Last few weeks I have been travelling and hence have not been able to contribute to the video analysis of the new CAT’14 Pattern Mock CATs. However while travelling I was able to create time to solve the papers and to write down how I attempted Mock CAT 3.  With positive feedback on my previous effort (on the new pattern Mock CAT 1), let me share with you my take on the new Pattern Mock CAT 3 despite the delay in completing this article. My apologies for this delay and will ensure that the subsequent articles are not delayed.

As usual I started the paper by attempting VALR section in 80 minutes and the balance 90 minutes were used for QADI.

VALR: Summary

• Round1: I went from Q51-100 sequentially and attempted the questions of Verbal Logic and English Usage. While going through these questions I also took a note of the RC passages and LR sets and tried to identify which of these should be attempted. This took me about 30 minutes in which I attempted 16 out of 20 questions.
• Round 2: Now I moved to RC, in R1 I had identified that I was not comfortable with the first passage and hence would not attempt it. I also identified that I am comfortable with the subject of the last three passages and would like to attempt them in the sequence given below:
• Q67-70 Presidents of USA
• Q82-85 Passage on happiness

I attempted 10 out of 12 questions from the three passages in a little less than 25 minutes.

• Round 3: As in the case of RC, in R1 I evaluated the LR sets also. I felt that the LR set on room allocation (Q 74-77) and LR set on circular arrangement (Q 86-88) are likely to be time consuming due to the number of people and also the amount of data, however between the two I was more inclined towards room allocation as it is a bit mathematical. I am comfortable the selection and mathematical LR sets and hence was sure that I would be attempting the remaining two LR sets (Q63-66 and 94-96). I first attempted the sets on selection (63-66), in this I did not mark the answer to Q66 as I got confused and left it after wasting a couple of minutes. The mathematical set (Q94-96) was extremely easy and I was able to attempt the three questions comfortably. These two sets took me less than 15 minutes and then I moved on to the set on room allocation. I however made mistakes in reading the data and was unable solve it in the first go, I solved it in the second attempt but spent around 10  minutes for this data set. In LR hence my attempt of 10 out of 11 questions in approximately 25 minutes..
• Total attempt in VALR was 36 questions.

• Round 1: I went sequentially from Q1-50 and attempted 11 questions that I was sure of solving in about a minute and half. I also identified the questions which could be considered for R2 and identified that all DI sets are attemptable but the first DI set is could be a bit complicated. Decided that I also identified that I may not be able solve questions 16 & 20. The total time spent in Round I was around 30 minutes.
• Round 2: I started this Round with the 5 DS questions in which I attempted all but Q42 which I left after spending some time and then attempted three DI sets (Share price, Institute forms and University professors) leading to 15 attempts in around 30 minutes.
• In remaining 30 minutes I went back to the QA questions that had been marked for R2 and attempted 11 questions but did not mark an answer to one question which I left after solving it partly.
• Total attempt in QADI was 36.

VALR Round 1: 30 minutes 16 attempts

Q51. Para Completion to be attempted by elimination of choices:

Choice (a): incorrect as it is out of scope. Religion and science are not mentioned in the passage.

Choice (b): could be correct on account of continuity and it provides a closure to the passage.

Choice (c): out of scope of the passage, this choice is introducing a new idea or thought.

Choice (d): out of scope on account of Darwinian evolution.

Q52. Sentence correction, to be attempted but since this is my weak area I will not mark the answer if not sure.

Answer has to be choice (b) or (c) as it should be “testimony to” and not “testimony of” but I could not eliminate between these two choices and hence I did not mark an answer.

Q53. Para Completion to be attempted by elimination of choices:

The passage contrasts the current and the ancient point of view on erotic life. The last line gives the point of view of the ancients and the correct answer choice should give our point of view.

Choice (a): incorrect on account t of continuity as it is not giving a contrast.

Choice (b): incorrect on account of scope (morality and lack of instinct)

Choice (c): could be correct on account of continuity as it is giving a contrasting view from the one attributed to the ancients.

Choice (d): incorrect on account of scope, Freud’s opinion on instinct is not the issue.

Q54. Para Completion to be attempted by elimination of choices:

The passage describes what happens when a person is possessed by a spirit and the correct answer choice should take this forward.

Choice (a): incorrect as it is out of scope. Military tactics of Polynesians is irrelevant.

Choice (b): incorrect on account of scale and scope has also been reduced to a specific case.

Choice (c): can be correct on account of continuity.

Choice (d): incorrect on account of continuity.

Q55. Para Jumble, to be attempted.

Statement D has to come before both A and E hence choice (a) and (d) can be eliminated.

Between the remaining choices went for choice (b) since statement C is a better opening statement as it introduces the idea and D takes off from there. Statement C gives the conventional definition of labour and statement D mentions that its scope has been reduced.

Q56. Para Jumble, to be attempted.

DC has to be a mandatory pair. While statement D talks about the artist statement C talks about the critic and then we have further explanation of criticism.

Q57. Data Sufficiency, to be attempted

Statement I implies that today is Wednesday or Sunday or Monday and hence is not sufficient to give the answer.

Statement II implies that today is Friday or Tuesday or Wednesday and hence is not sufficient to give the answer.

Taking both statements together we can say that today is Wednesday,

Q58-61. RC passage, to be attempted in Round 2 but noted the following on the rough sheet:

Q58-61, Long passage on “Freedom”, readable and can be considered.

Q62. Sentence correction, to be attempted

Statement D is incorrect it should be “A solution to this problem….”

Hence Choice (b) is incorrect since

Went through the other statements but not able to identify any error in Statements A, B and C hence left the questions without marking an answer.

Q63-66. LR set, to be attempted in Round 3 but noted the following in the rough sheet:

Q63-66 Set on Selection process, appears do-able.

Q67-70. RC passage, to be attempted in Round 2 but noted the following on the rough sheet:

Q67-70, Okay length, passage on American Presidents, preferable to the first RC passage.

Q71-73. Fill in the blanks, to be attempted

Q71. Second blank has to be “mediocre”

Q72. Second blank has to be “quotidian”

Q73. First blank has to be “disapproval” and second “suspected”

Q74-77. LR set, to be attempted in Round 3 but noted the following in the rough sheet:

Q74-77 Arrangement Set, 12 people in 6 x 2 rooms and 6 statements, do-able but the first set is preferable.

Q78-81. RC passage, to be attempted in R2. In the rough sheet wrote down:

Q78-81, Okay length, passage on business, to be attempted

Q82-85. RC passage, to be attempted in R2. In the rough sheet wrote down:

Q82-85, Okay length, passage on happiness, can be attempted.

Q86-88. LR set, to be attempted in R3. In the rough sheet wrote down:

Q86-88 Circular arrangement, 8 people 2 colours each, 7 statements, could be difficult.

Q89. Critical reasoning, attempted by elimination of choices.

Choice (a): could be correct. Drop in sales even after the company has been cleared of all charges indicates that the buyer is not fully convinced.

Choice (b): incorrect as “manufacturing” is out of scope.

Choice (c): incorrect, if the cheese of company X was always more expensive than its competitors then it should not have impacted the sales now.

Choice (d): incorrect as “bribes” is out of scope

Q90. Critical reasoning, attempted by elimination of choices.

To put one’s foot in the mouth is to say something that is illogical or insensitive or imprudent.

Choice (a): incorrect as the statement is not incoherent (disjointed or rambling).

Choice (b): incorrect, as the focus should be on the logic of the remark and not on the actress. Choice (c): correct because if people believe that depth and lightness are opposites and cannot be associated then the actress’ statement is illogical.

Q91. Vocabulary, attempted by elimination of choices.

Statement 1: Slaver (tray or a plate) is the correct word hence choice (a) and (d) are incorrect.

Statement II: not sure of the answer hence moved on to the next statement.

Statement III: Acclimation is the right word hence choice (c) is also incorrect and hence the answer should be choice (a) but still checked the remaining statements.

Statement IV: Timber refers to wood while timbre pertains to the quality of sound.

Statement V: Canopy of trees.

Q92. Vocabulary, attempted by elimination of choices.

Statement 1: not sure of the answer hence moved on to the next statement.

Statement II: Impassable is the correct word hence choice (d) is incorrect.

Statement III: Levy is a tax and hence cannot be the right word hence choice (b) is incorrect.

Statement IV: Millinery which refers to hats is the right word hence choice (a) is incorrect and Choice (c) should be the answer.

Statement V: Not sure of this one but it does not matter as we have already eliminated 3 options.

Q93. Para jumble – odd statement, to be attempted.

“He” in statement (a) and (c) is mentioned in statement (b) – Mark Blumberg and what is mentioned in statement (b) is explained and taken forward in statements (c) and (c), thus statement (d) thus not fit in.

Q94-96. LR set, to be attempted in R3. In the rough sheet wrote down:

Q94-96 Mathematical set, to be attempted

Q97. Summary of a passage, to be attempted by elimination of choices.

Choice (a): could be correct as the passage is on water pollution in Kanpur but has increased the scale of the problem by addition of the word “severe”.

Choice (b): Correct as it is within the scope and scale of the passage.

Choice (c): incorrect as “state government of Uttar Pradesh” is out of scope of the passage.

Choice (d): incorrect as the purity of the recycled water is out of scope.

Q98. Para jumble – odd statement, to be attempted.

Statement (a) gives a concept and statement (b) tells us that this is called “moksha”. Statement (d) is also connected as it takes the same idea forward.

Q99. Word Usage, to be attempted

I was able to identify that Choice (a) and (d) are correct in terms of usage of the word “fish” but could not eliminate any of the other two choices hence did not mark an answer.

Q100. Word Usage, to be attempted

I was able to identify that Choice (a) and (d) are correct in terms of usage of the word “close” but was not sure about the other two choices hence did not mark an answer.

Summary of VALR Round 1: In a little less than 30 minutes of R1, out of the 20 questions, I

• Attempted 16 questions – Q51, 53, 54, 55, 56, 57, 71, 72, 73, 89, 90, 91, 92, 93, 97 & 98.
• Did not mark an answer to 4 questions – Q52, 62, 99 & 100.
• Identified that in R2 I would attempt the following RC passages::
• Q67-70 Presidents of USA
• Q82-85 Passage on happiness
• Identified that in R3 I would attempt the following LR sets::
• Q63-66 Set on selection
• Q94-96 Mathematical set
• Q74-77 Room allocation set
• In case time is available then go for the remaining RC passage followed by the LR set. The RC passage is preferred over the LR set since a LR set usually needs to be solved completely before any question can be answered but in RC you can answer questions even without reading the complete passage.

VALR Round 2: 25 minutes 10 attempts

Q78. Went for elimination of choices

Choice (a): Correct as it can be inferred from the first couple of paragraphs of the passage.

Choice (b): Incorrect on account of the increased scale, thus choice (d) is also incorrect.

Choice (c): Incorrect on account of scope, “regulations” have not been discussed in the passage.

Q79. Choice (c) can be inferred directly from the sixth paragraph of the passage.

Q80. Choice (a) the word creative is used to explain and unethical practice hence the answer should be sarcastically.

Q81. Choices (a) and (d) were easy to eliminate but got stuck between the remaining two choices and left the question without marking the answer.

I should have eliminated choice (c) on account of it being very narrow and specific.

Q67-70. Passage on Presidents of USA

Q67. Refer to the first paragraph, verbal abuse is not mentioned.

Q68. Direct from the passage, all three statements are correct.

Q69. Went for elimination of choices

Choice (a) is mentioned in the fourth paragraph.

Choice (b) is mentioned in the fifth paragraph.

Choice (c) is mentioned in the fourth paragraph.

Choice (d) not mentioned in the passage and also cannot be inferred from the passage.

Q70. Choice (b) can be inferred from the last paragraph.

Q82-85. Found the passage easy to read and did not have any problem understanding it.

Q82. Choice (c) can be inferred from the first paragraph of the passage.

Q83. Choice (a), (b) and (c) are mentioned in the passage but not choice (d). Intentional activity and not “unintentional activity” is mentioned.

Q84. None of the choices can support the theory.

Q85. Eliminated choice (a) and (d) but was confused between the remaining two choices and hence did not mark an answer to this question.

Summary of VALR Round 2: In the approximately 25 minutes I attempted three RC passages marking the answers to 10 out of the 12 questions and left 2 unmarked.

VALR Round 3: 25 minutes 11 attempts

Q63-66. Made a table separating the men and women as per their profession and then eliminated choices in the first three questions (Q 63, 64 & 65) and marked the correct answers. However in Q66 I got confused, tried it twice (time wasted) and then left it unanswered. I spent about 8-9 minutes in this set.

Q63, 64 & 65: Marked the correct answer

Q94-66. Simple set, Q94 sold me that multiple cases are possible. Made cases for possible values of A, B, C & D and solved the three questions correctly. The time spent in this set was approximately 5 minutes.

Q94, 95 & 96: Marked the correct answer

Q74-77. This set took time was time consuming took about 6-7 minutes to make the table itself and along with the questions the total time was almost 12 minutes. I was however was able to get the answers to the four questions comfortably.

Q74,75, 76 & 77: Marked the correct answer

Summary of VALR Round 3: In the approximately 25 minutes I attempted three LR sets and marked the answers to 10 out of the 11 questions and left 1 unmarked.

QADI Round 1: 11 attempts 30 minutes

Q1. R2 – Functions, it is lengthy to read and can be time consuming.

Q2. R1 – Numbers, have done similar questions earlier.

Second rightmost non-zero digit of 207047 will be the ten digit of 20747 and this can be obtained by checking out the cyclicity of 7. The powers of number with the unit digit 7 will have the last two digits as given below:

2071 will have the last two digits as 07

2072 will have the last two digits as 07 x 07 = 49

2073 will have the last two digits as 07 x 49 = 63

2074 will have the last two digits as 07 x 63 = 01

2075 will have the last two digits as 07 x 01 = 07 = last two digits of 2071

The tens digit of these numbers can be 0 or 4 and since 0 is not available in the choices, the correct answer has to be 4.

Q3. R2 – Numbers, likely to be time consuming

Q4. R2 – Numbers and P&C, could be time consuming.

Q5. R1 – Numbers

Choice (a) is 1.414

Choice (b) is 1.442

41/4 = 21/2 = 1.414

Comparing 41/4 and 51/5 by raising both to the 20th power we get 45 and 54 which are 1024 and 625 respectively. Thus 31/3 values will keep on decreasing.

Q6. R1 – Mixtures. Lengthy to read but am usually able to solve these in short time.

Since Sanjay is selling milk at 10% over his cost price and has a overall profit of 43% thus he has a profit of 30% on account of addition of “x” liters water to pure milk because two successive increments of 30% and 10% are equal to a single increment of 43%.

Since the profit on account of addition of water to pure milk is 30% hence water should be 30% of pure milk.

Since pure milk and “x” liters water add up to 52 liters thus 130% of milk = 52 liters

Or pure milk should be 52/1.3 = 40 liters and water should be 52 – 40 = 12 liters

If Sanjay was selling the mixture at cost price after adding 12 liters of water to 60 liters of pure milk then his profit will be the same ass percentage of water added to milk = 12/60 = 20%

Q7. R1 – Time and Work, used SQC technique of assuming the number of men and women.

Assume:

Initially 2 men and 2 women can complete the piece of work in 120 days and also that a man does “m” units of work per day while a woman does “w” units of work per day.

The amount of work is 120 units

Thus in 1 day the amount of work completed will be (2m + 2w) units

• 120 x (2m + 2w) =  120
• m + w = 0.5

If one woman in the group is replaced by a man then there will be 3 men + 1 woman and as per the question they will finish the work in 96 days

• 96 x (3m + w) = 120
• 3m + w = 120/96 = 5/4 = 1.25

Solving the above two equations we get m = 3/8 units per day and w = 1/8 units per day

As per the question the two women in the group are replaced by men

• the amount of work done per day by 4 men = 4 x (3/8) = 1.5 units

Amount of work is 120 units hence the number of days required by 4 men to complete the work will be 120/1.5 = 80 days

Correct Answer: Choice (b) 80 days

Q8. R1 – Ratios

Ratio of number of coins with A to C = 1 : 3

Ratio of number of coins with C to B = 2 : 7

• Ratio of number of coins with A to B to C = 2 : 21 : 6
• Number of coins with A, B and C are 2x, 21x and 6x respectively
• Total number of coins should be a multiple of 2 + 21 + 6 = 29
• Choice (b) 54 is incorrect but the other three are multiples of 29 and hence cannot be eliminated.
• As per the question, 21x = 18 + 6 (2x) or x =2
• Total number of coins between A, B and C = 29x = 58

Correct Answer: Choice (d) 58 days

Q9. R1 – Mixtures

Vodka in the original mixture = 32 liters in a total of 50 liters = 64%

Step 1: Replace 10 liters of 50 liters of cocktail or replace 20% of mixture

• percentage of vodka in the mixture now = 80% of 64%

Step 2: Replace 20 liters of 50 liters of cocktail or replace 40% of mixture

• percentage of vodka in the mixture now = 80% of 64% of 60% 51.2% 0f 60% > 30%

Q10. R2 – TSD, these questions can usually be solved by rations but I take time in understanding the question hence a R2 question.

Q11-13. R2 DI set.

Noted on the rough sheet under DI:

Q 11–13 Two tables, Movies   Easy numbers but likely to be high on calculations          Attemptable

Q14. R2 – Geometry

Q15. R1 – Inequalities, used SQC technique to get the answer.

As per the equation the sum of roots is 9 and the product of roots is p

As per the question the difference between the roots is less than 7

• thus the roots ≥ 1 and roots ≤ 8
• the product of roots = p > 8, thus choice (a) and (d) are incorrect

the minimum difference between the roots will be when each root = 9/2

• the product of roots = p ≤ (9/2)2 = 81/4 , thus choice (b) is incorrect

Q16. R3 – Time and Work

Read the question but could not understand hence decided not to attempt.

Q17. R1 –Algebra, used SQC technique of substitution on numbers.

Checked the choices for various values of P and Q, since P + Q ≤ 6 took P and Q to be 5 and 1 respectively, choice (c) does not hold and hence is the correct answer.

Q18. R1 –Functions

g(6) = g(8-2) = -16/3

2f(x+3) = 3x/5, replacing x with x-3 we get,

2f(x) = 3(x-3)/5

f(x) = 3(x-3)/10

f(g(6)) = f(-16/3) = -25/10 = -5/2

Q19. R2 – Averages, could require calculation.

Q20. R3 – Algebra, likely to be calculation intensive and time consuming.

Q21. R2 – Algebra, may need to make cases.

Q22. R2 – Coordinate geometry, could be calculation intensive.

Q23. R1 – Cyclicity, have done similar questions earlier

Highest power of 2 that will completely divide 54! = 27 + 13 + 6 + 3 + 1 = 50

• highest power of 2 that will completely divide 54!20 = 50 x 20 = 1000
• a3 = 1000 thus a = 10

Q24. R2 – Set theory, long question

Q25-27. R2 – DI set

Noted on the rough sheet under DI:

Q25–27 Share price table         Calculations likely but easy numbers                  To be attempted

Q28. R2 – Geometry

Q29. R1 – Mensuration, used SQC technique of making cases.

Sum of three sides of the rectangle =100

If the sides are 25, 50 and 25 then area = 25 x 50 = 1250

• Choice (a), (c) and (d) are incorrect.

Q30. R2 – will need to make cases.

Q31-32. R2 – Algebra, new questions type may take time to understand.

Q33. R2 – Mensuration, will need to make cases

Q34-37. R2 DI set.

Noted on the rough sheet under DI:

Q 34-37 Pie Chart & Table      Simple data & easy numbers     To be attempted

Q38. R2 – Mensuration

Q39. R2 – Permutations & Combinations

Q40. R2 – Probability

Q41-45. R2 – Data Sufficiency

Q46. R2 – Permutations & Combinations

Q47-50. R2 DI set.

Noted on the rough sheet under DI:

Q 47-50 Bar chart with simple numbers            Calculations likely         To be attempted

Summary of Round 1:

• Time taken: about 30 minutes.
• Attempted 11 questions – Q 2, 5, 6, 7, 8, 9, 15, 17, 18, 23 & 29.  These were, for me, the easiest QA questions in the paper.
• Identified that I will try attempting all four DI sets and my order of preference will be:
• Q25-27 Share price table
• Q 47-50 Bar chart on forms of institutes
• Q 34-37 Pie & bar Chart
• Q 11-13Tables on movies
• Identified that Q 16 and 20 should not be attempted.

QADI Round 2A: 30 minutes 15 attempts

Started R2 with the 5 DS questions

Q41-45. DS, Solved four DS questions correctly.

Did not mark an answer to Q42, while I was sure that the two statements independently could not answer the questions I was not sure if the two statements could together answer the question and hence did not mark an answer.

Q25-27. DI Set on Share price

Solved all three questions without any problems, since the choices were not close in any question hence approximation was helpful in saving time.

Q47-50. DI Set on sale of forms

Solved all four questions without any problems, calculations however were higher in this set as compared to the previous one but the questions were not difficult.

Q34-37. DI Set on professors in universities.

I was able to solve this set also but it took some time for me to determine the values of P, Q, R and S as I initially made a calculation mistake and hence had to redo the set.

The five DS questions and the three DI sets (10 questions) took me about 30 minutes. With 25 attempts in approximately 60 minutes I now moved to the QA questions marked for Round 2.

QADI Round 2B: 30 minutes 10 attempts

Q1. If f(x) is divided by x then the reminder is a4

• f(0) = t = a4

Now p, q, r and t are in GP and t = a4

• p = a, q = a2 , r = a3
• f(x) = ax3 + a2x2 + a3x + a4

If f(x) divided by (x-a) then the remainder will be f(a)

• f(a) = 4a4, as per the question this has to be a perfect cube
• a = 2

Q3.  120 = 23 x 3 x 5

LCM (X, 120) = 1320 = 120 x 11

• X should be a multiple of 11 but not of 112 or higher powers so it is not a perfect square
• Choice (a) is incorrect

LCM (Y, 120) = 1680 = 120 x 14 = 120 x 2 x 7

• Y should be a multiple of 7 but not of 72 or higher powers so it is not be a perfect square

Choice (b) is incorrect

LCM (Z, 120) = 1800 = 120 x 15 = 23 x 32 x 52 or

• Z can be 32 x 52  or 2 x 32 x 52 or Z may be a perfect square
• Choice (c) is incorrect

Q4. Thus the number of 5 digit numbers that are multiples of 3 or 4 but not both

= multiples of 3 + multiples of 4 – multiples of 12

For the 5 digit number to be a multiple of 3, its sum of digits should be a multiple of 3

The digit sum of first 6 natural numbers = 21

For the 5 digit number to be a multiple of 3 the only digits that can be removed are either 3 or 6, thus one digit of the number will be either 3 or 6 and the remaining 4 digits will be 1, 2, 4 and 5.

• The number of 5 digit numbers that will be multiple of 3 = 2 x 5! = 240

Thus the answer will be more than 240

• Choice (d) 240 is incorrect

Last 2 digits of 5 digit numbers that are multiples of 4 will be: 12, 16, 24, 32, 36, 52, 56 & 64

The remaining 3 places can be filled in 4 x 3 x 2 = 24 ways

• Total number of numbers that are divisible by 4 = 24 x 8 = 192
• the answer will be less than 240 + 192 = 432
• Choice (a) 432 will be incorrect

Got confused while determining the number of 5 digit numbers that are multiple of 12 and hence left the question without marking the answer.

Q14. Solved by using the SQC technique of verifying the figure and approximating the answer.

In the question ADC is 90o and in the figure also it is 90o

As per the question

AO = 56, OD = 4, AC = 61 and AB = 5

In the figure OB : OD does not appear to be  greater than 5 : 4 hence BC should be pushed deeper in the circle.

Visual inspection of the figure tells us ABC is more than double of ABD, check the choices:

Choice (a) 11 : 14 < 1, hence incorrect

Choice (b) 14 : 3 > 2, could be correct

Choice (c) 3 : 11 < 1, hence incorrect

Choice (d) 11 : 9 < 2, hence incorrect

Q19. Assume: Average score before the second last test = x

Total number of tests = n + 2

On scoring 98 marks in the second last test the average increases by 1 (deviation of 1)

• 98 = Original average + Deviation from the average x total number of tests
• 98 = x + (1) (n + 1)
• x + n = 97

On scoring 70 marks in the last test the average dropped by 2 (deviation of -2)

• 70 = (x + 1) + (-2) (n + 2)
• x – 2n = 73

Solving the two equations we get n = 8

• total number of tests = n + 2 = 10

Q21. Solved by musing the SQC technique of making cases:

As per the question: a + 15b + 25c = 77, where a, b & c are natural numbers

• a + 5(3b + 5c) = 77
• 5(3b + 5c) = 77 – a
• there are 8 possible values of “a” which are = 2, 7, 12, 17, 22, 27, 32 & 37

Minimum value of b and c is 1, thus maximum value of a is 37

If a = 2 then 3b + 5c = 15, no values of b and c are possible

If a = 7 then 3b + 5c = 14, then b = 3 and c = 1

If a = 12 then 3b + 5c = 13, then b = 1 and c = 2

If a = 17 then 3b + 5c = 12, no values of b and c are possible

If a = 22 then 3b + 5c = 11, then b = 2 and c = 1

If a = 27 then 3b + 5c = 10, no values of b and c are possible

If a = 32 then 3b + 5c = 9, no values of b and c are possible

If a = 37 then 3b + 5c = 8, then b = 2 and c = 1

Thus four ordered triplets (a, b, c) are possible.

Q24. Solved this question by making a venn diagram.

Q28. Solved this question by using the SQC technique of drawing the figure and assuming the value of the side of square.

Let the side of the square = 2

Thus Area of the square = 4

• • Area of OFCG = 1
• Area of OFG = ½
• Area of OMN = (1/4) (OFG) = 1/8
• Area of MNGCF = 1 – 1/8 = 7/8

Assume the area of EHMN = x

Ratio of area of MNGCF to area EHNM = 7/8 : x = 7 : 8x

• In the choices the first number should be a multiple of 7
• Choice (b), (c) and (d) are incorrect

Correct Answer: Choice (a) 7 : 9

Q39. Could not understand how the question should be solved hence made a figure to understand.

If there are 4 children standing around a circle then we get a square and the number of distinct pairs in which children are:

• standing next to each other = 4 = n or the number of sides
• not standing side by side = 2 (along the two diagonals) = nC2 – n
• nC2 – n = 5n
• n = 13

Q40.  Probability of not getting a blue ball in two trials = 81/100 = (9/10)2

• Number of blue balls = 1 out of 10

Probability of getting a green ball in two consecutive trials = 49/100 = (7/10)2

• Number of green balls = 7 out of 10
• Number of red balls = 2 out of 10

Number of ways in which we can draw balls of three different colours = 3 x 2 x 1 = 6

Thus probability of getting a ball of three different colours in three consecutive trials

= 6 x (1/10) x (7/10) x (2/10) = 21/250

Q10. Let the speed of Ayesha be x km/hr and that of Bhumika = y km/hr

Ayesha started running at 5am and Bhumika at 6am

• At 6 am Ayesha has run x km

At 7 am the two meet and after 6 am in 1 hour Ayesha has run x km and Bhumika y km

• Ratio of speed of Ayesha to Bhumika = x : y

At the time of the second meeting, in the time after the first meeting at 7am:

Ayesha has run 2y km and Bhumika has run 4x km

• Ratio of speed of Ayesha to Bhumika = (x/y) = (2y/4x)
• (x/y)2 = ½
• x/y = 1/√2

Correct Answer: Choice (b) 1 : √2

GP 