GMAT Quantitative Practice

Using the identity (x + y)^2 = x^2 + y^2 + 2xy, we can solve for x^2 + y^2: (x + y)^2 = x^2 + y^2 + 2xy 10^2 = x^2 + y^2 + 2(21) 100 = x^2 + y^2 + 42 x^2 + y^2 = 100 - 42 = 58.

In the given code, each letter is represented by the sum of its position in the alphabet. For example, D (4th letter) is represented by 4, O (15th letter) is represented by 15, and G (7th letter) is represented by 7. Similarly, B (2nd letter) is represented by 2, A (1st letter) is represented by 1, and T (20th letter) is represented by 20. Therefore, BAT is written as 132.

The relative speed of the two trains is 70 mph + 60 mph = 130 mph. Therefore, it will take (1000 miles) / (130 mph) = 7.69 hours for the two trains to meet. Since the first train leaves at 10:00 AM and the second train leaves at 11:00 AM, the two trains will meet at 10:00 AM + 7.69 hours = 2:00 PM.

Number of women employees = 100 * 40% = 40 Number of men employees = 100 * 60% = 60 Number of married women employees = 40 * 20% = 8 Number of married men employees = 60 * 30% = 18 Total number of married employees = 8 + 18 = 26.

log(x + 1) - log(x - 1) = 2 log((x + 1)/(x - 1)) = 2 (x + 1)/(x - 1) = 10^2 x + 1 = 100(x - 1) x + 1 = 100x - 100 99x = 101 x = 101/99 = 3.

Sale price = Original price - Discount Discount = 20% of $20 = $4 Sale price = $20 - $4 = $16.

Area of the room = Length x Width Area = 12 feet x 8 feet = 96 square feet.

Average speed = Distance traveled / Time taken Average speed = 240 miles / 4 hours = 60 miles per hour.

Let the original number be x. Increased number = x + 20% of x = x + 0.2x = 1.2x Percentage decrease required = (Increased number - Original number) / Increased number x 100% = (1.2x - x) / 1.2x x 100% = 0.2x / 1.2x x 100% = 20%.

Profit in the second year = Profit in the first year + 10% of Profit in the first year Profit in the second year = $100,000 + 0.1 x $100,000 = $110,000.

Number of men employees = 100 * 60% = 60 Number of women employees = 100 * 40% = 40 Number of married men employees = 60 * 20% = 12 Number of married women employees = 40 * 30% = 12 Total number of married employees = 12 + 12 = 24.

The relative speed of the two trains is 70 mph + 60 mph = 130 mph. Therefore, it will take (1000 miles) / (130 mph) = 7.69 hours for the two trains to meet. Since the first train leaves at 10:00 AM and the second train leaves at 11:00 AM, the two trains will meet at 10:00 AM + 7.69 hours = 2:00 PM.

log(x + 1) - log(x - 1) = 2 log((x + 1)/(x - 1)) = 2 (x + 1)/(x - 1) = 10^2 x + 1 = 100(x - 1) x + 1 = 100x - 100 99x = 101 x = 101/99 = 3.

Sale price = Original price - Discount Discount = 20% of $20 = $4 Sale price = $20 - $4 = $16.

Area of the room = Length x Width Area = 12 feet x 8 feet = 96 square feet.