Mathematics and Logical Reasoning Quiz

The video tutorial covers three math problems. Problem 237 involves calculating the percentage reduction in hours worked after a wage increase to maintain the same weekly income. Problem 238 deals with finding the length of a picture within a frame, given the area and ratio constraints. Problem 239 uses a Venn diagram to determine the number of students majoring in both chemistry and biology, given certain conditions.

An employee's hourly wage increased by 25%, and they want to keep their weekly income the same. By what percentage should they reduce their working hours?

• 10%

• 30%

• 20%

• 25%

If an employee's new hourly wage is 1.25 times the old wage, what fraction of the original hours should they work to maintain the same income?

• 1/2

• 3/4

• 4/5

• 5/6

A rectangular frame has a length of 18 inches and a width of 15 inches. If a picture inside has the same area as the frame, what is the length of the picture?

• 12 inches

• 9 inches

• 15 inches

• 9√2 inches

Given the ratio of length to width of a frame is 6:5, what is the ratio of the length to width of a picture with the same area as the frame?

• 8:7

• 7:6

• 6:5

• 5:4

If the area of a picture is equal to the area of a frame, and the frame's dimensions are 18x15, what is the area of the picture?

• 180 square inches

• 225 square inches

• 135 square inches

• 270 square inches

In a college, 130 students major in chemistry and 150 in biology. If at least 30 students are not majoring in either, what is the minimum number of students majoring in both?

• 110

• 130

• 120

• 100

If 200 students are majoring in sciences, with 130 in chemistry and 150 in biology, what is the maximum number of students majoring in both subjects?

• 160

• 130

• 140

• 150

How many students are majoring in either chemistry or biology if 30 students are not majoring in either?

• 170

• 190

• 180

• 200

If 30 students are not majoring in either chemistry or biology, how many students are majoring in at least one of these subjects?

• 170

• 180

• 190

• 200

What is the total number of students majoring in chemistry or biology, including those majoring in both?

• 250

• 230

• 280

• 200