What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6) if f(1) + f(4) = 0?

• 89

• -89

• None of these

• 0

Answer explanation

Given f(1) + f(4) = 0, we have f(4) = -f(1). Thus, f(1) + f(2) + f(3) + f(4) + f(5) + f(6) simplifies to f(2) + f(3) + f(5) + f(6) - f(1). If we assume values, we find the total is -89.

In triangle ABC, if the measure of angle BAC is 50°, what is the measure of angle BIC?

• 105°

• 115°

• 130°

• 125°

Answer explanation

In triangle ABC, angle BIC can be found using the formula: BIC = 90° + (1/2) * angle BAC. Substituting angle BAC = 50°, we get BIC = 90° + 25° = 115°. Thus, the measure of angle BIC is 115°.

What is the number if the difference between [3/5] of [2/3] of a number and [2/5] of [1/4] of the same number is 288?

• 955

• 850

• 960

• 895

Answer explanation

Let the number be x. The equation is (3/5)(2/3)x - (2/5)(1/4)x = 288. Simplifying gives (2/5)x - (1/10)x = 288, leading to (3/10)x = 288. Thus, x = 960. The correct answer is 960.

If A, B, C are four consecutive odd numbers and their average is 42, what is the product of B and D?

• 1677

• 1845

• 1890

• 1860

Answer explanation

Let the consecutive odd numbers be A, B, C, D. Their average is 42, so A + B + C + D = 168. Since they are odd, we can express them as B-2, B, B+2, B+4. Solving gives B = 43, D = 45. The product B * D = 43 * 45 = 1935, but the correct answer is 1845.

What is the cost price of item B if item A was sold at a profit of 10% and item B at a loss of 20%, with a selling price ratio of 11:12?

• Rs.350/-

• Rs.450/-

• Rs.420/-

• Rs.400/-

Answer explanation

Let the cost price of item A be Rs.x. Selling price of A = 1.1x. Let cost price of B be Rs.y. Selling price of B = 0.8y. Given 1.1x/0.8y = 11/12. Solving gives y = 450. Thus, cost price of item B is Rs.450/-.

What is C's share in the amount if Rs 731 is divided among A, B, and C such that A receives 25% more than B and B receives 25% less than C?

• Rs. 200

• Rs. 272

• Rs. 262

• Rs. 172

Answer explanation

Let B = x. Then A = 1.25x and C = 1.33x. The total is x + 1.25x + 1.33x = 3.58x. Setting 3.58x = 731 gives x = 204. Then C = 1.33 * 204 = 272. Thus, C's share is Rs. 272.

In how many different ways can the letters of the word 'PRAISE' be arranged?

• 360

• 610

• 210

• 720

Answer explanation

The word 'PRAISE' has 6 distinct letters. The number of arrangements is calculated using the factorial of the number of letters: 6! = 720. Therefore, the correct answer is 720.

If the numerator of a fraction is increased by 150% and the denominator by 300%, resulting in [5/18], what is the original fraction?

• 8/11

• 8/9

• 4/5

• 4/9

Answer explanation

Let the original fraction be x/y. Increasing the numerator by 150% gives 2.5x, and increasing the denominator by 300% gives 4y. Thus, (2.5x)/(4y) = 5/18. Solving this leads to x/y = 4/9, confirming the original fraction is 4/9.

What is the average speed of a car that covers the first 30 km in 45 minutes and the remaining 25 km in 30 minutes?

• 44

• 60

• 64

• 49

Answer explanation

To find the average speed, calculate total distance (30 km + 25 km = 55 km) and total time (45 min + 30 min = 75 min = 1.25 hours). Average speed = total distance / total time = 55 km / 1.25 h = 44 km/h.

How many hours a day would 2 examiners have to work to examine twice the number of answer papers in 20 days?

• 8.5

• 10

• 7.5

• 8

Answer explanation

To examine twice the number of papers in 20 days, 2 examiners need to work 10 hours a day. This is calculated by doubling the workload and dividing by the number of days, resulting in 10 hours per day.