Class 11 PSA Quantitative Reasoning Test 02 (2013)

Tahir and Gagan rode in a 150 km bicycle race. The race was held on a 20 km track. Tahir averaged 30 km/h while Gagan averaged 15 km/h. How many times did Tahir pass Gagan during the race?

At 8:45 p.m. Saturday in Bangalore it is 10:15 am. Saturday in New York. Ravi wishes to ring his friend in New York at 7 am Sunday New York time. When should Ravi ring from Bangalore?

Trout are bred in a tank as fish for restaurants. Twenty trout are caught and each is tagged through the tail then released back into the tank. A week later, thirty trout are caught and it is found that two of them have a tail tag. Base on this evidence alone, what estimate can be made of the total number of trout in the tank?

The One Rupee coin weighs 4.85 g. Haji has a 2 kg bag of One Rupee coins. What is the value of this bag of coins?

Mrs. Ali gave a different number of apples to each of her live children. Any three of her children together received more apples than remaining two children. What is the least number of apples that Mrs. Ali could have given to one of her children?

Ravi sold his bicycle for Rs 1170. This was 10% less than he paid for it. How much did he pay for the bicycle?

Manu pays his rent every 4 weeks. He made his first payment on Friday February 1st 2013. When is his 3rd payment due?

Four small boys want to know their weights, but the weighing machine only weighs objects more than 40 kg. As each of the boys knows that his weight is less than this, they weigh themselves two at a time. The results of all possible paired weighing are: 48 kg, 49 kg, 52 kg, 53 kg, 56 kg and 57 kg. Mohinda, the tallest of the four boys, weighs the most. What does he weigh?

Arni bought a piece of timber that is 280 cm long. He wants to cut it into two pieces. The shorter piece needs to be 75% of the length of the longer piece. How long will the shorter piece be?

Paavan and Lahar are friends who have decided to travel to each other cities, 32 km apart. They both left from their own houses at 8 am, and their predicted journeys are sketched below. At which of following times did Paavan meet Labour on his journey?

All substances, whether they are solids, liquids or gases, are made up of particles. They density of a substance depends upon how close together its particles are. Solid substances usually have high densities because their particles are very close together while gases, which have large spaces between their particles, have very low densities. Density can be calculated by driving the mass (in grams) by its volume (in cubic centimetres). The table below shows the densities of different substances. Substance State \(c{m^3}\))Density (g/\(c{m^3}\) Air Gas 0.0012 Helium Gas 0.00016 Cork Solid 0.24 Oil Liquid 0.92 Water Liquid 1 Steel Solid 7.8 Lead Solid 11.3 Mercury Liquid 13.6 Objects will float in water if they have a density that is equal to, or lower than, the density of water. A piece of cork floats in water because cork has a lower density than water. A steel nail, has a density about 8 times that of water, sinks. Steel ships are able to float because they are solid pieces of metal like a nail. A ship’s hull is actually a steel shell filled mostly with air which is very light. As a result, the total mass of the ship is very low compared to its volume so it has a smaller average density. This density is lower than that of water and so the ship floats. As cargo is added to a ship, it sinks lower down into the water. Ships also float at different levels depending on the temperature of the water and whether it is fresh water or seawater. This is because the densities of warm water and cold water are different. The density of salt water is also different to the density of freshwater. The Plimsoll line shown below is a marking that can be found on the hulls of ships to indicate the safe level to which the ship can be loaded in different types of water. Which of the following statements is true?

All substances, whether they are solids, liquids or gases, are made up of particles. They density of a substance depends upon how close together its particles are. Solid substances usually have high densities because their particles are very close together while gases, which have large spaces between their particles, have very low densities. Density can be calculated by driving the mass (in grams) by its volume (in cubic centimetres). The table below shows the densities of different substances. Substance State \(c{m^3}\))Density (g/\(c{m^3}\) Air Gas 0.0012 Helium Gas 0.00016 Cork Solid 0.24 Oil Liquid 0.92 Water Liquid 1 Steel Solid 7.8 Lead Solid 11.3 Mercury Liquid 13.6 Objects will float in water if they have a density that is equal to, or lower than, the density of water. A piece of cork floats in water because cork has a lower density than water. A steel nail, has a density about 8 times that of water, sinks. Steel ships are able to float because they are solid pieces of metal like a nail. A ship’s hull is actually a steel shell filled mostly with air which is very light. As a result, the total mass of the ship is very low compared to its volume so it has a smaller average density. This density is lower than that of water and so the ship floats. As cargo is added to a ship, it sinks lower down into the water. Ships also float at different levels depending on the temperature of the water and whether it is fresh water or seawater. This is because the densities of warm water and cold water are different. The density of salt water is also different to the density of freshwater. The Plimsoll line shown below is a marking that can be found on the hulls of ships to indicate the safe level to which the ship can be loaded in different types of water. What is the mass of 1 litre of air?

All substances, whether they are solids, liquids or gases, are made up of particles. They density of a substance depends upon how close together its particles are. Solid substances usually have high densities because their particles are very close together while gases, which have large spaces between their particles, have very low densities. Density can be calculated by driving the mass (in grams) by its volume (in cubic centimetres). The table below shows the densities of different substances. Substance State \(c{m^3}\))Density (g/\(c{m^3}\) Air Gas 0.0012 Helium Gas 0.00016 Cork Solid 0.24 Oil Liquid 0.92 Water Liquid 1 Steel Solid 7.8 Lead Solid 11.3 Mercury Liquid 13.6 Objects will float in water if they have a density that is equal to, or lower than, the density of water. A piece of cork floats in water because cork has a lower density than water. A steel nail, has a density about 8 times that of water, sinks. Steel ships are able to float because they are solid pieces of metal like a nail. A ship’s hull is actually a steel shell filled mostly with air which is very light. As a result, the total mass of the ship is very low compared to its volume so it has a smaller average density. This density is lower than that of water and so the ship floats. As cargo is added to a ship, it sinks lower down into the water. Ships also float at different levels depending on the temperature of the water and whether it is fresh water or seawater. This is because the densities of warm water and cold water are different. The density of salt water is also different to the density of freshwater. The Plimsoll line shown below is a marking that can be found on the hulls of ships to indicate the safe level to which the ship can be loaded in different types of water. Why does a ship sink when a large enough hole has been torn in its hull and water enters the ship?

Liquids that have different densities form layers. The liquid with the lowest density floats at the top and the densest liquid sinks to the bottom. The diagram below shows 3 contains. Each container holds two different liquids. In total, 4 different liquids are shown. The diagram proves that

Read the following passage and answer the questions that follow: If you open up nearly any electronic device, you will see many small bead-like components with coloured stripes on them. The components are called resistors and they are used to control the amount of electrical current that flows through different circuit sections in the device. Most resistors have a central core made of a mixture of carbon and ceramic. A wire made of a material such as copper or nichrome is then wrapped around this core. Finally, the resistor is coated in enamel, leaving a wire poking out from either end of the resistor. The degree to which a resistor reduces the size of the current flowing through its branch of the circuit is called is resistance. The resistance value is measured in ohms (written as \(\Omega \)). When the resistance is increased, the current that flows through the resistor is proportionally decreased. So a resistor that has a low value of resistance allows a large amount of current to flow through it. Where two resistors are made of the same material, a long wire will have a higher resistance than a short wire of the same diameter. A very long wire will need to be wrapped around the core many more times than a short wire. This means that the resistance is also directly proportional to the number of coils. The cross-sectional area of the wire also affects the resistance. The larger the cross-section of the wire, the more easily an electric current can glow through it. In other words, the resistance of the wire is inversely proportional to the area of its cross-section. Nichrome wire with a 1 mm diameter is coiled around a 5 cm long carbon core to form a resistor. The diameter of the core is 1 cm and the wire is coiled in such a way that the entire length of the core is covered with only one layer of wire. If the resistance of the nichrome wire is 2 per metre, the wire wrapped around the core will have a total resistance that is closet to

Read the following passage and answer the questions that follow: If you open up nearly any electronic device, you will see many small bead-like components with coloured stripes on them. The components are called resistors and they are used to control the amount of electrical current that flows through different circuit sections in the device. Most resistors have a central core made of a mixture of carbon and ceramic. A wire made of a material such as copper or nichrome is then wrapped around this core. Finally, the resistor is coated in enamel, leaving a wire poking out from either end of the resistor. The degree to which a resistor reduces the size of the current flowing through its branch of the circuit is called is resistance. The resistance value is measured in ohms (written as \(\Omega \)). When the resistance is increased, the current that flows through the resistor is proportionally decreased. So a resistor that has a low value of resistance allows a large amount of current to flow through it. Where two resistors are made of the same material, a long wire will have a higher resistance than a short wire of the same diameter. A very long wire will need to be wrapped around the core many more times than a short wire. This means that the resistance is also directly proportional to the number of coils. The cross-sectional area of the wire also affects the resistance. The larger the cross-section of the wire, the more easily an electric current can glow through it. In other words, the resistance of the wire is inversely proportional to the area of its cross-section. Nichrome wire with a 1 mm diameter is coiled around a 5 cm long carbon core to form a resistor. The diameter of the core is 1 cm and the wire is coiled in such a way that the entire length of the core is covered with only one layer of wire. Four resistors are made using carbon cores. The core of each resistor has been wrapped with copper wire, but the wires have differing lengths and cross-sections as shown in the table below. Resistor Length (cm) \((m{m^2})\) / Cross-sectional Area \((m{m^2})\) A 10 2 B 20 4 C 30 3 D 40 5 Which pair of resistors has the same resistance?

Read the following passage and answer the questions that follow: If you open up nearly any electronic device, you will see many small bead-like components with coloured stripes on them. The components are called resistors and they are used to control the amount of electrical current that flows through different circuit sections in the device. Most resistors have a central core made of a mixture of carbon and ceramic. A wire made of a material such as copper or nichrome is then wrapped around this core. Finally, the resistor is coated in enamel, leaving a wire poking out from either end of the resistor. The degree to which a resistor reduces the size of the current flowing through its branch of the circuit is called is resistance. The resistance value is measured in ohms (written as \(\Omega \)). When the resistance is increased, the current that flows through the resistor is proportionally decreased. So a resistor that has a low value of resistance allows a large amount of current to flow through it. Where two resistors are made of the same material, a long wire will have a higher resistance than a short wire of the same diameter. A very long wire will need to be wrapped around the core many more times than a short wire. This means that the resistance is also directly proportional to the number of coils. The cross-sectional area of the wire also affects the resistance. The larger the cross-section of the wire, the more easily an electric current can glow through it. In other words, the resistance of the wire is inversely proportional to the area of its cross-section. Nichrome wire with a 1 mm diameter is coiled around a 5 cm long carbon core to form a resistor. The diameter of the core is 1 cm and the wire is coiled in such a way that the entire length of the core is covered with only one layer of wire. When resistors are connected in series, the electrical current passes through them one after one after another. When they are connected in parallel, the current splits to travel through them ate the same time. Which one of the diagram below shows ALL of the resistor in parallel with each other?

Read the following passage and answer the questions that follow: If you open up nearly any electronic device, you will see many small bead-like components with coloured stripes on them. The components are called resistors and they are used to control the amount of electrical current that flows through different circuit sections in the device. Most resistors have a central core made of a mixture of carbon and ceramic. A wire made of a material such as copper or nichrome is then wrapped around this core. Finally, the resistor is coated in enamel, leaving a wire poking out from either end of the resistor. The degree to which a resistor reduces the size of the current flowing through its branch of the circuit is called is resistance. The resistance value is measured in ohms (written as \(\Omega \)). When the resistance is increased, the current that flows through the resistor is proportionally decreased. So a resistor that has a low value of resistance allows a large amount of current to flow through it. Where two resistors are made of the same material, a long wire will have a higher resistance than a short wire of the same diameter. A very long wire will need to be wrapped around the core many more times than a short wire. This means that the resistance is also directly proportional to the number of coils. The cross-sectional area of the wire also affects the resistance. The larger the cross-section of the wire, the more easily an electric current can glow through it. In other words, the resistance of the wire is inversely proportional to the area of its cross-section. Nichrome wire with a 1 mm diameter is coiled around a 5 cm long carbon core to form a resistor. The diameter of the core is 1 cm and the wire is coiled in such a way that the entire length of the core is covered with only one layer of wire. Some resistors are too small to have their value printed on them numerically. Instead, they have their resistance value coded as a series of coloured bands painted around their ends. Each colour stands for a different number or multiplier as shown in the table below. Band Colour Band A Value Band B Value Band C Multiplier Black 0 0 1 Brown 10 1 10 Red 20 2 100 Orange 30 3 1000 Yellow 40 4 10000 Green 50 5 100000 Blue 60 6 1000000 Violet 70 7 10000000 Grey 80 8 100000000 White 90 9 1000000000 Gold 0.1 Silver 0.01 For example, a resistor marked with brown, blue and yellow bands would have a value of (10+6) \(\times \) 10000=160000 \(\Omega \) An electrician needs to replace a resistor that is marked with violet, green and gold bands with a new resistor that has twice the resistance value of the odd one. In order, what are the colours of the bands for the new resistor?