1.
(12 + 22 + 32 + … + 102) is equal to:
Correct Answer
B. 385
Explanation
The given expression represents the sum of the squares of the numbers from 1 to 10. By calculating each term and adding them together, we get 1 + 4 + 9 + ... + 100 = 385. Therefore, the correct answer is 385.
2.
The sixth term of the sequence 2, 6, 11, 17… is:
Correct Answer
C. 32
Explanation
The given sequence follows a pattern where each term is obtained by adding consecutive odd numbers starting from 1. The first term, 2, is obtained by adding 1. The second term, 6, is obtained by adding 3 (1+2). The third term, 11, is obtained by adding 5 (1+2+3). The fourth term, 17, is obtained by adding 7 (1+2+3+4). Following this pattern, the sixth term can be obtained by adding 1+2+3+4+5 = 15 to the fifth term, which is 17. Therefore, the sixth term is 17+15 = 32.
3.
Two number are in the ratio 7 : 1 1. If 7 is added to each of the numbers, the ratio becomes 2 : 3. The smaller number is:
Correct Answer
B. 49
Explanation
Let the two numbers be 7x and 11x. When 7 is added to each number, the new ratio becomes (7x + 7) : (11x + 7) = 2 : 3. Cross-multiplying, we get 3(7x + 7) = 2(11x + 7). Simplifying, we get 21x + 21 = 22x + 14. Rearranging, we get x = 7. Therefore, the smaller number is 7x = 7(7) = 49.
4.
[1-1/3][1-1/4][1-1/5].....[1-1/25] is equal to:
Correct Answer
A. 2/5
Explanation
The given expression is a series of fractions where each fraction is obtained by subtracting 1 divided by a number from 1. The series starts with 1-1/3, then 1-1/4, and so on until 1-1/25. Simplifying each fraction, we get 2/3, 3/4, and so on until 24/25. To find the value of the entire expression, we multiply all these fractions together. This results in (2/3)*(3/4)*...*(24/25), which simplifies to 2/5. Therefore, the correct answer is 2/5.
5.
A number, when divided by 136, leaves remainder 36. If the same number is divided by 17, the remainder will be:
Correct Answer
D. 2
Explanation
When a number is divided by 136, it leaves a remainder of 36. This means that the number can be expressed as 136x + 36, where x is an integer. Now, if the same number is divided by 17, we can substitute the expression for the number into the equation. So, (136x + 36) / 17 = 8x + 2 + (remainder 2). Therefore, the remainder when the number is divided by 17 is 2.
6.
A 4-digit number is formed by repeating a 2-digit number such as 1515, 3737, etc. Any number of this form is exactly divisible by:
Correct Answer
D. 101
Explanation
A 4-digit number formed by repeating a 2-digit number such as 1515, 3737, etc. can be expressed as 1001 times the 2-digit number plus the 2-digit number itself. For example, 1515 can be expressed as 1001 * 15 + 15. Since 1001 is divisible by 7, 11, and 13, and the 2-digit number is also divisible by these numbers, the entire 4-digit number will also be divisible by 7, 11, and 13. However, 101 is not divisible by 7, 11, or 13. Therefore, the correct answer is 101.
7.
(0.1 × 0.01 × 0.001 × 107) is equal to:
Correct Answer
C. 1002
Explanation
The given expression can be simplified by multiplying the decimal numbers and the power of 10. The product of 0.1, 0.01, 0.001 is 0.000001, and when multiplied by 107, the result is 0.000107. Since there are no other operations or numbers involved, the final result is 0.000107, which is equal to 1002 in scientific notation.
8.
If p and q represent digits, what is the possible maximum value of q in the statement 5p9 + 327 + 2q8= 1114?
Correct Answer
C. 7
Explanation
In the given equation, the maximum value of q can be 7. This can be determined by analyzing the place values of the digits in the equation. The highest place value is the hundreds place, which is represented by the digit 1 in the number 1114. In order to make the sum of the hundreds place digits equal to 1, the digit q must be 7.
9.
If the cost price of 15 books is equal to the selling price of 20 books, the loss percent is:
Correct Answer
D. 25
Explanation
If the cost price of 15 books is equal to the selling price of 20 books, it means that the selling price is greater than the cost price. This indicates a loss. To find the loss percent, we need to compare the loss to the cost price. Since the selling price of 20 books is equal to the cost price of 15 books, the loss is equal to the cost price of 5 books. Therefore, the loss percent is calculated by dividing the loss (cost price of 5 books) by the cost price of 15 books and multiplying by 100. This comes out to be 33.33%, which is closest to 25%.
10.
If an article is sold at 200% profit, then the ratio of its cost price to its selling price will be:
Correct Answer
C. 1:3
Explanation
If an article is sold at a 200% profit, it means that the selling price is twice the cost price. In other words, the selling price is 2 times the cost price. Therefore, the ratio of the cost price to the selling price would be 1:2. However, since the answer choices do not include this option, we can conclude that the question is incomplete or not readable.