Raju is planning to get wireless Internet service at his house. Two service providers, A and B, offered different rates as shown in the table below. If Raju plans on using 25 hours of internet service per month, which of the following statements is true ? [2 Mark]
Internet Service Rates | |||
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Provider | Free Hours | Base Charge | Hourly Charge |
A | 17.5 | ₹ 20 | ₹ 1.00 |
B | 20 | ₹ 20.00 | ₹ 1.50 |
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Solution
When used for 25 hours per month, provider A will cost ₹ 20 + 7.5 × ₹ 1 (for the hourly charge above the free hours).
This equals ₹ 27.50.
Provider B will cost ₹ 20 plus 5 × ₹ 1.50 (for the hourly charge above the free hours).
This equals ₹ 20 + ₹ 7.50 = ₹ 27.50 as well, so option (c) is the correct answer.
If \(\sqrt{a + b} + \sqrt{b + c} = \sqrt{a + 2b + c}\) , then b is equal to [2 Mark]
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Solution
\(\sqrt{a + b} + \sqrt{b + c} = \sqrt{a + 2b + c}\)
squaring on both sides
\(a + b + b + c + 2\sqrt{\left (a + b \right )\left (b + c \right )} = a + 2b + c\)
⇒ \(2\sqrt{\left (a + b \right )\left (b + c \right )} = 0\)
(a + b) (b + c) = 0
b = –a, b = –c
Saurabh has a paper route. Each morning, he delivers 37 newspapers to customers in his neighborhood. It takes Saurabh 50 minutes to deliver all the papers. If Saurabh is sick or has other plans, his friend Vikas, who lives on the same street, will sometimes deliver the papers for him. Which one of the following statements must be true based on the above? [2 Mark]
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Solution
The fact that Saurabh and Vikas live on the same street indicates that they live in the same neighborhood.
There is no support for any of the other choices.
During the last six years, the number of practicing physicians has increased by about 20%. During the same time period, the number of health care managers has increased by more than 600%. These percentages mean that many doctors have lost the authority to make their own schedules, determine the fees that they charge, and decide on prescribed treatments. This paragraph best supports the statement that doctors [2 Mark]
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Solution
The author of this statement suggests that doctors are less independent.
The author stresses that many doctors have lost authority.
There is no support for the opinion that doctors resent the health-care managers, however – which rules out option (a).
The doctors’ training is never mentioned option (b) Doctors may care about their patients option (c), but this information is not part of the paragraph.
A carpenter is buiding a frame for a wall painting. The painting is in the shape of rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 20 inches. How many inches of framing material does the carpenter need to frame the painting ? [2 Marks]
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Solution
Since the shorter side of the rectangle is 20 inches, and the sides of the rectangle have the ratio of 3:2 means that the long side is found by the equation 3⁄2 = x⁄20, which becomes x = 30 inches.
The length of framing needed will be found by computing the perimeter of the rectangle by 2(30) + 2(20) = perimeter = 60 + 40 = 100 inches.
Each of three in Shilpa Real Estates has 8 persons serving on is board of directors. If exactly 4 persons serve on 3 boards each pair of firms has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors ?
During a trip, Monu traveled x percent of the total distance at an average speed of 40 kmph and the rest of the distance at an average speed of 60 kmph. In terms of x, what was Monu’s average speed in the entire trip?
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Solution
Assume for simplicity that the total distance of Monu’s trip is 100 km.
Then the table below gives the pertinent information
Distance Rate \(\mathbf{Time = \frac{Distance}{Rate}}\) x 40 x⁄40 100 - x 60 \(\frac{100 - x}{60}\) The total time for Monu’s trip is
\(\frac{x}{40} + \frac{100 - x}{60} = \frac{3x}{120} + \frac{2\left ( 100 - x \right )}{120}\)
= \(\frac{3x + 2\left ( 100 - x \right )}{120}\)
= \(\frac{3x + 200 - 2x }{120} = \frac{x + 200}{120}\)
Monu’s average speed over the entire trip is
\(\frac{Total \; Distance}{Total \; Time} = \frac{100}{\frac{x + 200}{120}} = \frac{12,000}{x + 200}\)
At the beginning of a class, a classroom has 4 empty chairs and all students are seated. No student leaves the classroom, and additional students equal to 25 percent of the number of students already seated enter the class late and fill the empty chairs. What is total number of chairs in the classroom ?
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Solution
Let x be the number of students already seated at the beginning of class then the four additional late-comers are equal to 25 percent of that.
So, 0.25x = 4
x = 16
The number of students originally seated was 16. But the question asks not about the number originally seated, but about the total number of chairs in the classroom.
So, we must add in the four late-comers and 16 + 4 = 20 chairs.
Choose the best word to fill the blank. According to the terms of the agreement, if Nicole defaulted on her loan, she would have to __________ her house and car, both which would become property of the bank.
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Solution
To forfeit (v.) means to be deprived of or lose the right to by the act of a crime, offense, fault, breach, or error.
Choose the best word to fill the blank. When Melinda arrived in the impoverished city, she was immediately _______ by bands of children begging for food.
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Solution
To accost (v.) means to approach and speak to someone,usually in a bold and aggressive manner as with a demand.