Question-06
(a) For his morning walk, Aslam went 110 meters towards east from his house and then turned right to keep walking for 40 meters before turning right again. After continuing to walk for 50 more meters, he turned right again and kept walking for another 120 meters, before he sat down on a bench at the park. How far was the bench located from his house?
SOLUTION
(b) The income of a company decreased by 10% and 15% in two successive years. What is the percentage of decrease in income after two years?
SOLUTION
To find the % decrease in income after two years, use the formula
The negative sign represents the decrease in income. Thus, the % of decrease in income after two years is 23.5%.
(c) What do you understand by mental ability scales? Differentiate between aptitude and intelligence.
Answer:
Mental ability scale phrase is used to characterise an individual’s ability to learn, comprehend instructions, and solve problems. Scales that evaluate specialised constructs including linguistic, mechanical, numerical, social, and spatial aptitude are included in general mental ability tests. The total score is seen to be the most relevant element, accounting for more diversity in individual performance than specialised talents.
Specialized talents and personal strengths and limitations are reflected in aptitude. Aptitudes are innate abilities, or particular abilities, for accomplishing or learning specific things fast and readily. They have something to do with genetics. Musical and creative ability are two examples of such abilities. While intelligence is described as an individual’s ability to acquire knowledge and comprehend difficult circumstances, aptitude is defined as the ability to apply that knowledge. For example, a person may be intellectual enough to learn about military, naval, and air force or defence-related topics, but he may lack the ability to put such information into reality in real life.
(d) Discuss the factors affecting intelligence.
Answers:
Studies have shown that there are several factors that affect the intelligence of a person. The factors are as follow:
1. Genetic influence
The intelligence trait runs in a family. According to research, identical twins’ IQs are more comparable than fraternal twins’ IQ. Moreover, adopted children raised together in the same setting have IQs that are more comparable to siblings raised together in the same family.
2. Social and economic influence
The environment has a significant impact on intelligence. Intelligence is influenced by factors such as a child’s home environment and parenting, education and access to learning resources, and nutrition, among others. Financially, the status of one’s parent, neighbourhood, and environmental condition affects the environment.
• Gender
The studies have shown that women perform well in the memorisation and verbal test; whereas, men perform significantly well in the spatial and mathematical ability test.
• Health and physical development
Health also plays a vital role in the growth of one’s intelligence. For instance, a healthy and physical fit person would have greater chances to achieve its goal; whereas, a handicapped child would suffer due to the hindrances in its way. Since, the sense of gaining achievement related to one’s ability, the health and physical fitness acts a paramount factor affecting intelligence.
Question-07
(a) The sum of three consecutive odd numbers is 273. What are the three odd numbers?
SOLUTION
Let the three odd numbers be
Thus, the three consecutive odd numbers are
 |
(b) Find the missing number in the series:
• 4, 16, 36, 64, ?, 144
• 30, 29, 27, ?, 20, 15
• 1, 7, 15, 25, ?, 51
• 0, 2, 6, 12, 20, 30, ?
• 48, 24, 72, 36, 108, ?
SOLUTION
In such types of questions, one need to find the rule followed in forming the number pattern. To do so, understand the relationship between the consecutive numbers in the series.
(A) 4, 16, 36, 64, ?, 144
In the question, every term of the series is the square of the even numbers in ascending order. Even numbers are 2, 4, 6, 8, …
So, the missing number is 100. Hence, the series would be 4, 16, 36, 64, 100, 144.
(B) 30, 29, 27, ?, 20, 15
In the question, the successive terms of the series is reduced by a number, which keeps increasing by 1 from the previous number every time.
The difference increases by 1, like 1, 2, 3, 4, and 5. Therefore, the difference between 27 and the unknown term must be 3. Kindly, note it’s totally up to the aspirant to find difference between the terms by subtracting the 1st by 2nd or vice versa.
Hence, the series would be 30, 29, 27, 24, 20, 15.
(C) 1, 7, 15, 25, ?, 51
The difference increases by 2, like 6, 8, 10, 12, and 14. Therefore, the difference between the unknown term and 25 must be 12 (10+2).
Kindly, note it’s totally up to the aspirant to find difference between the terms by subtracting the 1st by 2nd or vice versa.
Hence, the series would be 1, 7, 15, 25, 37, 51.
(D) 0, 2, 6, 12, 20, 30, ?
The difference between the terms follows the ascending even order pattern or it increases by 2, like 2, 4, 6, 8, 10, 12, and 14. Therefore, the difference between the unknown term and 30 must be 12 (10+2).
Kindly, note it’s totally up to the aspirant to find difference between the terms by subtracting the 1st term by the 2nd term or vice versa.
Hence, the series would be 0, 2, 6, 12, 20, 30, 42.
(E) 48, 24, 72, 36, 108, ?
In this question, dividing the first term by second term, and third term by second gives 2. Similarly, the rule is applied for the fifth and sixth term.
Hence, the series would be 48, 24, 72, 36, 108, 54.
(F) Find the correct word from the given jumbled spellings:
i. THRSI
ii. GNDREA
iii. SCHAMOT
iv. ONLNDO
v. HIODALY
Answer:
|
S.
No |
Jumbled
word |
Correct
word |
|
1 |
THRSI |
Shirt |
|
2 |
GNDREA |
Danger/
Garden |
|
3 |
SCHAMOT |
Stomach |
|
4 |
ONLNDO |
London |
|
5 |
HIODALY |
Holiday |
(G) Sara’s mother is 6 times old than Sara, where as her brother Ali is twice as old as Sara. In three years’, time the sum of their ages will be 72. How old are Sara Ali, and their mother now?
SOLUTION
Let the age of Sara be x.
Her mother’s age is 6x.
Ali’s age is 2x.
In three years’, time, their ages would be
It is given, the sum of their ages will be 72 after 3 years.
So,
Hence, Sara’s age is 7, her mother’s age is 42, and Ali’s age is 14.
Question-08
(a) What do you understand by Sampling? Discuss non – probability sampling.
Answer:
Sampling:
In statistical analysis, sampling is the act of selecting a predefined number of observations from a larger population. Depending on the sort of study being conducted, the methods utilised to sample from a broader population may include simple random sampling or systematic sampling. There are two types of sampling methods: Probability and Non-Probability Sampling.
Non-Probability Sampling:
In Non – Probability Sampling individuals are chosen based on non-random criteria in a non-probability sample, and not every individual has a chance of being included. The purpose of such type of sampling isn’t to test a hypothesis on a broader scale but to a smaller one.
The Non – Probability Sampling is further categorised into the following:
1. Convenience sampling
The population that is easily available or accessible to the researchers is called convenience sampling. For instance, a survey form filled by a specific class in school but not the entire school.
• Voluntary response sampling
In this type, instead researcher approaching to the participants, voluntarily population comes in to the contact of the researcher. For instance, sending a survey form link in the social media groups, only those people would fill form who voluntarily wants to participate; otherwise, other people wouldn’t fill it.
• Purposive sampling
In a part of qualitative sampling, the researcher chooses only those samples that have a significant purpose in the research. For instance, a researcher wants to collect the experiences of the students being handicapped. For this, the researcher has to collect the opinions of inly those students who are handicapped, not who are physically fit.
• Snowball sampling
In this type of sampling, a researcher gets into the contact of the participants with the help of other participants. For instance, a researcher wants to know the number of orphans in the district. For this, he may contact a participant – an orphan – who makes the researcher come into the contact with other orphans he know.
(b) Aslam is willing to use the stylish ceramic tiles in the lounge of his under – construction house. The shape of the tile is right triangle, having the length of the two legs 12 cm and 4cm. Each tile cost Rs. 15. How much will it cost to fill the lounge of 8 meters length and 6 metres width with these tiles.
SOLUTION
First, find the area of one tile.
Thus, the cost of tiles to fill the lounge would be Rs. 300,000.
(c) During a sale a clerk was putting new price tags on each item. On one sweater, he accidently raised the price by 20% instead of lowering the price by 20%. As a result, the price on the tag was Rs. 80, too high. What was the original price of the sweater?
SOLUTION
The price on the tag was 80 at the 20% increase in actual price, which means that the price Rs 80 is at the 120% of actual price of sweater.
Let the actual price of sweater be x.
The original price of the sweater is Rs. 67
(d) If in a certain language, BROTHER is written as QDGSNQA, then in the same language SISTER would be written as …..?
Answer:
Solution
In the language, the word BROTHER is equivalent to ODGSNQA. On observing it closely, one may find the following pattern:
In language, a letter that comes first in the word BROTHER has to be compared to the last letter of the word in language QDGNQA. Moreover, the compared letter is always a previous letter of a letter in the word BROTHER.
So, for the word SISTER, the word in the language would be QDSRHR
