4), so the next first-level difference is +20, giving 43 + 20 = 63.

In CSC Number Series (Second-Order Differences), what is the next number in the sequence: 3, 7, 15, 27, 43, ___?

63. First-level differences are +4, +8, +12, +16. Second-level differences are constant (+4), so the next first-level difference is +20, giving 43 + 20 = 63.

12 hours. Net filling rate per hour = 1/4 - 1/6 = (3 - 2)/12 = 1/12 of the tank per hour, so total time = 12 hours.

38. Let the four consecutive even integers be x, x+2, x+4, x+6. Then 4x + 12 = 140 -> 4x = 128 -> x = 32. The largest integer is x + 6 = 38.

1/8 = 0.125 (12.5%); 3/8 = 0.375 (37.5%); 5/8 = 0.625 (62.5%); 7/8 = 0.875 (87.5%); 1/6 = 0.1667 (16.67%); 5/6 = 0.8333 (83.33%).

In CSC Motion Word Problems (Opposite Directions / Meeting), two buses leave stations 360 km apart at the same time and travel toward each other at 50 km/h and 70 km/h. In how many hours will they meet?

3 hours. When moving toward each other (or in opposite directions), relative speed is the sum of their speeds: v_rel = 50 + 70 = 120 km/h. Time = Distance / v_rel = 360 km / 120 km/h = 3 hours.

Maturity value A = P(1 + r)^t = 10,000 × (1.10)² = 10,000 × 1.21 = PHP 12,100. Total compound interest earned = PHP 12,100 - PHP 10,000 = PHP 2,100.

13 employees. Since 10 speak neither, 60 - 10 = 50 employees speak at least one language. By the Inclusion-Exclusion Principle, |I ∩ C| = |I| + |C| - |I ∪ C| = 35 + 28 - 50 = 13.

PHP 32,000. Total ratio parts = 2 + 3 + 4 = 9 parts. Value of 1 part = PHP 72,000 / 9 = PHP 8,000. Largest share (4 parts) = 4 × PHP 8,000 = PHP 32,000.

In CSC Ratio and Proportion (Inverse Proportion), if 6 clerks can encode a voter registry in 10 days, how many days will it take 15 clerks working at the same rate to complete the job?

4 days. In inverse proportion, Workers₁ × Days₁ = Workers₂ × Days₂ -> 6 × 10 = 15 × D₂ -> D₂ = 60 / 15 = 4 days.

Maturity value A = P(1 + r)^t = 10,000 × (1.10)² = 10,000 × 1.21 = PHP 12,100. Total compound interest earned = PHP 12,100 - PHP 10,000 = PHP 2,100.

Use Cross-Multiplication: compare 5/8 vs. 7/11 -> 5×11 = 55 vs. 8×7 = 56, so 7/11 > 5/8. Next compare 7/11 vs. 2/3 -> 7×3 = 21 vs. 11×2 = 22, so 2/3 > 7/11. Thus 2/3 is the largest.

In CSC Age Word Problems, Maria is currently 3 times as old as her daughter Ana. In 12 years, Maria will be twice as old as Ana. How old are Maria and Ana now?

Ana is 12 years old and Maria is 36 years old. Let Ana = x and Maria = 3x. In 12 years: 3x + 12 = 2(x + 12) -> 3x + 12 = 2x + 24 -> x = 12, and 3x = 36.

12:30 PM (after 3 hours of pursuit).

280 sq. meters. Since Perimeter = 2(L + W) = 68, L + W = 34. With L = W + 6, we get 2W + 6 = 34 -> W = 14 m and L = 20 m. Area = 20 × 14 = 280 m².

8:03:00 AM. Find the LCM of 12, 18, and 30: 12 = 2²·3, 18 = 2·3², 30 = 2·3·5 -> LCM = 2² × 3² × 5 = 180 seconds = 3 minutes.

In CSC Divisibility Rules, how do you test instantly if a large number is divisible by 3, 4, 8, 9, and 11?

By 3: sum of digits is divisible by 3. By 4: last 2 digits form a number divisible by 4. By 8: last 3 digits form a number divisible by 8. By 9: sum of digits is divisible by 9. By 11: alternating sum and difference of digits is 0 or a multiple of 11.

28%. Remaining price factor = (1 - 0.20) × (1 - 0.10) = 0.80 × 0.90 = 0.72 (72% of original), so total discount = 100% - 72% = 28% (or formula: d1 + d2 - (d1·d2)/100 = 20 + 10 - 2 = 28%).

12 hours. Net filling rate per hour = 1/4 - 1/6 = (3 - 2)/12 = 1/12 of the tank per hour, so total time = 12 hours.

32%. New Area = (1.20 L) × (1.10 W) = 1.32 LW, which is a 32% increase.

In CSC Geometry, the perimeter of a rectangular lot is 68 meters and its length is 6 meters more than its width. What is the area of the lot?

280 sq. meters. Since Perimeter = 2(L + W) = 68, L + W = 34. With L = W + 6, we get 2W + 6 = 34 -> W = 14 m and L = 20 m. Area = 20 × 14 = 280 m².

23. Step 1 (Parentheses & Exponents): 48 ÷ 6 × 4 - 9. Step 2 (Multiplication and Division strictly from LEFT TO RIGHT): (48 ÷ 6) × 4 - 9 = 8 × 4 - 9 = 32 - 9 = 23.

28%. Remaining price factor = (1 - 0.20) × (1 - 0.10) = 0.80 × 0.90 = 0.72 (72% of original), so total discount = 100% - 72% = 28% (or formula: d1 + d2 - (d1·d2)/100 = 20 + 10 - 2 = 28%).

3 hours. When moving toward each other (or in opposite directions), relative speed is the sum of their speeds: v_rel = 50 + 70 = 120 km/h. Time = Distance / v_rel = 360 km / 120 km/h = 3 hours.

In CSC Number Series (Alternating / Interleaved Series), what is the next number in the sequence: 2, 20, 4, 17, 8, 14, 16, ___?

11. Odd positions double each time (2, 4, 8, 16), while even positions decrease by 3 each time (20, 17, 14, 11). The 8th term is an even position: 14 - 3 = 11.

3.6 days. In 4 days alone, Alex completes 4 × (1/10) = 4/10 = 2/5 of the work, leaving 3/5 of the work. Their combined rate is 1/10 + 1/15 = 5/30 = 1/6 per day. Time for remaining work = (3/5) ÷ (1/6) =…

12 bills of PHP 100 (and 18 bills of PHP 50).

By 3: sum of digits is divisible by 3.

In CSC Work Problems, Alex can finish an audit report in 10 days, and Bea can finish it in 15 days. Alex works alone for 4 days and then Bea joins him. How many MORE days will it take them working together to finish the remaining work?

3.6 days. In 4 days alone, Alex completes 4 × (1/10) = 4/10 = 2/5 of the work, leaving 3/5 of the work. Their combined rate is 1/10 + 1/15 = 5/30 = 1/6 per day. Time for remaining work = (3/5) ÷ (1/6) = 18/5 = 3.6 days.

PHP 50,000. Using I = P·r·t, solve for P = I / (r·t) = 9,000 / (0.06 × 3) = 9,000 / 0.18 = PHP 50,000.

56 committees. Since order within a committee does not matter, use Combinations: C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = 56.

28%. Remaining price factor = (1 - 0.20) × (1 - 0.10) = 0.80 × 0.90 = 0.72 (72% of original), so total discount = 100% - 72% = 28% (or formula: d1 + d2 - (d1·d2)/100 = 20 + 10 - 2 = 28%).

In CSC Simple Interest Problems, how much principal must be invested at 6% simple annual interest to earn PHP 9,000 in interest over 3 years?

PHP 50,000. Using I = P·r·t, solve for P = I / (r·t) = 9,000 / (0.06 × 3) = 9,000 / 0.18 = PHP 50,000.

280 sq. meters. Since Perimeter = 2(L + W) = 68, L + W = 34. With L = W + 6, we get 2W + 6 = 34 -> W = 14 m and L = 20 m. Area = 20 × 14 = 280 m².

By 3: sum of digits is divisible by 3.

215. The pattern is n³ - 1 for n = 1, 2, 3, 4, 5, 6: 1³-1=0, 2³-1=7, 3³-1=26, 4³-1=63, 5³-1=124, and 6³-1 = 216 - 1 = 215.

In CSC Percentage Problems, after a 20% discount, a laptop was sold for PHP 32,000. What was the original marked price before the discount?

PHP 40,000. A 20% discount means the sale price is 80% (0.80) of the original price: Original Price = 32,000 / 0.80 = PHP 40,000 (do NOT add 20% of 32,000).

11. Odd positions double each time (2, 4, 8, 16), while even positions decrease by 3 each time (20, 17, 14, 11). The 8th term is an even position: 14 - 3 = 11.

48 km/h (NOT 50 km/h). For equal distances, Average Speed is the harmonic mean: 2·v₁·v₂ / (v₁ + v₂) = 2(40)(60) / (40 + 60) = 4,800 / 100 = 48 km/h.

56 committees. Since order within a committee does not matter, use Combinations: C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = 56.

In CSC Compound Interest Problems, if PHP 10,000 is invested at 10% annual interest compounded annually for 2 years, what is the final maturity value and total compound interest earned?

Maturity value A = P(1 + r)^t = 10,000 × (1.10)² = 10,000 × 1.21 = PHP 12,100. Total compound interest earned = PHP 12,100 - PHP 10,000 = PHP 2,100.

12 meters, using the 5-12-13 Pythagorean triple (h = √(13² - 5²) = √(169 - 25) = √144 = 12 m). Common CSC Pythagorean triples to memorize: (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

For any two numbers, A × B = GCF(A, B) × LCM(A, B). For 12 (2²·3), 15 (3·5), and 20 (2²·5), take the highest power of each prime: LCM = 2² × 3 × 5 = 60.

Ana is 12 years old and Maria is 36 years old. Let Ana = x and Maria = 3x. In 12 years: 3x + 12 = 2(x + 12) -> 3x + 12 = 2x + 24 -> x = 12, and 3x = 36.

In CSC Fractions & Decimals, what are the exact decimal and percentage equivalents of 1/8, 3/8, 5/8, 7/8, 1/6, and 5/6?

1/8 = 0.125 (12.5%); 3/8 = 0.375 (37.5%); 5/8 = 0.625 (62.5%); 7/8 = 0.875 (87.5%); 1/6 = 0.1667 (16.67%); 5/6 = 0.8333 (83.33%).

PHP 40,000. A 20% discount means the sale price is 80% (0.80) of the original price: Original Price = 32,000 / 0.80 = PHP 40,000 (do NOT add 20% of 32,000).

12 bills of PHP 100 (and 18 bills of PHP 50).

In CSC Geometry (Pythagorean Triples), a ladder 13 meters long leans against a vertical wall with its foot 5 meters from the base of the wall. How high up the wall does the ladder reach?

12 meters, using the 5-12-13 Pythagorean triple (h = √(13² - 5²) = √(169 - 25) = √144 = 12 m). Common CSC Pythagorean triples to memorize: (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Use Cross-Multiplication: compare 5/8 vs. 7/11 -> 5×11 = 55 vs. 8×7 = 56, so 7/11 > 5/8. Next compare 7/11 vs. 2/3 -> 7×3 = 21 vs. 11×2 = 22, so 2/3 > 7/11. Thus 2/3 is the largest.

PHP 32,000. Total ratio parts = 2 + 3 + 4 = 9 parts. Value of 1 part = PHP 72,000 / 9 = PHP 8,000. Largest share (4 parts) = 4 × PHP 8,000 = PHP 32,000.

12:30 PM (after 3 hours of pursuit).

In CSC Algebra (Consecutive Integers), the sum of four consecutive even integers is 140. What is the largest of these four integers?

38. Let the four consecutive even integers be x, x+2, x+4, x+6. Then 4x + 12 = 140 -> 4x = 128 -> x = 32. The largest integer is x + 6 = 38.

86. Required total sum for 5 quizzes = 5 × 86 = 430. Current sum of 4 quizzes = 82 + 85 + 88 + 89 = 344. Required 5th score = 430 - 344 = 86.

8:03:00 AM. Find the LCM of 12, 18, and 30: 12 = 2²·3, 18 = 2·3², 30 = 2·3·5 -> LCM = 2² × 3² × 5 = 180 seconds = 3 minutes.

In CSC Successive Discounts, what single equivalent discount rate is equal to successive discounts of 20% and 10%?

28%. Remaining price factor = (1 - 0.20) × (1 - 0.10) = 0.80 × 0.90 = 0.72 (72% of original), so total discount = 100% - 72% = 28% (or formula: d1 + d2 - (d1·d2)/100 = 20 + 10 - 2 = 28%).

215. The pattern is n³ - 1 for n = 1, 2, 3, 4, 5, 6: 1³-1=0, 2³-1=7, 3³-1=26, 4³-1=63, 5³-1=124, and 6³-1 = 216 - 1 = 215.

8 liters. Using the solute balance equation: 0.30(20) + 1.00(x) = 0.50(20 + x) -> 6 + x = 10 + 0.5x -> 0.5x = 4 -> x = 8 liters.

13 employees. Since 10 speak neither, 60 - 10 = 50 employees speak at least one language. By the Inclusion-Exclusion Principle, |I ∩ C| = |I| + |C| - |I ∪ C| = 35 + 28 - 50 = 13.

In CSC Statistics (Weighted Mean), a student scored 82, 85, 88, and 89 on four quizzes. What score must they get on the 5th quiz to achieve an average of 86 across all 5 quizzes?

86. Required total sum for 5 quizzes = 5 × 86 = 430. Current sum of 4 quizzes = 82 + 85 + 88 + 89 = 344. Required 5th score = 430 - 344 = 86.

1/8 = 0.125 (12.5%); 3/8 = 0.375 (37.5%); 5/8 = 0.625 (62.5%); 7/8 = 0.875 (87.5%); 1/6 = 0.1667 (16.67%); 5/6 = 0.8333 (83.33%).

4 days. In inverse proportion, Workers₁ × Days₁ = Workers₂ × Days₂ -> 6 × 10 = 15 × D₂ -> D₂ = 60 / 15 = 4 days.

48 km/h (NOT 50 km/h). For equal distances, Average Speed is the harmonic mean: 2·v₁·v₂ / (v₁ + v₂) = 2(40)(60) / (40 + 60) = 4,800 / 100 = 48 km/h.

In CSC Word Problems with LCM, three traffic lights flash every 12 seconds, 18 seconds, and 30 seconds, respectively. If they flash together at 8:00:00 AM, at what time will they next flash together?

8:03:00 AM. Find the LCM of 12, 18, and 30: 12 = 2²·3, 18 = 2·3², 30 = 2·3·5 -> LCM = 2² × 3² × 5 = 180 seconds = 3 minutes.

4 days. In inverse proportion, Workers₁ × Days₁ = Workers₂ × Days₂ -> 6 × 10 = 15 × D₂ -> D₂ = 60 / 15 = 4 days.

3 hours. When moving toward each other (or in opposite directions), relative speed is the sum of their speeds: v_rel = 50 + 70 = 120 km/h. Time = Distance / v_rel = 360 km / 120 km/h = 3 hours.

12 meters, using the 5-12-13 Pythagorean triple (h = √(13² - 5²) = √(169 - 25) = √144 = 12 m). Common CSC Pythagorean triples to memorize: (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

In CSC Ratio and Proportion (Partitive Proportion), a bonus of PHP 72,000 is divided among three employees in the ratio 2 : 3 : 4. How much does the employee with the largest share receive?

PHP 32,000. Total ratio parts = 2 + 3 + 4 = 9 parts. Value of 1 part = PHP 72,000 / 9 = PHP 8,000. Largest share (4 parts) = 4 × PHP 8,000 = PHP 32,000.

Ana is 12 years old and Maria is 36 years old. Let Ana = x and Maria = 3x. In 12 years: 3x + 12 = 2(x + 12) -> 3x + 12 = 2x + 24 -> x = 12, and 3x = 36.

PHP 50,000. Using I = P·r·t, solve for P = I / (r·t) = 9,000 / (0.06 × 3) = 9,000 / 0.18 = PHP 50,000.

23. Step 1 (Parentheses & Exponents): 48 ÷ 6 × 4 - 9. Step 2 (Multiplication and Division strictly from LEFT TO RIGHT): (48 ÷ 6) × 4 - 9 = 8 × 4 - 9 = 32 - 9 = 23.

In CSC Mixture Problems, how many liters of pure alcohol (100%) must be added to 20 liters of a 30% alcohol solution to produce a 50% alcohol solution?

8 liters. Using the solute balance equation: 0.30(20) + 1.00(x) = 0.50(20 + x) -> 6 + x = 10 + 0.5x -> 0.5x = 4 -> x = 8 liters.

32%. New Area = (1.20 L) × (1.10 W) = 1.32 LW, which is a 32% increase.

1/8 = 0.125 (12.5%); 3/8 = 0.375 (37.5%); 5/8 = 0.625 (62.5%); 7/8 = 0.875 (87.5%); 1/6 = 0.1667 (16.67%); 5/6 = 0.8333 (83.33%).

11. Odd positions double each time (2, 4, 8, 16), while even positions decrease by 3 each time (20, 17, 14, 11). The 8th term is an even position: 14 - 3 = 11.

CSC CSE-PPT Numerical Reasoning: Fractions/Decimals/Percentages, Ratio & Proportion, Number Series, Age/Work/Motion Word Problems, Interest & Statistics

Covers the Numerical Ability section of the CSC CSE-PPT (Professional and Sub-Professional): PEMDAS, Fractions, Decimals, Percentages, Ratio and Proportion, Number & Alphanumeric Series, Age Problems, Work & Tank Problems, Distance-Speed-Time Motion Problems, Mixture Problems, Simple & Compound Interest, Markup/Discount, and Basic Statistics/Probability.

Level: intermediate
Languages: en → en
Cards: 32
Markdown: CSC CSE-PPT Numerical Reasoning: Fractions/Decimals/Percentages, Ratio & Proportion, Number Series, Age/Work/Motion Word Problems, Interest & Statistics (.md)

Flashcards (32)