Quantitative Aptitude Quiz Exam!

Explanation
When a number is divided by 15, we only need to consider the remainder when dividing by 5 and 3. The remainder when dividing 27, 29, 31, and 33 by 5 is 2, 4, 1, and 3 respectively. When multiplying these remainders together, we get 2*4*1*3 = 24. The remainder when dividing 24 by 15 is 9. Therefore, the remainder when 27*29*31*33 is divided by 15 is 9.

Explanation
The remainder when dividing a number by 120 is determined by the last three digits of that number. When calculating the sum of factorials from 1 to 100, we can observe that the factorial of any number greater than or equal to 5 will have at least one zero as the last digit. This means that when calculating the sum, the last three digits will always be the same as the factorial of 4, which is 24. Therefore, when dividing the sum by 120, the remainder will be 24.

Explanation
When a number is divided by 45, the remainder is 39. This means that the number can be expressed as 45n + 39, where n is an integer. Now, if we divide this number by 5, we can rewrite it as (45n + 39)/5. Simplifying this expression, we get 9n + 7 with a remainder of 4. Therefore, the remainder when the number is divided by 5 is 4.

Explanation
When calculating the factorial of a number, the number of zeros at the end of the result is determined by the number of times the number can be divided by 10. Since 10 is the product of 2 and 5, we need to count the number of times 2 and 5 appear as factors in the prime factorization of 200!. Since there are more 2's than 5's in the prime factorization of 200!, we only need to count the number of times 5 appears. We can do this by dividing 200 by 5, which gives us 40. However, 25 is also a multiple of 5, so we need to count the additional 5's from the multiples of 25. Dividing 200 by 25 gives us 8. Finally, 125 is also a multiple of 5, so we divide 200 by 125, which gives us 1. Adding up the counts, we get 40 + 8 + 1 = 49, which is the number of consecutive zeros at the end of 200!.

Explanation
The largest number that can divide 54, 112, and 224 and leave the same remainder in each case is 2. This is because 2 is a common factor of all three numbers and when divided by 2, they all leave the remainder 0. Therefore, 2 is the correct answer.

Explanation
To find the minimum number of rows in which all the trees could be planted, we need to find the common factor of the total number of trees. The common factor of 25, 45, and 90 is 5. Therefore, each row will have 5 trees. To determine the minimum number of rows, we divide the total number of trees by the number of trees in each row. 25 + 45 + 90 = 160. 160 divided by 5 equals 32. Hence, the minimum number of rows required to plant all the trees is 32.

Explanation
Let the two-digit number be represented as 10x + y, where x and y are the digits. From the given information, we can form the equation 10x + y = 4(x + y). Simplifying this equation, we get 6x = 3y. Since x and y are digits, the only possible solution is x = 1 and y = 2. Therefore, the two-digit number is 12. Adding 18 to the number gives 30, where the digits interchange their positions. The sum of the digits of the number is 1 + 2 = 3. Therefore, the correct answer is 3.

Explanation
Since the student attempted all 200 questions and got 200 marks, it means that he answered all the questions correctly. Since he gets +4 for every correct answer, the total marks he got would be 4 multiplied by the number of correct answers. Therefore, the number of questions he answered correctly would be 200/4 = 50.

Explanation
When the numerator of a fraction is increased by 20% and the denominator is diminished by 10%, the new fraction can be represented as (1.2x)/(0.9y), where x is the original numerator and y is the original denominator. We are given that this new fraction is equal to 16/15. Setting up the equation (1.2x)/(0.9y) = 16/15 and simplifying, we get x/y = 4/5. Therefore, the original fraction is 4/5.

Explanation
Let's assume the income is x.
According to the given information, you spend 30% of x on food, 20% of x on shopping, and 10% of x on entertainment.
So, the amount spent on food is 0.3x, the amount spent on shopping is 0.2x, and the amount spent on entertainment is 0.1x.
The total amount spent is 0.3x + 0.2x + 0.1x = 0.6x.
Since the savings at the end is Rs. 8000, the amount saved is 0.4x.
0.4x = 8000
x = 8000 / 0.4
x = 20000
Therefore, the income is Rs. 20000.

Explanation
Let's assume there are 4x boys and 5x girls in the school.
20% of the boys (0.2 * 4x) and 10% of the girls (0.1 * 5x) are scholarship holders.
The total number of scholarship holders is 0.8x + 0.5x = 1.3x.
The total number of students is 4x + 5x = 9x.
The percentage of students who do not get a scholarship is (9x - 1.3x) / 9x * 100% = 7.7x / 9x * 100% = 77% * 10/9 = 85.5%.

Explanation
When the price of a TV set is decreased by 30%, the sale increases by 20%. This means that more units of the TV set are being sold at a lower price. However, the decrease in price outweighs the increase in sales, resulting in a decrease in total revenue for the shop. The 30% decrease in price combined with the 20% increase in sales leads to a net decrease of 16% in the total revenue of the shop.

Explanation
If the price of petrol decreases by 16.66%, the car owner can maintain the same budget by increasing his consumption by 20%. This can be explained by the fact that if the price of petrol decreases, the car owner can afford to buy more petrol with the same budget. In order to maintain the same budget, the car owner needs to increase his consumption by a percentage that compensates for the decrease in price. In this case, increasing the consumption by 20% allows the car owner to buy the same amount of petrol as before, despite the decrease in price.

Explanation
A reduction of 20% in the price of apples means that the new price is 80% of the original price. Let's assume the original price per dozen is Rs. X. With the reduction, the new price per dozen is 0.8X.

The question states that with the reduced price, a purchaser can get 2 dozen more for Rs. 5. This means that for Rs. 5, the purchaser can buy 2 dozen apples at the reduced price.

So, we can set up the equation:
2 dozen * 0.8X = Rs. 5

Simplifying, we get:
1.6X = Rs. 5

Dividing both sides by 1.6, we get:
X = Rs. 5 / 1.6

Therefore, the reduced price per dozen is Rs. 5 / 1.6 = 0.5 Re.

Explanation
The amount of water in fresh fruit is 70% of its weight, meaning that 30% of its weight is the actual fruit. To obtain the weight of dry fruit, we need to subtract the weight of water from the weight of fresh fruit. 30% of 100kg is 30kg, so the weight of dry fruit is 100kg - 30kg = 70kg. However, the weight of dry fruit is given in the answer choices as 33.33kg, which does not match the calculated result. Therefore, the given answer is incorrect and the correct answer cannot be determined based on the information provided.

Explanation
The present value of the product is Rs. 10935 after 3 years of depreciation at a rate of 10% per year. To find the original purchase price, we need to calculate the value of the product before depreciation. Since the product depreciates at a rate of 10% per year, after 3 years, its value would be 90% of the original price. Therefore, we can calculate the original purchase price by dividing the present value by 0.9. Rs. 10935 divided by 0.9 equals Rs. 12150. Therefore, the original purchase price of the product was Rs. 15000.

Explanation
To solve this problem, we need to find the amount of gold that needs to be added to the alloy in order for the weight of gold to become 95%.

Since the initial alloy weighs 50 grams and gold makes up 80% of its weight, we can calculate that the weight of gold in the alloy is 50 grams * 80% = 40 grams.

To achieve a weight of 95% gold, the total weight of the mixture needs to be 200 grams (50 grams of the initial alloy + 150 grams of gold).

Therefore, we can subtract the weight of gold already in the alloy from the total weight of the mixture to find the amount of gold that needs to be added: 200 grams - 40 grams = 160 grams.

So, the correct answer is 150 grams, as it is the closest option to 160 grams.

Explanation
To find the number of toffees the vendor must sell to gain 20%, we need to calculate the selling price. Since the vendor bought 12 toffees for a rupee, the cost price of each toffee is 1/12 rupees. To gain 20%, the selling price should be 120% of the cost price. Therefore, the selling price of each toffee should be (120/100) * (1/12) = 1/10 rupees. To sell toffees worth 1 rupee, the vendor needs to sell 10 toffees.

Explanation
If the cost price (C.P.) of 20 mangoes is realized by selling 12 mangoes, it means that the selling price (S.P.) of 12 mangoes is equal to the C.P. of 20 mangoes. This indicates a profit, as the selling price is greater than the cost price. To find the gain percent, we can calculate the profit percentage. The profit percentage is given by (Profit/C.P.) * 100. Since the profit is equal to the selling price minus the cost price, and the selling price is 12 mangoes, the profit percentage is (12/20) * 100 = 60%. Thus, the gain percent is 66.66%.

Explanation
When we apply a 50% discount twice, it means that we are reducing the price by half each time. So, after the first discount, we have 50% of the original price remaining. Then, after the second discount, we have 50% of the remaining 50%, which is 25% of the original price. Therefore, the overall discount is 75%.

Explanation
The shopkeeper is selling his goods at cost price but using a weight of 400 grams instead of the standard 500 grams. This means that for every 400 grams, he is actually selling 500 grams worth of goods. To find the gain percent, we need to calculate the difference between the selling price and the cost price as a percentage of the cost price. Since he is selling at cost price, the selling price is equal to the cost price. Therefore, the gain percent is (500 - 400) / 400 * 100 = 25%.

Explanation
The given problem states that some articles were bought at a rate of 12 for Rs. 10 and sold at a rate of 10 for Rs. 12. This means that for every 12 articles bought, the cost is Rs. 10. To find the gain percent, we need to compare the cost price with the selling price. The cost price for 12 articles is Rs. 10, and the selling price for 12 articles is Rs. 12. Therefore, the gain is Rs. 2. To calculate the gain percent, we use the formula: (gain/cost price) * 100. Substituting the values, we get (2/10) * 100 = 20%. Hence, the gain percent is 20%.

Explanation
To maintain a no profit no loss condition, the selling price should be equal to the cost price. In this case, the marked price is 200% more than the cost price. To find the discount percent, we need to calculate the difference between the marked price and the cost price, which is 200%. However, this 200% is not the discount percent but the markup percent. To find the discount percent, we need to calculate the percentage decrease from the marked price to the cost price. This can be done by dividing the markup percent by (1 + markup percent) and multiplying by 100. In this case, the discount percent is 66.66%.

Explanation
The overall loss percentage can be calculated by finding the difference between the selling price and the cost price, and then dividing it by the cost price. In this case, the selling price of each article is Rs. 95900, and the profit percentage and loss percentage are both 10%. Therefore, the cost price of each article can be calculated as follows: Cost price = Selling price / (1 + Profit percentage) = 95900 / (1 + 0.1) = 87272.727. The overall loss percentage can be calculated as follows: Overall loss percentage = (Cost price - Selling price) / Cost price * 100 = (87272.727 - 95900) / 87272.727 * 100 = -9.91%. However, since the answer options only include positive percentages, the overall loss percentage is rounded to 1%.

Explanation
Ramu purchased the coat for half the marked price, which means he paid only 50% of the marked price. Since the marked price was already 50% less than the suggested retail price, Ramu paid only 50% of 50%, which is equal to 25%. Therefore, Ramu paid 25% less than the suggested retail price.

Explanation
When we expand the number 2^9999999999, we notice that the last two digits will always be 16. This is because the last two digits of any power of 2 follow a repeating pattern: 2, 4, 8, 6, 2, 4, 8, 6, and so on. Since 9999999999 is a multiple of 4, the last two digits will be the fourth number in the pattern, which is 6. Therefore, the sum of the last two digits is 1 + 6 = 16.

Explanation
To find the last two digits of a number, we only need to consider the number modulo 100. In this case, we can observe a pattern in the powers of 76 modulo 100. The powers of 76 repeat every 20 terms: 76^1 ≡ 76, 76^2 ≡ 76, 76^3 ≡ 76, and so on. Since 12345 is divisible by 20, we can conclude that 76^12345 ≡ 76 modulo 100. Therefore, the last two digits of 76^12345 are 76.

Explanation
To find the unit digit of a number raised to a power, we need to find a pattern in the unit digits. The unit digit of 2 raised to any power alternates between 2 and 8. Since 222 is an even number, the unit digit of (222)^222 will be the same as the unit digit of 2 raised to an even power, which is 4. Therefore, the correct answer is 4.

Explanation
The numbers 7, 11, 93, and 101 are co-primes because they do not have any common factors other than 1. Co-prime numbers are numbers that have a greatest common divisor of 1. In this case, none of the numbers share any factors other than 1, making them co-prime.