General Practice Test 1 Nddc Scholarship
General Practice Test 1 Nddc Scholarship
Question 71
You're driving your car on the highway at 75 mph, and you notice a sign that says you are 75 miles from your destination. So if you continue driving at that speed, you'd be there in an hour. When you have driven one mile and you are now 74 miles from your destination, you drop your speed down to 74 mph. So, you drive that first mile at 75 mph; when you are 74 miles from your destination, you drop your speed down to 74 mph; and then 73 mph, 72 mph ... and so on. Until, finally, you get down to 1 mile from your destination and you're driving at one mile per hour. If you do this, how long is it going to take you to travel the entire 75 miles, rounding it to the nearest hour?
Each mile is travelled at a different speed. The total time is the sum of the time taken for each mile:\[\text{Total time} = \frac{1}{75} + \frac{1}{74} + \frac{1}{73} + \cdots + \frac{1}{1}\]This is the harmonic series up to 75 terms.
The sum of this series is approximately:\[\approx \ln(75) + \gamma \approx 4.317 + 0.577 = 4.894\]Rounding to the nearest hour gives 5 hours.
The sum of this series is approximately:\[\approx \ln(75) + \gamma \approx 4.317 + 0.577 = 4.894\]Rounding to the nearest hour gives 5 hours.
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Question 72
Assuming you have enough coins of 1, 5, 10, 25 and 50 cents, how many ways are there to make change for a dollar?
This is a classic combinatorial problem involving partitioning 100 cents using denominations of 1, 5, 10, 25, and 50 cents. By systematically counting all unique combinations without regard to order, the total number of ways to make change sums to 292.
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Question 73
If I have a normal coin with a heads and tails; a 6-sided die; and a bag containing 4 blue and 2 red marbles, what is the probability of me flipping a heads, rolling a 4, and picking out a red marble?
Probability of flipping a head = \(\frac{1}{2}\).
Probability of rolling a 4 on a fair die = \(\frac{1}{6}\).
Probability of picking a red marble = \(\frac{2}{6} = \frac{1}{3}\).
Multiply the independent probabilities:\[\frac{1}{2} \times \frac{1}{6} \times \frac{1}{3} = \frac{1}{36}\]\[\frac{1}{36} \approx 0.027\]This gives the required probability.
Probability of rolling a 4 on a fair die = \(\frac{1}{6}\).
Probability of picking a red marble = \(\frac{2}{6} = \frac{1}{3}\).
Multiply the independent probabilities:\[\frac{1}{2} \times \frac{1}{6} \times \frac{1}{3} = \frac{1}{36}\]\[\frac{1}{36} \approx 0.027\]This gives the required probability.
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Question 74
Can you replace the question marks with maths symbols ( + - / x ) and make the equation correct:
(7 ? 1) ? (5 ? 2) ? (2 ? 3) = 20
(7 ? 1) ? (5 ? 2) ? (2 ? 3) = 20
By testing operations, using addition consistently gives a correct structure:\[(7 + 1) + (5 + 2) + (2 + 3) = 8 + 7 + 5 = 20\]This satisfies the equation exactly, confirming the correct choice.
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Question 75
A person that represents the interest of his/her country abroad is known as ----------------
An ambassador is an official diplomatic representative sent by a country to another nation to represent its interests, maintain relations, and handle international affairs on behalf of the home country.
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Question 76
There are--------- continents in the world
The widely accepted number of continents is seven: Africa, Antarctica, Asia, Australia, Europe, North America, and South America. These divisions are based on geographical and cultural distinctions.
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Question 77
The dentition of an adult is made up of the following-------------
Adult human dentition consists of four main types of teeth: incisors for cutting, canines for tearing, bicuspids (premolars) for crushing, and molars for grinding. These categories describe the functional arrangement of teeth in the mouth.
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Question 78
A person who studies stars is called---------------
A person who studies stars and celestial bodies is properly called an astronomer. However, among the given options, 'astrologer' is the closest related term, although it refers to someone who studies the supposed influence of stars and planets on human affairs rather than their scientific properties. The other options are unrelated to the study of stars.
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Question 79
bat, sheep, __, elephant
The sequence arranges mammals in increasing order of size. A bat is smaller than a sheep, and an elephant is very large. The missing animal must therefore be larger than a sheep but smaller than an elephant. A horse fits this condition appropriately, while the others are either too small or too large.
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Question 80
Albert is a keen dog admirer and over the years has had a number of dogs. He has had an Alsatian, a Dalmatian, a Poodle and a Great Dane, but not necessarily in that order. Albert had Jamie first. The Dalmatian was an adored pet before the Great Dane. Sammy the Alsatian, was the second dog Albert loved. Whitney was housed before the Poodle and Jimmy was not a Great Dane. Can you tell each of the dogs' name and the order in which Albert had them?
From the clues:
Jamie was the first dog.
Sammy the Alsatian was the second dog.
The Dalmatian came before the Great Dane.
Whitney came before the Poodle.
Jimmy was not the Great Dane.
Arranging these constraints consistently leads to the sequence where Jamie is the Dalmatian first, followed by Sammy the Alsatian, then Whitney the Great Dane, and finally Jimmy the Poodle. This arrangement satisfies all the given conditions without contradiction.
Jamie was the first dog.
Sammy the Alsatian was the second dog.
The Dalmatian came before the Great Dane.
Whitney came before the Poodle.
Jimmy was not the Great Dane.
Arranging these constraints consistently leads to the sequence where Jamie is the Dalmatian first, followed by Sammy the Alsatian, then Whitney the Great Dane, and finally Jimmy the Poodle. This arrangement satisfies all the given conditions without contradiction.
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