Math and Number Puzzles

0.3535... is 35/99 and 0.2525... is 25/99. Their sum is 60/99. Simplified to lowest terms, this is 20/33. The product of the numerator (20) and denominator (33) is 20 * 33 = 660.

After the first 10% reduction, the price becomes 0.9x. The subsequent 20% reduction applies to this new price: 0.8 × 0.9x = 0.72x. Option C simplifies to x - 0.3x + 0.02x = 0.72x, which correctly accounts for the compound discount.

Since x = -2, substitute this into the first equation: 2(-2) + 3y = 5. This simplifies to -4 + 3y = 5, then 3y = 9, so y = 3. The intersection point is (-2, 3).

To find the smallest number of whole pizzas needed for lunch, we need to find the total amount of pizza that the group of 7 friends will eat.

Each person eats at least 3/4 of a pizza, which can be written as 3/4 * 1 = 3/4 of a pizza per person.

To find the total amount of pizza eaten by the group, we multiply the amount eaten per person by the number of people:

(3/4) * 7 = 21/4 = 5.25 pizzas

Since we cannot have a fraction of a pizza, we round up to the nearest whole number. Therefore, the smallest number of whole pizzas needed for lunch is 6.

Now let's go through each option and explain why it is right or wrong:

A. 6: This option is correct. If each person eats at least 3/4 of a pizza, then 6 whole pizzas would be enough for the group of 7 friends.

B. 5: This option is incorrect. 5 whole pizzas would not be enough for the group of 7 friends, as each person eats at least 3/4 of a pizza.

C. 28: This option is incorrect. 28 whole pizzas would be more than enough for the group of 7 friends, as each person eats at least 3/4 of a pizza.

D. 11: This option is incorrect. 11 whole pizzas would not be enough for the group of 7 friends, as each person eats at least 3/4 of a pizza.

The correct answer is A. 6.

Since 75% of the solution is water, the remaining 25% must be pure acid. For 20 liters of solution, 25% × 20 = 5 liters of pure acid. Option A (15) represents the water portion, not the acid.

The sequence is based on squaring the digits of the previous number and adding them: 7^2 + 2^2 = 53; 5^2 + 3^2 = 34; 3^2 + 4^2 = 25; 2^2 + 5^2 = 29. Finally, 2^2 + 9^2 = 4 + 81 = 85.