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A passage is followed by questions pertaining to the passage. Read the passage and answer the questions. Choose the most appropriate answer.
Meteorological seasons are reckoned by temperature, with summer being the hottest quarter of the year and winter the coldest quarter of the year. Using this reckoning, the Roman calendar began the year and the spring season on the first of March, with each season occupying three months. In 1780 the Societas Meteorologica Palatina, an early international organization for meteorology, defined seasons as groupings of three whole months. Ever since, professional meteorologists all over the world have used this definition. So, in meteorology for the Northern hemisphere: spring begins on 1 March, summer on 1 June, autumn on 1 September, and winter on 1 December.
Ecologically speaking, a season is a period of the year in which only certain types of floral and animal events happen (e.g.: flowers bloom—spring; hedgehogs hibernate—winter). So, if we can observe a change in daily floral/animal events, the season is changing.
Traditional seasons are reckoned by insolation, with summer being the quarter of the year with the greatest insolation and winter the quarter with the least. In traditional reckoning, the seasons begin at the crossquarter days. The solstices and equinoxes are the midpoints of these seasons.
In Australia, the traditional aboriginal people defined the seasons by what was happening to the plants, animals and weather around them. This led to each separate tribal group having different seasons, some with up to eight seasons each year. However, most modern Aboriginal Australians follow either four or six meteorological seasons, as do nonAboriginal Australians.
In India, and in the Hindu calendar, there are six seasons or Ritu: Hemant (prewinter), Shishira (Winter), Vasanta (Spring), Greeshma (Summer), Varsha (Rainy) and Sharad (Autumn).
Q. In the context of this passage, which of the following options best describes the meaning of ‘insolation’?
The passage is about how the duration and start of seasons are calculated or figured out. In this context the word insolation has been used to describe the phenomena of changes in season brought about by the angle of the Sun in relation to the Earth.
►Option 2 is ruled out because this (‘therapeutic exposure’) would not fit in the context of the seasons.
►Option 3 is ruled out as there is no reference to ‘protection’ in the passage.
►Option 4 is too generalised an answer.
►Option 1, with solar radiation striking Earth, makes a perfect allusion to the subject matter  seasons. In the context in which it is mentioned, the word is used to signify that, “summer has the greatest insolation (solar radiation striking earth) and winter has the least (solar radiation striking earth)”.
Hence, the correct answer is option 1.
A passage is followed by questions pertaining to the passage. Read the passage and answer the questions. Choose the most appropriate answer.
Meteorological seasons are reckoned by temperature, with summer being the hottest quarter of the year and winter the coldest quarter of the year. Using this reckoning, the Roman calendar began the year and the spring season on the first of March, with each season occupying three months. In 1780 the Societas Meteorologica Palatina, an early international organization for meteorology, defined seasons as groupings of three whole months. Ever since, professional meteorologists all over the world have used this definition. So, in meteorology for the Northern hemisphere: spring begins on 1 March, summer on 1 June, autumn on 1 September, and winter on 1 December.
Ecologically speaking, a season is a period of the year in which only certain types of floral and animal events happen (e.g.: flowers bloom—spring; hedgehogs hibernate—winter). So, if we can observe a change in daily floral/animal events, the season is changing.
Traditional seasons are reckoned by insolation, with summer being the quarter of the year with the greatest insolation and winter the quarter with the least. In traditional reckoning, the seasons begin at the crossquarter days. The solstices and equinoxes are the midpoints of these seasons.
In Australia, the traditional aboriginal people defined the seasons by what was happening to the plants, animals and weather around them. This led to each separate tribal group having different seasons, some with up to eight seasons each year. However, most modern Aboriginal Australians follow either four or six meteorological seasons, as do nonAboriginal Australians.
In India, and in the Hindu calendar, there are six seasons or Ritu: Hemant (prewinter), Shishira (Winter), Vasanta (Spring), Greeshma (Summer), Varsha (Rainy) and Sharad (Autumn).
Q. In the context of this passage, which of the following options best describes the meaning of ‘reckon’?
According to the first two lines of the passage, “Meteorological seasons are reckoned by temperature, with summer being the hottest quarter of the year and winter the coldest quarter of the year. Using this reckoning, the Roman calendar began the year and the spring season on the first of March, with each season occupying three months.” All the options are valid synonyms of ‘reckon’, but in this context, the meaning is that of ‘calculating’ or figuring out the start and end of the seasons.
Hence, the correct answer is option 4.
A passage is followed by questions pertaining to the passage. Read the passage and answer the questions. Choose the most appropriate answer.
Meteorological seasons are reckoned by temperature, with summer being the hottest quarter of the year and winter the coldest quarter of the year. Using this reckoning, the Roman calendar began the year and the spring season on the first of March, with each season occupying three months. In 1780 the Societas Meteorologica Palatina, an early international organization for meteorology, defined seasons as groupings of three whole months. Ever since, professional meteorologists all over the world have used this definition. So, in meteorology for the Northern hemisphere: spring begins on 1 March, summer on 1 June, autumn on 1 September, and winter on 1 December.
Ecologically speaking, a season is a period of the year in which only certain types of floral and animal events happen (e.g.: flowers bloom—spring; hedgehogs hibernate—winter). So, if we can observe a change in daily floral/animal events, the season is changing.
Traditional seasons are reckoned by insolation, with summer being the quarter of the year with the greatest insolation and winter the quarter with the least. In traditional reckoning, the seasons begin at the crossquarter days. The solstices and equinoxes are the midpoints of these seasons.
In Australia, the traditional aboriginal people defined the seasons by what was happening to the plants, animals and weather around them. This led to each separate tribal group having different seasons, some with up to eight seasons each year. However, most modern Aboriginal Australians follow either four or six meteorological seasons, as do nonAboriginal Australians.
In India, and in the Hindu calendar, there are six seasons or Ritu: Hemant (prewinter), Shishira (Winter), Vasanta (Spring), Greeshma (Summer), Varsha (Rainy) and Sharad (Autumn).
Q. Based on the passage, we can infer all the statements, except:
►Option 1 is correct because it is mentioned in the passage that ‘Ecologically speaking, a season is a period of the year in which only certain types of floral and animal events happen... so, if we can observe a change in daily floral/animal events, the season is changing’. And ‘In Australia, the traditional aboriginal people defined the seasons by what was happening to the plants, animals and weather around them’. Therefore, this statement can be inferred.
►Option 2 can also be inferred because it is mentioned  ‘In 1780 the Societas Meteorologica Palatina... defined seasons... Ever since, professional meteorologists all over the world have used this definition...’
►Option 4 can also be inferred because it is mentioned, ‘...a season is a period of the year in which only certain types of floral and animal events happen...hedgehogs hibernate— winter... So, if we can observe a change...the season is changing.’
►Option 3 cannot be inferred because the statement itself is incorrect. The passage mentions The solstices and equinoxes are the midpoints of these seasons’. Therefore, summer does not begin on the day of the solstice.
Hence, the correct answer is option 3.
A passage is followed by questions pertaining to the passage. Read the passage and answer the questions. Choose the most appropriate answer.
Meteorological seasons are reckoned by temperature, with summer being the hottest quarter of the year and winter the coldest quarter of the year. Using this reckoning, the Roman calendar began the year and the spring season on the first of March, with each season occupying three months. In 1780 the Societas Meteorologica Palatina, an early international organization for meteorology, defined seasons as groupings of three whole months. Ever since, professional meteorologists all over the world have used this definition. So, in meteorology for the Northern hemisphere: spring begins on 1 March, summer on 1 June, autumn on 1 September, and winter on 1 December.
Ecologically speaking, a season is a period of the year in which only certain types of floral and animal events happen (e.g.: flowers bloom—spring; hedgehogs hibernate—winter). So, if we can observe a change in daily floral/animal events, the season is changing.
Traditional seasons are reckoned by insolation, with summer being the quarter of the year with the greatest insolation and winter the quarter with the least. In traditional reckoning, the seasons begin at the crossquarter days. The solstices and equinoxes are the midpoints of these seasons.
In Australia, the traditional aboriginal people defined the seasons by what was happening to the plants, animals and weather around them. This led to each separate tribal group having different seasons, some with up to eight seasons each year. However, most modern Aboriginal Australians follow either four or six meteorological seasons, as do nonAboriginal Australians.
In India, and in the Hindu calendar, there are six seasons or Ritu: Hemant (prewinter), Shishira (Winter), Vasanta (Spring), Greeshma (Summer), Varsha (Rainy) and Sharad (Autumn).
Q. According to the passage:
Both the options have been mentioned verbatim in the passage.
Hence, the correct answer is option 3.
In the following sentences one word or phrase has been used incorrectly. Choose the word that must be changed or modified or deleted to make the sentence correct. There are sentences without any errors too.
There are fairly stringent conditions attached from the provision of affordable housing in the village.
“Attached from” should be corrected to ‘attached to’. Hence, the correct answer is option 2.
Select the most OPPOSITE of the given word from the given choices.
LACUNA
“Lacuna” means ‘a break, pause or interruption’. Its opposite would be “continuation.” Hence, the correct answer is option 3.
Fill in the blanks with the most appropriate pair of words from the given options.
Around the table reigned that noisy ________ which usually prevails at such a time among people sufficiently free from the demands of social position not to feel the ________ of etiquette.
The clues in the sentence are “free from the demands of social position” and “noisy”. You know that the people around that table are at ease with each other. Therefore “hilarity” which means ‘cheerfulness; merriment; mirthfulness’ fits the first blank whereas “trammels” which means ‘a hindrance or impediment to free action; restraint’ fits the second. “Indecency” means ‘obscenity or indelicacy’ and “hedonism” means ‘devotion to pleasure as a way of life’ both are misfits. Therefore, option 1 is eliminated. “Haplessness” means ‘unlucky; luckless; unfortunate’ and does not fit the first blank. Therefore, option 2 is eliminated. “Facetiousness” means ‘lacking serious intent; concerned with something nonessential, amusing, or frivolous’. Though the latter probably makes sense there, “discipline” simply does not make sense with ‘noisy’ and hence option 4 is eliminated.
Hence, the correct answer is option 3.
An “iconoclast” is a person who attacks cherished beliefs, traditional institutions.
An “atheist” doesn’t believe in a deity or god.
An “agnostic” is ‘a person who holds that the existence of the ultimate cause, as God, and the essential nature of things are unknown and unknowable, or that human knowledge is limited to experience, therefore he doubts the existence of God’. Option 2 does not share the same antonymous relationship as option 1.
A “philanderer” is ‘a man who carries on a sexual affair, especially an extramarital affair, with a woman one cannot or does not intend to marry’. “Debauchery” is ‘excessive indulgence in sensual pleasures; intemperance’. A “philanderer” on some level believes in “debauchery”, hence option 3 is eliminated.
A “devotee” indulges in “idolatry” which is ‘the worship of idols or excessive devotion’. Therefore, option 4 is eliminated.
Hence, the correct answer is option 1.
Choose the correct spelling from the options given below.
To convert to another religion or belief system.
The correct spelling of the word is “proselytize”.
Options 1, 3 and 4 spell the word incorrectly.
Hence, the correct answer is option 2.
Choose the appropriate option from among the ones given below
Which of the following sentences does not use a pleonasm?
A “pleonasm” is the usage of more words than necessary to add rhetoric to a sentence.
In option 1, the word “most” is unnecessary since ‘unkindest’ is already in the superlative form.
In the second option, since a gift is something that is given to a person without expecting a payment in return, the word “free” isn’t required.
In the third sentence, the act of raising one’s hands implies moving them upwards; hence, the word “up” is unnecessary.
Thus, the fourth statement which contains no such redundancy is the correct answer.
Hence, the correct answer is option 4.
The following question consists of a set of labelled sentences. These sentences, when properly sequenced, form a coherent paragraph. Choose the most logical order of sentences from the options.
A. Apart from their postwar singles, all their motorcycles had used this distinctive layout until the early 1980s.
B. Bayerische Motoren Werke started building motorcycle engines and then motorcycles after World War I.
C. Many Bayerische Motoren Werke Motorcycles are still produced to this pattern, which is designated the “R series”.
D. These had a “boxer twin” engine, in which an aircooled cylinder protrudes into the airflow from each side of the machine.
E. Their first notable motorcycle, after the failed Helios and Flink, was the “R32” in 1923.
There is a clear link between D and A. A follows D as A speaks about the layout which is described in D.
Out of B and C, C cannot be the opening sentence of the sequence because it speaks about the structure described in D and implies that C can come only after D has been covered in the paragraph. This eliminates options 3 and 4.
B introduces Bayerische Motoren Werke as a motorcycle maker. E speaks about the motorcycle models of Bayerische Motoren Werke.
D starts with “These had a boxer twin engine...” and describes the layout that the motorcycles had. This implies that D is immediately preceded by E.
There is only one option (option 2) which satisfies all the conditions.
Hence, the correct answer is option 2.
The verb form of ‘like’ appears in 6 (likened)  where the act of showing something to be similar to something else is described. Therefore, 16. Options 1 and 3 can be easily eliminated.
The use of like as a noun appears in sentence 5 (likeness) where the word means ‘the image of, or resemblance’. Option 4 can be eliminated.
Sentence 7 uses ‘like’ as a preposition, where the meaning is ‘in a like manner with; similarly to’.
Sentence 8 uses the adverb ‘likewise’, meaning ‘in the same way’.
Hence, the correct answer is option 2
Identify the CORRECT sentence or sentences.
A. If we redistribute wealth from the better to worse, we can help feed the hungry people.
B. Every morning I ate the burnt breakfast, drank the foul coffee and spoke to nobody.
C. Critics claim that the Indian government unfairly favors the IITs when educational dollars are doled out.
The intended meaning in sentence A is the equal distribution of wealth among the “better off’ meaning 'economically fortunate people' and “worse off’ meaning 'economically less fortunate people'. So, the phrase to be used in sentence A is “worse off’ to make the sentence grammatically correct.
In sentence C, “educational” has been wrongly used. “Educational” is an adjective and dollars cannot be described as educational. Hence, the correct usage here is the noun “education” along with “dollars” which is also a noun, both forming the noun phrase “education dollars".
Sentence B is correct.
Hence, the correct answer is option 2.
Choose the grammatically correct option from the following
The correct sentence is  “He was thinking of buying a new car,” she said.
The rest of the options have tense errors.
Hence, the correct answer is option 3.
Choose the correct option.
When someone refers to someone or something as “the bee’s knees” they mean that it is:
Referring to something as “the bee’s knees” is an informal way of saying that something is ‘excellent or of the highest quality’. Hence, the correct answer is option 2.
The amount of milk delivered by a milkman to a house is 98 litres over a period of 1 month. During this period, the average milk consumption in that house on weekdays (total 22 days) is 3 litres per day. Find the average daily consumption in that house on weekends, if the month is April.
Average milk consumption on weekdays (total 22 days) is 3 litres per day.
►Total milk consumed on weekdays = 22 x 3 = 66 litres
►Total milk delivered in January = 98 litres So total milk delivered (and consumed) on weekends = 98  66 = 32 litres
►Number of weekend days in April = Total days  Number of weekdays = 30  22 = 8
►Average milk consumption on weekends = 32/8 = 4 litres
If 15^{7k3} > 1; which of the following is true about k ?.
15^{7k3} > 1
► => 15^{7k3} > 15^{0}
► => 7k3 > 0 => k > 3 / 7
What is the value of log_{6} 169 x log_{13} 6 x log_{7} 64 x log_{4} 49?
log_{6} 169 x log_{13} 6 x log_{7} 64 x log_{4} 49
► = log 13^{2} / log 6 x log 6 / log 13 x log 4^{3} / log 7 x log 7^{2} / log 4
► = 2 x 1 x 3 x 2
► = 12
The difference between the simple interest and compound interest earned on a sum placed for two years at 8% is Rs.30.72, when the interest is compounded annually. If the interest were to be compounded on a halfyearly basis, what would the difference in the two interest amount approximately be?
Consider annual compounding.
Interest for the first year is the same, irrespective of whether it is simple interest or compound interest.
Hence, the difference between the two interest amounts is due to the extra compound interest earned in the second year.
The C.l. earned in the first year is added to the original principal and this sum becomes the principal for the second year.
Hence, the situation is equivalent to placing (original principal + C.l. of first year (say x)) at 8% simple interest for one year.
Hence, effectively, Rs.30.72 is the simple interest earned by placing Rs. x at 8% S.l. for a year 30.72 = x(0.08) x = 384
This is also the S.l. earned by keeping the original principal at 8% for a year
Original principal = 384 / 0.08 = 4800
Hence, at halfyearly compounding, amount due at the end of 2 years = 4800[1 +
(4 / 100)] ^{4 }= 5615.32
C.l. = 5615.32  4800 = Rs. 815.32
S.l. for Rs.4,800 at 8% for 2 years = (4800 x 8 x 2) / 100 = Rs. 768
Required difference = 815.32  768 = Rs. 47.32
What is the total number of ways in which 101 prizes can be distributed among 5 boys if each boy receives an odd number of prizes?
Let x_{1}, x_{2}, x_{3}, x_{4} and x_{5} be the number of prizes given to the 5 boys respectively.
We have x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 101 Since each boy received odd number of prizes, let
► x_{1} = 2y_{1}  1, x_{2} = 2y_{2}  1, x_{3} = 2y_{3}  1, x_{4} = 2y_{4 } 1, x_{5} = 2y_{5}  1
where y_{1,} y_{2,} y_{3}, y_{4} and ys are positive integers
So we have (2y_{1}  1) + (2y_{2}  1) (2y_{3}  1) (2y_{4 } 1) (2y_{5}  1) = 101
► i.e y_{1} + y _{2 }+ y_{3 }+ y_{4}, + y_{5} = 53
Now imagine that these 53 prizes are placed one beside the other. So we have 52 spaces in between these prizes. To divide them into 5 groups, we need to select 4 spaces from the available 52 spaces which can be done in ^{52}C_{4} ways.
What is the next term in the following series? 12, 14, 116, 1136, ?
Observe that the series does not show a clear subtraction based or multiplication based pattern.
However, observe that 1^{2} = 1 and 2^{2} = 4.
Similarly, 1^{2 }= 1 and 4^{2} = 16 Thus, the logic followed is as follows:
► First term = 12
► Second term = 1^{2}2^{2 }= 14
► Third term = 1^{2}4^{2} = 116
► Fourth term = 1^{2}1^{2}6^{2} = 1136
► Fifth term = 1^{2}1^{2}3^{2}6^{2} = 11936
In a certain language, if SMILE is coded as XRNQJ, how is MOUSE coded in that language?
S + 5 = X, M + 5 = R, l + 5 = N, L + 5 = Q and E + 5 = J Thus, each letter is replaced by a letter that is 5 places ahead in the alphabet.
Consider the letters of MOUSE.
M + 5 = R, 0 + 5 = T, U + 5 = Z, S + 5 = X and E + 5 = J Thus, MOUSE is coded as RTZXJ.
Answer the following question based on the information given below.
The figures below provide some data about the subjects taken by all students of a particular school. The square, circle, triangle and rectangle represent Biology, Physics, Maths and Chemistry respectively. The number inside each figure represents the number of students studying each subject. Study the diagram carefully and answer the questions.
Q. How many students study Physics and Maths but not Biology or Chemistry?
Number of students studying Physics and Maths but not Biology or Chemistry is given by the number inside the circle and triangle but outside the square and rectangle.
This condition is satisfied by the number 7.
Answer the following question based on the information given below.
The figures below provide some data about the subjects taken by all students of a particular school. The square, circle, triangle and rectangle represent Biology, Physics, Maths and Chemistry respectively. The number inside each figure represents the number of students studying each subject. Study the diagram carefully and answer the questions.
Q. How many students study atleast two subjects?
Total number of students = 4 + 8 + 25 + 3 + 2 + 27 + 9 + 18 + 2 + 5 + 6 + 14 + 7 + 2 + 11 + 12 = 155
Number of students studying exactly one subject = 4 + 8 + 9 + 27 + 5 + 12 + 11 + 2 = 78
Number of students studying atleast two subjects = 155  78 = 77.
An item is marked at Rs.200 and a discount of 25% is given on MP. The item costs Rs. 80 and another item worth Rs. x is sold with it (at cost). The overall profit made was 50%. Find x (in Rs.).
SP of first item = 0.75 x 200 = Rs. 150 and CP of this item = Rs. 80
CP and SP of the other item = Rs. x (as it is being sold at cost).
Total CP in the transaction = Rs. (80 + x)
Total SP in the transaction = Rs. (150 + x)
Since profit = 50%
► 150 + x= 1.5(80 + x)
► 150 + x= 120 + 1.5x
► x = 60.
Three unbiased dice are thrown simultaneously. What is the probability that the sum of the three numbers on them is divisible by 4?
When three unbiased dice are thrown, there are 63 = 216 combinations possible.
The least possible sum is 3 and the highest possible sum is 18.
The multiples of 4 in this range are 4, 8, 12 and 16
Sum = 4:
Obtained for the combination (1,1, 2).
This combination can be made in 3!/2! = 3 ways
Sum = 8:
Obtained for the combinations(1, 1,6) possible in 3!/2! = 3 ways (1,2, 5)  possible in 3! = 6 ways (1, 3, 4)  possible in 3! = 6 ways (2, 2, 4)  possible in 3!/2! = 3 ways (2, 3, 3)  possible in 3!/2! = 3 ways
Total number of ways = 3 + 6 + 6 + 3 + 3 = 21
Sum = 12:
Obtained for the combinations
(1, 5, 6)  possible in 3! = 6 ways
(2, 4, 6)  possible in 3! = 6 ways
(2, 5, 5)  possible in 3!/2! = 3 ways (3, 3, 6)  possible in 3!/2! = 3 ways
(3, 4, 5)  possible in 3! = 6 ways
(4, 4, 4)  possible in 1 way
Total number of ways = 6 + 6 + 3 + 3 + 6 + 1 = 25
Sum = 16:
Obtained for the combinations
(4, 6, 6)  possible in 3!/2! = 3 ways
(5, 5, 6)  possible in 3!/2! = 3 ways Total number of ways = 3 + 3 = 6 Overall total unmber of ways = 3 + 21 + 25 + 6 = 55
Required probability = 55 / 216 = 0.254
Distance between A and B is 100 m. If P and Q start simultaneously from A and B respectively, then they meet in 4 seconds. If P and Q start simultaneously from A to reach B, then P beats Q by 20 m. How much time will P take to cover 200 m at the same speed?
Let the speeds of P and Q be p and q respectively.
Given that P beats Q by 20 m. This means that the time taken by P to cover 100 m is same as that taken by Q to cover 80 m. Therefore, 4p = 5q.
Given that P and Q start simultaneously from A and B respectively, and they meet in 4 seconds.
⇒ 500 / 9p = 4
⇒ p = 125 / 9 m/s
Time taken by P to cover 200m = 200 / p = 200 x 9 / 125 = 14.4 seconds
Answer the questions based on the following graph.
Six friends played seven online games each, in the same week, and their respective scores are given below. The pie chart gives the game wise breakup for Vikas.
Q. If the 2nd game’s score hadn’t been added to Vikas’ total score due to some technical error, then his rank would____. The total score of all the other players remains the same.
The score of Vikas in the 2nd game = 0.2 * 3000 = 600
Thus, Vikas’ score would now become 3000  600 = 2400.
There was no change in the score of the other players.
Vikas’ original rank was 2nd and his new rank is still 2^{nd}.
Thus, there is no change in his rank.
Answer the questions based on the following graph.
Six friends played seven online games each, in the same week, and their respective scores are given below. The pie chart gives the game wise breakup for Vikas.
Q. What is the combined score of Vikas in the 4th, 5th and 7th games put together?
Total score of Vikas = 3000
The 4^{th}, 5^{th} and 7^{th} together account for (15 + 16 + 9)% i.e. 40% of his total score.
Therefore, his combined score in these three games taken together = 0.4 * 3000 = 1200.
Answer the questions based on the following graph.
Six friends played seven online games each, in the same week, and their respective scores are given below. The pie chart gives the game wise breakup for Vikas.
Q. If Deepu and Mayank respectively scored 10% and 15% of their total score in the 3^{rd} game, then by what percentage was the score of Mayank in the 3^{rd} game more than the score of Deepu in the 3^{rd} game?
Deepu’s score in the 3^{rd} game = 0.1 x 2200 = 220
Mayank’s score in the ^{3rd }game = 0.15 x 3200 = 480
In the figure given below, ABC and DEF are two identical right angled triangles that are right angled at B and E respectively.
Q. If the area of the shaded region is one  seventeenth of the area of the entire figure, the ratio DC : AF = ?
Let the area of the shaded region be x and the area of the unshaded region in each triangle be a.
The area of the entire figure is 17x.
a + x + a = 17x
a = 8x
A(ΔABC) = <2 + x = 8x + x = 9x
A(ΔABC): A(ADOC) = 9x : x = 9 : 1
Since ∠B and ∠E are right angles, ΔABC and ΔDOC are similar.
In two similar triangles, ratio of areas is the square of ratio of sides.
AC : DC = 3 : 1
Since AC = AD + DC, AD = 2DC Similarly, CF = 2DC
DC : AF = DC : (2DC + DC + 2DC) = 1 : 5 = 0.2.
A certain sum amounts to 5 times the principal in 40 years under Simple Interest. Calculate the Rate of Interest per annum.
Amount = Principal + Interest 5P = P + 1
4P = I
4P = (PNR) / 100
NR = 100 x 4
40 x R = 100 x 4
R = 10%
Group Question
Answer the following question based on the information given below.
The scorecards of 150 students in a school are collected and analysed. The scorecards have scores for only three subjects viz. Science, Maths and English. For each of these subjects, the qualifying marks are 80% of the total. The number of students who got qualifying marks in all three subjects is half the number of students who have got qualifying marks in only English. The sum of the number of students getting qualifying marks in only Maths and only Science is equal to the number of students getting qualifying marks in both Science and Maths, but not English.35 students got qualifying marks in Science and English but not Maths while 20 students got qualifying marks in English and Maths but not Science. Each student qualified in atleast one subject. 100 students qualified in English.
Q. If all the students getting qualifying marks in all three subjects are selected for a competition, how many students are selected for the competition?
Let the basic Venn diagram be as shown below:
Based on the information given,
► c + d + e + f = 100
Also, c = 35, f = 20 and 2d = e
► 35 + d + 2d + 20 = 100
► d = 15
Hence, 15 students were selected for the competition.
Group Question
Answer the following question based on the information given below.
The scorecards of 150 students in a school are collected and analysed. The scorecards have scores for only three subjects viz. Science, Maths and English. For each of these subjects, the qualifying marks are 80% of the total. The number of students who got qualifying marks in all three subjects is half the number of students who have got qualifying marks in only English. The sum of the number of students getting qualifying marks in only Maths and only Science is equal to the number of students getting qualifying marks in both Science and Maths, but not English.35 students got qualifying marks in Science and English but not Maths while 20 students got qualifying marks in English and Maths but not Science. Each student qualified in atleast one subject. 100 students qualified in English.
Q. How many students got the qualifying marks in Science?
Consider the solution to the previous question.
Every student qualified in atleast one subject.
► a + b + c + d + e+ f + g = 150
Also, c + d + e + f = 100 and a + g = b
► 2b + 100 = 150
► a + g = b = 25
Number of students that got the qualifying marks in Science = a + 6 + c + d
However, the individual value of a and g cannot be found.
Hence, the required sum cannot be found.
The HCF of two numbers is 3 and their LCM is 105. If the difference between these two numbers is 6, what is the larger number?
Let a and b be the two numbers, such that a is the larger of the two.
► a x b = LCM x HCF = 105 x 3 = 315
► a  b = 6 and ab = 315
► a(a  6) = 315
► a^{2}  6a  315 = 0
► a = 21 or a = 15
Since a is the larger of the two numbers, a = 21
One day Ram starts to his office half an hour late. In order to reach in time, he increased his speed by 50%. But he reached office 15 minutes earlier than his usual time. How much time does Ram normally take to reach office?
Let Ram's usual speed be x m per minute New speed = 1.5x m per minute With speed 1.5x m per minute, he took 30 + 15 = 45 minutes less than the normal time to cover the same distance.
Assume that Ram takes t minutes at x m per minute tx= (t  45)(1.5x) 0.5fx = 67.5x
t = 135 minutes
A cube of edge 3 cm is cut into smaller cubes of edge 1 cm. The ratio of the total surface area of all the smaller cubes to the surface area of the larger cube is equal to:
Surface area of cube of side 1cm = 6 x 1 * 1 = 6 cm^{2} Number of cubes of side 1 cm = 27
Total surface area of all small cubes = 27 x 6 cm^{2} Surface area of the larger cube = 6 * 3 x 3 = 9 x 6 cm^{2}
Required ratio = (27 x 6) : (9 x 6) = 3 : 1
To be divisible by 72, the number has to be divisible by both 8 and 9.
For the number to be divisible by 8, the last three digits have to be divisible by 8.
Since the last three digits are 6a2, a can be 3 or 7 for this number to be divisible by 8.
For the number to be divisible by 9, the sum of all the digits has to be divisible by 9.
sum of all the digits = m + a + 9
If a = 3, sum of the digits = m + 12. For m + 12 to be divisible by 9, m has to be 6
If a = 7, sum of the digits = m + 16. For m + 16 to be divisible by 9, m has to be 2
Hence two cases are possible.
m  a = 6  3 = 3 or 2  7 =  5
The price of a commodity is increased by x% and then a discount of x% is offered. What is the final cost price of that commodity? Assume the original cost of the commodity to be y.
Let y = Rs. 100 and x = 10
Price after increase = Rs. 110 and price after discount = Rs. 99
Since the final price is less than the initial value, options 2 and 4 can be directly eliminated.
In options 1 and 3, substitute the value of x and y.
Only option 1 gives the final value as Rs. 99.
Hence, option 1.
Alternatively, Original price = y Price after increase of x% = y (1 + x / 100)
► = y (1 + x / 100) (1  x / 100)
► = y (1  x^{2} / 100^{2})
Lines AD, BE and CF are parallel to each other such that lines p and q are transversal to these lines. Line p intersects AD, BE and CF at X, Y and Z respectively while line q intersects them at L, M and N respectively. If XY : XZ = 2 : 3 and LM = 4 units, MN = ?
AD, BE and CF are parallel lines and p and q are the transversals
► XY / YZ = LM / MN
► XY : XZ = 2 : 3
► XY / YZ = 2 / 1 = LM / MN
► LM = 4
► MN = 4/2 = 2 units
Which among the following options will replace the blank in the series below?
ABC, GHIJ,______ , YZ ?
Observe that the first term comprises the first three letters  ABC  and then, the next three letters  DEF  are skipped.
The next term starts with the next letter i.e. G and this term has four letters  GHIJ.
Hence, to test this pattern, you can skip the four letters after J  KLMN  and start the next term with O.
Since the first and second term had three and four letters respectively, the third term should have five letters.
Hence, the third term should be OPQRS.
If you want to verify the logic, skip the next five letters  TUVWX  and observe that the next term starts with Y (as it should).
Hence, the missing term is OPQRS.
What should come in the place of the question mark?
Sum of the first row = 1 + 1 = 2
Sum of the second row = 1 + 1 + 1 = 3 Sum of the third row = 5 = (3 + 2)
Sum of the fourth row = 8 = (5 + 3) Thus, sum of (n + 2)^{th} row = sum of (n + 1 )^{th} row + sum of n^{th} row
sum of the fifth row = 8 + 5 = 13
1 + 3 + 2 + 2 + 2 + 7 = 13
Hence, 3 should replace the question mark.
Sarita has two sons  one of whom is Tarun. Also, the mother of Palak has only two sons  Tarun and Aakash. How is Palak related to Sarita?
Palak’s mother has only two sons, Tarun and Aakash. Hence, Palak has to be the sister of both Tarun and Aakash.
Tarun is also Sarita’s son.
So, Palak is the daughter of Sarita.
Refer to the following data and answer the questions that follow:
In an MBA entrance exam, a candidate attempts X questions correctly and Y questions incorrectly such that X = 2Y  5. Each correct answer fetches 1.5 marks whereas for each incorrect answer 0.5 marks are deducted.
Q. What is the total number of questions asked in the exam, if a candidate attempts all the questions but goes wrong in 12 of them?
Since the candidate attempts all the questions and gets 12 questions wrong, X + Y = total and Y = 12
► X = 2Y  5 = 2(12)  5 = 19
Total questions = X + Y = 19 + 12 = 31
Refer to the following data and answer the questions that follow:
In an MBA entrance exam, a candidate attempts X questions correctly and Y questions incorrectly such that X = 2Y  5. Each correct answer fetches 1.5 marks whereas for each incorrect answer 0.5 marks are deducted.
Q. If a student has the same number of correct and incorrect answers, what is his score?
Here, X = Y
Y = 2 Y  5 which gives Y = X = 5
A student gets 1.5 marks for each correct answer and loses 0.5 marks for each incorrect answer.
Total marks = 1.5(5)  0.5(5) = 7.5  2.5 = 5.0
Answer the question based on the passage given below.
The prevailing belief in Santa Claus should be deemed not only outdated but also harmful to children. There are still those who continue to believe that a redrobed fat old man travels around the world on a sleigh drawn by reindeer, climbs down chimneys and delivers presents to good children while they sleep. But who has chimneys in their homes these days? And the postal department does not deliver letters addressed to Santa Claus because he doesn’t exist. Worse, there is something sinister about propagating the idea to children that a stranger can enter one’s home in the middle of the night.
Q. Which of the following statements would strengthen the argument?
The main argument in the passage is that The prevailing belief in Santa Claus should be deemed not only outdated but also harmful to children’.
The author focuses his attention on the effect that this belief has on children. The correct answer should state the harmful effect of this belief on children.
Option 2 has no reference to Santa Claus.
Option 3 would weaken rather than strengthen the argument.
The former part of option 4 strengthens and the latter part weakens the core assertion.
Option 1 gives a clear reason why the belief is harmful to children parents will begin by lying to children about Santa Claus and then later about other things.
Hence, the correct answer is option 1.
Answer the following question based on the information given below.
In a certain mathematical code, a $ b implies a ÷ b, a # b means a  b, a % b means a + b and a & b means a x b.
Q. What will be the last digit of the simplified expression 34 $ 2 & 8 % 7 # 20 & 5? Assume that the rules of BODMAS apply.
34 $ 2 & 8 % 7# 20 & 5
= 34 ÷ 2 x 8 + 7  2 0 * 5
► = 1 7 x 8 + 7  2 0 x 5
► = 136 + 7  1 0 0
► = 43
Thus, the required last digit is 3.
Answer the following question based on the information given below.
In the figure above, rectangle represents males, circle represents Indians, triangle represents teachers and square represents science graduates.
Q. Which of the following regions represents male science graduates who are not Indians but are teachers?
Male science graduates who are not Indians but are teachers implies the region lying within the rectangle, square and triangles but outside the circle.
Region E satisfies these conditions.
Answer the following question based on the information given below.
In the figure above, rectangle represents males, circle represents Indians, triangle represents teachers and square represents science graduates.
Q. Which of the following regions represents Indian females who are teachers but not science graduates?
Indian females means the region within the circle but outside the rectangle i.e. regions I, J and M.
Teachers who are not science graduates implies the region lying within the triangle but outside the square.
Among regions, I, J and M, only region I satisfies theses conditions.
Answer the following question based on the information given below.
In the figure above, rectangle represents males, circle represents Indians, triangle represents teachers and square represents science graduates.
Q. Region L corresponds to which of the following?
Region L lies within the circle, rectangle and square but outside the trigangle.
Thus, it represents Indian males who are science graduates but not teachers.
A is lost in a city which has roads in the form of a 7 x 6 grid as shown in the figure. He has to reach B who is at the diagonally opposite end of the city. All routes from one node to another are equidistant. In how many ways can he travel to meet B given that he takes the shortest path?
To reach B by the shortest path, A has to ensure that he always move to the west or towards the north. If he ever travels towards the south or east, the route becomes longer.
Thus, if A wants to reach B by the shortest path, he has to go west 6 times and go north 7 times.
He has to take a set of 13 routes i.e. 7 north and 6 west.
Thus, the number of ways in which A can reach B is a permutation of 13 routes where 7 (N) and 6 (W) are repeated.
Group Question
Answer the following question based on the information given below.
Six children  Pran, Qadir, Ram, Suman, Teena and Uday  went to a stationary shop and bought two items each out of pencil, pen, eraser and sharpener. No child bought the same combination of items. The price of a pencil, pen, eraser and sharpener were Rs. 7, Rs. 12, Rs. 9 and Rs. 4 respectively. The total money spent by Pran, Ram, and Uday was Rs. 19, Rs. 16 and Rs. 16 respectively. Teena and Pran bought a common item. Qadir, Ram and Suman bought a common item. Teena spent less than Rs. 20
Q. What amount (in Rs) was spent by Teena?
Pencil = Rs. 7, Pen = Rs. 12, Sharpener = Rs. 4 and Eraser = Rs. 9
The amount paid by Teena can be one of 6 combinations:
► 7 + 12= 19
► 7 + 4= 11
► 7 + 9 = 16
► 12 + 4= 16
► 12 + 9 = 21
► 4 + 9 = 13
Since Teena spent less than Rs. 20, the combination (12, 9) can be directly rejected.
Now, Pran spent Rs. 19. This is only possible for the combination (7, 12) i.e. when Pran bought a pencil and a pen.
Now, Teena and Pran bought a common item and Teena could not have had the same combination as Pran.
Hence, the combinations (7, 12) and (4, 9) are not possible for Teena.
Finally, Ram as well as Uday spent Rs. 16 each.
This is possible for the combinations (7, 9) and (4, 12). Hence, Ram and Uday had these combinations (in no specific order).
Since no two people had the same combination, Teena could only have paid in the combination (7, 4) i.e. Teena bought a pencil and a sharpener.
Hence, Teena paid 7 + 4 = Rs. 11
Group Question
Answer the following question based on the information given below.
Six children  Pran, Qadir, Ram, Suman, Teena and Uday  went to a stationary shop and bought two items each out of pencil, pen, eraser and sharpener. No child bought the same combination of items. The price of a pencil, pen, eraser and sharpener were Rs. 7, Rs. 12, Rs. 9 and Rs. 4 respectively. The total money spent by Pran, Ram, and Uday was Rs. 19, Rs. 16 and Rs. 16 respectively. Teena and Pran bought a common item. Qadir, Ram and Suman bought a common item. Teena spent less than Rs. 20
Q. Which of the following items was definitely purchased by Suman?
Consider the solution to the previous question.
Pran = pen and pencil
Teena = pencil and sharpener
Now, Ram = pen and sharpener or Ram = pencil and eraser.
Qadir, Ram and Suman bought a common item. This implies that whetever item was common to them was not bought by anyone else.
Let Ram = pen and sharpener
The pen could not have been common to Qadir, Ram and Suman as Pran had also bought a pen.
Similarly, the sharpener could not have been common to Qadir, Ram and Suman as Teena had also bought a sharpener.
Thus, in this case, there would be no item common to the three people.
Hence, Ram could not have bought the pen and sharpener.
Hence, Ram bought a pencil and an eraser.
Hence, Uday purchased a pen and a sharpener.
Since Teena has already bought a pencil, the item common to Qadir, Ram and Suman is an eraser.
Now, one of Qadir and Suman bought a pen and the other bought an eraser.
Thus, the items purchased by all the people are as shown below.
Thus, Suman definitely purchased an eraser.
Group Question
Answer the following question based on the information given below.
Six children  Pran, Qadir, Ram, Suman, Teena and Uday  went to a stationary shop and bought two items each out of pencil, pen, eraser and sharpener. No child bought the same combination of items. The price of a pencil, pen, eraser and sharpener were Rs. 7, Rs. 12, Rs. 9 and Rs. 4 respectively. The total money spent by Pran, Ram, and Uday was Rs. 19, Rs. 16 and Rs. 16 respectively. Teena and Pran bought a common item. Qadir, Ram and Suman bought a common item. Teena spent less than Rs. 20
Q. Who among the following children did not buy a pencil?
Consider the solution to the previous questions.
Teena, Ram and Pran bought a pencil each.
Group Question
Answer the following question based on the information given below.
Six children  Pran, Qadir, Ram, Suman, Teena and Uday  went to a stationary shop and bought two items each out of pencil, pen, eraser and sharpener. No child bought the same combination of items. The price of a pencil, pen, eraser and sharpener were Rs. 7, Rs. 12, Rs. 9 and Rs. 4 respectively. The total money spent by Pran, Ram, and Uday was Rs. 19, Rs. 16 and Rs. 16 respectively. Teena and Pran bought a common item. Qadir, Ram and Suman bought a common item. Teena spent less than Rs. 20
Q. What amount was spent by Qadir?
Consider the solution to the previous questions.
Qadir bought an eraser and a sharpener/pen.
Hence, he could have spent Rs 13 or Rs 21.
The numbers in the second box are obtained by rearranging the digits of numbers in the first box. The numbers that don’t satisfy this are 569 and 986.
DIRECTIONS for the question: Answer the following question as per the best of your judgment.
Fill in the + OR  signs in between these numbers so that they give correct answers:
1 2^{3} 3^{3} 1 4^{3} = 31
► 1 – 2^{3} – 3^{3} + 1 + 4^{3} = 31.
The total of three consecutive even numbers is 36 more than the average of these three numbers. Which of the following is the second of the three numbers?
Suppose the three numbers are (2x – 2), 2x and (2x + 2). Mean is middle number that is 2x. Then A.T.Q. 6x = 36 + 2x. Solving this yields x = 9. Therefore the second number must be 18.
Find the missing term in the following letter series PU, AG, LQ, WC, HM?
There are 4 alphabets missing between P and U. There are 5 alphabets missing between A and G. The same differences are repeated for the other pairs of letters. So, the next pair in the series should be SY.
DIRECTIONS for the question: Go through these steps carefully and answer the question that follows.
Step 1: p = 0, q = 0, r = l, s = 0
Step 2: s = q + r
Step 3: Replace q by r
Step 4: Replace r by s
Step 5: Print s
Step 6: Increment p by 1
Step 7: lf p = 10 go to step 9 otherwise go to step 8
Step 8: Go to step 2
Step 9: Stop
If step 1 starts with p = 6, q = 0, r = 3, s = 0, what would be the last value of s be?
I^{st} we have, p = 6, q = 0, r = 3, s = 0
Step 2: s = q + r = 0+3 = 3
Step 3: Replace q by r i.e. q = 3
Step 4: Replace r by s i.e. r = 3
Step 5: Print s i.e. s = 3
Step 6: Increment p by 1 i.e. p = 6 + 1 = 7
Step 7: lf p = 10 go to step 9 otherwise go to step 8: s = q + r = 3 + 3 = 6
Step 3: q = 3
Step 4: r = 6
Step 5: s = 6
Step 6: p = 7 + 1 = 8
Step 7: s = 3 + 6 = 9
Step 3: q = 6
Step 4: r = 9
Step 5: s = 9
Step 6: p = 8 + 1 = 9
Step 7: s = 6 + 9 = 15
Step 3: q = 9
Step 4: r = 9
Step 5: s = 15
Step 6: p = 9 + 1 = 10
Step 7: Stop
Therefore, the last value of s is 15.
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