Analysis

Students must be a relieved lot today. CAT-14 is finally over and may be it feels anticlimactic – isn’t it? Its over??## Is this what we were preparing for all this time. We can not just understand but relate to the feeling. So what was it like. Here are some pointers of changes

1. VA was full of changes. Not a single question that was based on vocabulary against almost 33.33% of the VA questions that used to be word based over the last several years. The focus was squarely on reading skills. Even essence questions made an entry. Essence of a paragraph, Jumbled up paragraphs, Odd one out in a parajumble, inference to be drawn from a para and 16 questions from four RC sections. Everything screamed for better readers.

If you have been a regular reader of the newspapers and magazines and have been writing central ideas of the passages regularly as mandated at CHEM – remain assured you are expected to do well in such a section.

2. Overall, the VA section was much simpler in terms of toughness or complexity levels as compared to CATs over the last few years. If you have been preparing consistently, here was a section to score well competitively speaking. For a change the options weren’t “razor-thick close”. One could eliminate options with fair ease.

3. Passages were taken from a variety of reading sources that comprise leading magazines globally to Wikipedia. Once again stressing the need to read regularly and varied.

4. QA was full of sitters. After a long time the QA section was such a simple one. Arithmetic was the flavor of the day. Percentages, Ratios, Time and Work, Distance and Time, Averages & Alligation and the Good old Number theory – everything found a place. The questions were as an aptitude test should be – simple but with that harmless twist in the language which careful readers will pick. Also questions required quick and good structuring from the test taker to be able to solve quickly. All in all those of you CHEMpions – if you practiced your ratios approach well, there should be no trouble in doing all of them quickly and accurately.

5. Geometry had its fair share with almost 7 questions. What the questions needed us to do was to quickly draw and visualize the situation. The questions were based on simple properties of Triangles and Circles primarily. The single mensuration question in the evening slot was volume questions almost similar to a Twister question on mensuration in the CHEM courseware. Once again even if you have done your “Thrust” material at CHEM – ALL of the geometry questions were sitters for you.

6. Algebra – kept itself restricted to Linear, quadratic equations and sequences and progressions – with a question on calendar, one on coordinate Geometry and another question on Trigonometry popping up here and there. Although the questions on these not so popular topics were very simple – even if you avoided them you can be excused because there were so many others equally simple and so mush practiced already that one had a field time scoring in the QA section.

7. Our Guess is, that as a CHEMpion, out of the 36 QA questions in the first section, you could have easily attempted 27-30 questions in something like 60 min with near 100% accuracy. Now if that is a lofty expectation then too you should crack this section completely. J

8. Data Interpretation and Logical reasoning were Tough in the morning and not so tough in the evening slots. At least three cases in the morning slot – one in DI and two in LR were full of scattered data and multiple possibilities. Even the questions were a little twisted. Would have required a lot of patience to work themselves out. In comparison the cases in the evening slots were simpler. There was only once case based on vein diagrams that had clues given in a very scattered manner and could have posed a little problem in arranging all of it. However, the evening slot was far more manageable. LR had all the standard cases of Linear/circular sequencing, mathematical reasoning, conditional logical reasoning and the Analytical variety too. A notable exception was complete absence of Data Sufficiency. Verbal reasoning has not been appearing since many years now and so it continued.

9. If you have practiced the Material thoroughly there should be no trouble in negotiating most of these cases. We do think that the number of attempts in the morning slot would have to be lesser due to slightly tougher cases in DI/LR.

So overall, we think that a 55 to 60 attempts in the morning slot and 60-65 attempts in the evening slot (with more or less even attempts in both the sections) would be a good number of attempts. If you are able to achieve that with approximately 90-95% accuracy then you should be sitting pretty expecting a good score for top calls. You can adjust the numbers downward for lower percentiles.

A very detailed analysis of CAT 2014 follows. This is a hasty effort and hence has a lot of typo and formatting errors. They are being corrected and will be OK by evening of 17th Nov 2014. Hope you appreciate the painstaking efforts of our faculty in bringing all of these together for you.

Do write to us at help@chgroup.in with your feedback and comments.

Wishing you a very Successful life ahead of you. Take Care.

 


Quantitative Ability & Data Interpretation
Question 1
Question:

An equilateral triangle has an incircle which is circumcircle to a square with Radius 1. What is the area of triangle?

  1. \frac{3\sqrt{3}}{2}
  2. 3\sqrt{3}
  3. 12
  4. 6


Solution:

Given PQRS of side 1 unit Hence PR = \sqrt{}2 unit (diagonal) This PR will be the diameter of incircle

Therefore, radius = 1/\sqrt{}2

Also if ‘a’ denotes the side of equilateral triangle then radius of incircle r = a/2\sqrt{}3

Therefore, a/2\sqrt{}3 = 1/\sqrt{}2.

Therefore,  a = \sqrt{}6

Hence area of equilateral triangle \sqrt{}3/4 a2 = \sqrt{}3/4 (\sqrt{}6)2 = 3\sqrt{}3/2 sq.units.

 


Question 2
Question:

The area of a regular hexagon ABCDEF is 60. What is the area of triangle ACE.

  1. 30
  2. 25
  3. 40
  4. 20


Solution:

Ans : 30

Given area of Hexagon ABCDEF = 60 sq cm

Let O is the center of the hexagon. Join O with A, C and E. then The figure is divided into six equal and congruent triangles. Hence

area of \sqrt{} ACE = 30 sq cm

(Since it contains 3 triangles)

 


Question 3
Question:

A month has 3 even dates on Monday. Which day is the 15th of the month?

  1. Friday
  2. Sunday
  3. Saturday
  4. Wednesday

 


Solution:

Ans : Sunday

Solutions :

In a given month three Mondays comes on even dates only possible case is 2, 9,, 16, 23, 30

Therefore on 15th of this month, these will be Sunday.


Question 4
Question:

ax+2 b3x = a1-x b5x. What is the value of xlog10(b/a). 

  1. log\sqrt{a}
  2. log a
  3. 3/2 log a
  4. log 9/6

 


Solution:

Ans : log10 (a1/2)

ax+2 b3x = a1-x b5x

   a1 = (b/a)2x

   = log a = 2x log b/a

   = ½ log a = x log b/a

   = log \sqrt{a} = xlog b/a


Question 5
Question:

X started from a point A towards B and at the same time Y started from B towards X. X reached B in an hour and Y reached A in 84 minutes. In how much time after they started did they meet each other?

  1. 35 min
  2. -32 min
  3. 24 min
  4. 30 min


Solution:

35 minutes

Given x travels from city A to city B in 60 mins and y travels from city B to city A in 84 mins.

 

Let x be the distance between A and B

Then Speed of x = Sx = x/60

Speed of y = Sy =  x/84

Relative Speed = Sx + Sy = = (x/60) +(x/84)

\ Time taken before they cross = Relative Distance/Relative speed = x / (sx + sy)

=  60×84/144 = 35 min


Question 6
Question:

  1. How many five digit numbers formed using 1, 2, 3 using the numbers atleast once?
  1. 150
  2. 180
  3. 240
  4. None of these


Solution:

There are 6 possible cases, we can make numbers using

I 1 (thrice), 2 (once), 3 (once) No. of ways = 5!/3! = 20

II 1 (once), 2 (thrice), 3 (once) No. of ways = 5!/3! = 20

III 1 (once), 2 (once), 3 (thrice) No. of ways = 5!/3! = 20

IV 1 (twice), 2 (twice), 3 (once) No. of ways = 5!/3!2! = 30

V 1 (thrice), 2(once), 3 (twice) No. of ways = 5!/2!2! = 30

VI 1 (once), 2 (twice) 3 (twice) No. of ways = 5!/2!/2! = 30

Total no. of ways = 20 + 20 + 20 + 30 + 30 + 30 = 150


Question 7
Question:

No. of zeroes in 1 x 2 x 3 x ________x 1000

  1. 249
  2. 248
  3. 250
  4. None


Solution:

Ans : a


Question 8
Question:

In a can of 3 litres glycerin if one litre is taken and then the can is again filled with water. This process is again repeated with the mixture. What will be the ratio of glycerin to water in the can?  

  1. 4 : 5
  2. 8 : 3
  3. 5 : 4
  4. 1 : 1


Solution:

Ans. (a)

3

2

 

 

3

2

9

 

4

Ratio of G : W = 4 : 5.

Solutions:

Total

 

Glycerine after 1st exchange water

 

Glycerine after 2nd exchange water

 

3

:

2

 

 

 

 

 

3

:

2

 

9

 

 

 

4

5

\ Glycerine : Water = 4 : 5


Question 9
Question:

What will be the remainder of 20142014 when divided by 5.

  1. 1
  2. 0
  3. 2
  4. 3


Solution:

1.

Reminder


Question 10
Question:

For which points (a + b) x + (a – b) y = 2a + 3b satisfies

  1. (2, 1)
  2. (5/2, -1/2) 
  3. (3 -1/2) 
  4. None of these


Solution:

Ans (5/2 ,-1/2)

 (a + b) x + (a – b) = 2a + 3b

(a- b)y = a[2 – x] + b[3 – x]

y =  [a(2-x)+b(3-x)] /(a-b)

Put the given options (x, y) = (5/2 , -1/2)


Question 11
Question:

For which condition log10(1 + n) – log10(n) < log10(1.01)

  1. n > 100
  2. n < 100
  3. n > 10
  4. n < 10


Solution:

Ans. n > 100

Given log10(n + 1) – log10n < log10(1.01)


Question 12
Question:

Ages of Three brothers are in the ratio of 4 : 5 : 8. If age of Elder brother is two less than nine times the difference of other two brothers. Then what is the sum of ages of all of them?

  1. 17
  2. 51
  3. 34
  4. 68


Solution:

Ans. –34

Solutions

Given ages of three brothers, say A, B, C be 4 : 5 : 8

Then given 9[5x – 4x] = 8x + 2

= x = 2


Question 13
Question:

In a class having two section the average weight is 55.8kg if average of section A is 56.4kg and of section B 54.2 kg. then what will be the ratio of students of section A and B.

  1. 3 : 8
  2. 8 : 3
  3. 5 : 7
  4. 1 : 4


Solution:

Ans. 8 : 3.

Ratio of students = 8 : 3.


Question 14
Question:

Subodh sold two watches. One of Neha at profit of 25% and one to Seema at loss of 25%. If Neha sold it to Gautam at a loss of 20%. Then which of the following statements is true.

  1. Gautam & Subodh bought the watch at same price.
  2. Gautam spent 40% less than Seema
  3. Neha bought at 20% less than Gautam
  4. All of these


Solution:

Ans. (a)

Subodh

Neha

Gautam

4

5

 

 

4

5

                Hence subodh and Gautam bought water at same price

 


Question 15
Question:

What will be the remainder of  x2014 + x – 1 / x – 1

  1. 1        
  2. 0        
  3. 2014
  4. -2


Solution:

Ans. (a).

Reminder of x2014 + x – 1 / x–1 ® x2014 /x–1 + x–1/ x – 1
(x2014 – 12 / x – 1) + 0 [Remainder Zero]
-1
[xa - ba will be completely divisible by x – b if a is even]

 


Question 16
Question:

A contractor hires 150 workers for a project to be completed in 180 days. If in 60 days only one-fourth work is done. Then how many extra workers needed to complete the project in time?

 

  1. 75      
  2. 60      
  3. 225  
  4. 50


Solution:

Ans (a)
150/1 = 2x/3
= x = 225

= Extra workers required = 225 – 150 = 75


Question 17
Question:

In a triangle if one of the angle is twice the sum of other two angles. Then what can be the maximum possible value of the smallest angle?

  1. pi/6
  2.  pi/3
  3. pi/4
  4. pi/2


Solution:

In a triangle ABC

                Let angle B = 2[angle A + angle C]

                = angle B = 120°

                = angle A + angle C = 60°

                Hence maximum possible values of smallest angle would be 30° = pi/6


Question 18
Question:

If Arithsmetic means of ten numbers is 25. and none of them is less than 20. Then the value of one of them can be atmost

  1. 70
  2. 75
  3. 100
  4. 80


Solution:

Ans. 70

 

Given Arithmetic mean of ten numbers is 25 Hence total is 250

Now to get the maximum value of the set fwe have to take the minimum value of other numbers i.e 20.

Hence x + 20 x 9 = 250

x = 70


Question 19
Question:

If Rimi travels from city A to city B and then do city A. friend Mini travels from city B to city A on the same road and Then back again They meet for the first time at a distance of 60 m from A and second time at a distance of 30 m from B. what is the total distance between A and B2.

  1. 150 m
  2. 120 m
  3. 180 m
  4. 200 m


Solution:

From both, we can say that

60/(d + 30) = (d + 60)/(d + 120)

Solving, we get d = 60

Therefore, total distance = 150 m.

 


Question 20
Question:

AB is side of square with centre O and then on the circle with centre O, on the minor arc AB there exist a point C. then what is the angle angle OCA?

  1. 135°
  2. 45°
  3. 75°
  4. 120°


Solution:

Ans. 135°.

Given

ABCD is a square

angle ADB = 45°

= angle ACB = 135° [Cycle in quadrilateral opp. angles are supplementary]

 


Question 21
Question:

In a triangle in which AB = 9 cm, AC = 12 cm and BC = 15 cm and a point 0 lies on BC which is circumcentre of triangle ABC  what will be the area of triangle 0AB

  1. 27
  2. 90
  3. 54
  4. 18


Solution:

Ans 27.

Given O is the circumcenter, Now triangle ABC is a right angled triangle. Since it satisfies pythagorous theorem [92 + 122 = 152]

= arc BAC forms a semicircle  [because angle A = 90°]

= BC is diameter = 15 cm

= OB = 15/2 cm

= OA = 15/2 cm

Area of triangle ABC = 1/2 x 9 x 12 = 54 therefore area of AOB = 54/2 = 27.
 

 


Question 22
Question:

In a rhombus the diagonals are in the ratio of 1 : \sqrt{}3.Then what is the smallest angle of rhombus

  1. 60°
  2. 45°
  3. 30°
  4. 15°


Solution:

Ans. (a)Solutions :

1 x 2 x 3 x ………….. x 1000 = 1000

                No. of zeroes in 1000 =  1000/5 + 1000/52 + 1000/53 + 1000/54 +…………..

                = 200 + 40 + 8 + 1 + 0 + …………..

                = 249

Let AC & BD be diagonals and interest at 0.

Given AC : BD = Ö3 : 1 Þ Let AC = 2Ö3  BD = 2

Then AO : OD = Ö3 : 1

= AD2 = (Ö3)2 + (1)2 = 2

Now AB = AD = 2cm   Also BD = 2cm

therefore, \Delta ADB is equilateral triangle

Hence smallest angle in rhombus is 60°


Question 23
Question:

If x3, y3, z3 are in G.P. then which of the following holds

a

  1. log x, log y, log z are in A.P.
  2. (log x)3, (log y)3, (log z)3 are in A.P.
  3. log x, log y, log z are in G.P.\
  4. log x, log y, log z are in H.P.


Solution:

If x3, y3, z3 are in G.P.

y6 = x3 z3

Taking log, 6 log y = 3[log x + log z]

2log y = log x + log z

[If 2b = a + c then a, b, c are in A.P.]

Therefore, log x, log y, log z are in A.P.


Question 24
Question:

For natural no. X, Given x2 + 31 is a perfect square. How many possible values of x exist

  1. 1
  2. 2
  3. Infinite
  4. Not possible


Solution:

1

x2 + 31 = perfect square = y2

                Þ y2 – x2 = 31

                (y – x) (y + x) = 31 x 1

                \ y – x = 1

                And y + x = 31

                Only one such value is possible

   [x = 15, y = 16]


Question 25
Question:

For positive value of a and b given

f(x) = a – x2 + 1 and g(x) = x2 + b + 3 and f(2) g(1) < 0

  1. a < 3
  2. b > 3
  3. a > 2
  4. b < 2


Solution:

Ans. a < 3

f(x) = x – x2 + 1

                g(x) = x2 + b + 3

                f(2) g(1) < 0

                (a – 4 + 1) (1 + 6 + 3) < 0

                (a – 3) (b + 4) < 0

                = a < 3

 


Question 26
Question:

What cannot be the value of 4sin x cosx (1 + sin x cosx)

  1. –1
  2. 0
  3. 3
  4. 4


Solution:

4 sin x cos x [1 + sin x cos x]

The max. value exist at x = 45°

Therefore, 4 x 1/\sqrt{}2 x 1/\sqrt{}2 [1 + (1/\sqrt{}2)2]

= 4/2 [1 + 1/2] = 3

Hence 4 cannot be the value of 4 sin x cos x [1 + sin x cos x]


Question 27
Question:

Given a list of consecutive odd integers, the first number denotes the total number of integers in the list. If six times the first number exceeds the average of all the numbers by 2013, then what is the total number of integers in the list.

  1. 503
  2. 501
  3. 505
  4. 507


Solution:

Here all the values depend on the total no. of Integers. Hence we will check by picking up each option individually. Take option (a) 503

If 503 is the total no. of integers in the list. It will also be the first no. of square. The last no. could be find out

Last no. = 503 + (503 – 1)2

= 503 + 1004 = 1507

The series / list will be [503, 505, 507,………..1507]

Avg. will be (a + l)/2 = (503 + 1507)/2 = 1005

Given condition 6(503) – 1005 = 3018 – 1005 = 2013 satisfies.


Question 28
Question:

If m ◇ n = m2n then what is the value of

(3 ◇ 4) ◇ 2 =

  1. 332
  2. 412
  3. 316
  4. 46


Solution:

332

(3 ◇ 4) ◇ 2 = (38) ◇ 2 =  332


Question 29
Question:

An exam consists of twenty multiple choice questions having three options each. In how many ways a student answer the questions correctly but alternatively?

  1. 211
  2. 210
  3. 210x 20P10
  4. None 


Solution:

There are two ways in which he can answer the question as required

I

 

R

 

W

 

R

 

W

…………

 

(R ® Right)

II

 

W

 

R

 

W

 

R

…………

 

W ® Wrong)

Now in case I; the 1st question can be answered correctly in one way only and for the 2nd question it can be answered wrong in two ways & so on………..

1 x 2 x 1 x 2 x……… = 110 x 210 = 210 ways

Same number of ways lies for Case II also.

Therefore total no. of ways = 210 + 210 = 211.


Question 30
Question:

The graph of the function f(x) = ax2 + bx + c is symmetric around x = p then the value of p is

  1. P= -(b/a)
  2. P= b/a
  3. P= b/2a
  4. P= -b/2a


Solution:

Given f(x) = ax2 + bx + c

= a [x2 + b/a x + c/a]

= a [x2 + 2 x b/2a x x + (b/2a)2 – (b/2a)2 + c/a]

= a [[x + b/2a]2 + (4ac – b2)/4a2]

This graph is symmetric around x = –b/2a

Therefore, P = –b/2a


Question 31
Question:

Given a, b are roots of quadratic equation x2 + ax + b then the roots of the quadratic equation bx2 + ax + 1 would be

  1. 1/α,1/β
  2. 1/ α2,1/β2
  3. a + b, a– b
  4. None


Solution:

Given quadratic equation x2 + ax + b = 0

Then product of roots αβ = b

Sum of roots α+β =-q

Next quadratic equation bx2 + ax + 1 = 0

Then product of roots αβ = 1/b =1/ αβ

Hence clearly by visualising options

New roots are α = 1/ α and  β=1/ β


Question 32
Question:

Given (3p + 6q + r + 2s) (3p – 6q – r + 2s) = (3p + 6q – r – 2s) (3p – 6q + r – 2s)

then which of the following is true?

  1. p : r = q : s
  2. p : q = s : r
  3. p : r = s : q
  4. None of these


Solution:

(3p + 6q + r + 2s)/(3p + 6q – r – 2s) = (3p – 6q + r – 2s)/(3p – 6q – r + 2s)              

Reversing Componendo & Dividendo.

= (3p + 6q)/(r + 2s) = (3p – 6q)/(r-2s)

= (p + 2q)/(p-2q) = (r + 2s)/(r – 2s)

Again Reversing Componendo & Dividendo

p/2q = r/2s 

= p/r = q/5 = p : r = q : s


Question 33
Question:

The sum of A.P. of n numbers is n(n + 8) and n > 1 then common difference would be

d = 3
d = 2
d = 1
d = 4

Solution:

Ans. (b)

Given Sn = n (n + 8)

Put n = 2 S2 = 2 (2 + 8) = 20 = T1 + T2

Put n = 3 S3 = 3 (3 + 8) = 33 = T1 + T2­ + T3

n = 4 S4 = 4 (12) = 48 = T1 + T2 + T3 + T4

Therefore, T3 = 33 – 20 = 13

T4 = 48 – 33 = 15

Hence common difference is 2.


Question 34
Question:
Solution:


Question 35

CASE

 500 Students participated in an exam for 3 colleges X, Y and Z. 106 students got a call from at least one of the colleges. Students getting a call from only X, students getting a call from only Y and students getting a call from only Z are in the ratio 1:3:4. The number of students getting a call from only X and Z, the number of students getting a call from only X and Y and the number of students getting a call from only from Y and Z are in the ratio 1:2:3. The number of students getting a call from only Y is twice of the number of students getting a call from all the three colleges. Half of the students getting a call from Z got call from at least one more college.

Question:

How many got a call from all the three colleges?

Solution:

12

Let the number of people with offers from all the three colleges by x. Then according to the condition, the number of people with offer from Y only is 2x. Also the ratio of number of people with offers by X only, Y only and Z only is 1:3:4. So let us consider total number of people with offers from all the colleges be 3x and Y only as 6x to make them integers. So the number of people with calls from Z only will be 8x. Let us also take X and Z only, X and Y only and Y and Z only be y, 2y and 3y.

Now according to the given condition

8x = y + 3y + 3x

or 5x = 4y

Now adding all the values of the Venn diagram we get

2x + 6x + 8x + 3x + y + 2y + 3y = 106

19x + 6y = 106

Substituting the value of y we get x = 4


Question 36

CASE

 500 Students participated in an exam for 3 colleges X, Y and Z. 106 students got a call from at least one of the colleges. Students getting a call from only X, students getting a call from only Y and students getting a call from only Z are in the ratio 1:3:4. The number of students getting a call from only X and Z, the number of students getting a call from only X and Y and the number of students getting a call from only from Y and Z are in the ratio 1:2:3. The number of students getting a call from only Y is twice of the number of students getting a call from all the three colleges. Half of the students getting a call from Z got call from at least one more college.

Question:

How many offers were made by the colleges?

Solution:

160

Let the number of people with offers from all the three colleges by x. Then according to the condition, the number of people with offer from Y only is 2x. Also the ratio of number of people with offers by X only, Y only and Z only is 1:3:4. So let us consider total number of people with offers from all the colleges be 3x and Y only as 6x to make them integers. So the number of people with calls from Z only will be 8x. Let us also take X and Z only, X and Y only and Y and Z only be y, 2y and 3y.

Now according to the given condition

8x = y + 3y + 3x

or 5x = 4y

Now adding all the values of the Venn diagram we get

2x + 6x + 8x + 3x + y + 2y + 3y = 106

19x + 6y = 106

Substituting the value of y we get x = 4


Question 37

CASE

 500 Students participated in an exam for 3 colleges X, Y and Z. 106 students got a call from at least one of the colleges. Students getting a call from only X, students getting a call from only Y and students getting a call from only Z are in the ratio 1:3:4. The number of students getting a call from only X and Z, the number of students getting a call from only X and Y and the number of students getting a call from only from Y and Z are in the ratio 1:2:3. The number of students getting a call from only Y is twice of the number of students getting a call from all the three colleges. Half of the students getting a call from Z got call from at least one more college.

Question:

Based on above case

Solution:

Let the number of people with offers from all the three colleges by x. Then according to the condition, the number of people with offer from Y only is 2x. Also the ratio of number of people with offers by X only, Y only and Z only is 1:3:4. So let us consider total number of people with offers from all the colleges be 3x and Y only as 6x to make them integers. So the number of people with calls from Z only will be 8x. Let us also take X and Z only, X and Y only and Y and Z only be y, 2y and 3y.

Now according to the given condition

8x = y + 3y + 3x

or 5x = 4y

Now adding all the values of the Venn diagram we get

2x + 6x + 8x + 3x + y + 2y + 3y = 106

19x + 6y = 106

Substituting the value of y we get x = 4


Question 38

CASE

 500 Students participated in an exam for 3 colleges X, Y and Z. 106 students got a call from at least one of the colleges. Students getting a call from only X, students getting a call from only Y and students getting a call from only Z are in the ratio 1:3:4. The number of students getting a call from only X and Z, the number of students getting a call from only X and Y and the number of students getting a call from only from Y and Z are in the ratio 1:2:3. The number of students getting a call from only Y is twice of the number of students getting a call from all the three colleges. Half of the students getting a call from Z got call from at least one more college.

Question:

Based on above case

Solution:

Let the number of people with offers from all the three colleges by x. Then according to the condition, the number of people with offer from Y only is 2x. Also the ratio of number of people with offers by X only, Y only and Z only is 1:3:4. So let us consider total number of people with offers from all the colleges be 3x and Y only as 6x to make them integers. So the number of people with calls from Z only will be 8x. Let us also take X and Z only, X and Y only and Y and Z only be y, 2y and 3y.

Now according to the given condition

8x = y + 3y + 3x

or 5x = 4y

Now adding all the values of the Venn diagram we get

2x + 6x + 8x + 3x + y + 2y + 3y = 106

19x + 6y = 106

Substituting the value of y we get x = 4


Question 39

CASE

Eight teams A, B, C, D, E, F, G and H participate in a tournament. The teams are divided into two groups of four each. Every team of the group plays one match each with all the other teams of that group. Each day two games are played and thus the tournament gets over in 6 days. The result of a match is either a win or draw. If a team wins the match it gets 3 points. In case of a draw 1 point is awarded to both the teams. If a team loses a match, it gets 0 points. Following is the table of points at the end of each day.

 

A

B

C

D

E

F

G

H

Day 1

3

1

0

0

0

0

0

1

Day 2

3

4

1

0

0

1

0

0

Day 3

 

 

 

 

 

 

 

 

Day 4

 

 

 

 

 

 

 

 

Day 5

 

 

 

 

 

 

 

 

Day 6

 

 

 

 

 

 

 

 

 

Question:

Which 2 teams teams are in the same group?

(a)  A and B

(b) B and C

(c) D and E

(d) E and F


Solution:


Question 40

CASE

Eight teams A, B, C, D, E, F, G and H participate in a tournament. The teams are divided into two groups of four each. Every team of the group plays one match each with all the other teams of that group. Each day two games are played and thus the tournament gets over in 6 days. The result of a match is either a win or draw. If a team wins the match it gets 3 points. In case of a draw 1 point is awarded to both the teams. If a team loses a match, it gets 0 points. Following is the table of points at the end of each day.

 

A

B

C

D

E

F

G

H

Day 1

3

1

0

0

0

0

0

1

Day 2

3

4

1

0

0

1

0

0

Day 3

 

 

 

 

 

 

 

 

Day 4

 

 

 

 

 

 

 

 

Day 5

 

 

 

 

 

 

 

 

Day 6

 

 

 

 

 

 

 

 

 

Question:

Which of the following statements are true?

(a) C played on Day 3

(b) G played on day 5

(c) …….

(d) ……


Solution:


Question 41

CASE

Eight teams A, B, C, D, E, F, G and H participate in a tournament. The teams are divided into two groups of four each. Every team of the group plays one match each with all the other teams of that group. Each day two games are played and thus the tournament gets over in 6 days. The result of a match is either a win or draw. If a team wins the match it gets 3 points. In case of a draw 1 point is awarded to both the teams. If a team loses a match, it gets 0 points. Following is the table of points at the end of each day.

 

A

B

C

D

E

F

G

H

Day 1

3

1

0

0

0

0

0

1

Day 2

3

4

1

0

0

1

0

0

Day 3

 

 

 

 

 

 

 

 

Day 4

 

 

 

 

 

 

 

 

Day 5

 

 

 

 

 

 

 

 

Day 6

 

 

 

 

 

 

 

 

 

Question:

Based on above case

Solution:


Question 42

CASE

Eight teams A, B, C, D, E, F, G and H participate in a tournament. The teams are divided into two groups of four each. Every team of the group plays one match each with all the other teams of that group. Each day two games are played and thus the tournament gets over in 6 days. The result of a match is either a win or draw. If a team wins the match it gets 3 points. In case of a draw 1 point is awarded to both the teams. If a team loses a match, it gets 0 points. Following is the table of points at the end of each day.

 

A

B

C

D

E

F

G

H

Day 1

3

1

0

0

0

0

0

1

Day 2

3

4

1

0

0

1

0

0

Day 3

 

 

 

 

 

 

 

 

Day 4

 

 

 

 

 

 

 

 

Day 5

 

 

 

 

 

 

 

 

Day 6

 

 

 

 

 

 

 

 

 

Question:

Based on above case

Solution:


Question 43

CASE

Following is the table containing Students who appeared and passed in exam of Maths and Physics from three schools A, B and C. The data is written in the form of X/Y where X means number of students who passed the exam and Y represents total number of students who appeared in the exam. There are 1800 students in School A, 1500 students in school B and 1200 students in school C.

 

 

Maths

Physics

Maths and Physics

 

Males

Females

Males

Females

Males

Females

A

650/1000

450/800

700/1000

600/800

500/1000

400/800

B

 

 

 

 

 

 

C

 

 

 

 

 

 

 

Question:

If proportion of males clearing Maths paper and proportion of males clearing physics paper is X and Y respectively and proportion of females clearing Maths paper and proportion of females clearing physics paper is M and N respectively then which of the following is true

  1. X > Y ; M > N
  2. X > Y; M < N
  3. X < Y; M > N
  4. X < Y; M < N


Solution:


Question 44

CASE

Following is the table containing Students who appeared and passed in exam of Maths and Physics from three schools A, B and C. The data is written in the form of X/Y where X means number of students who passed the exam and Y represents total number of students who appeared in the exam. There are 1800 students in School A, 1500 students in school B and 1200 students in school C.

 

 

Maths

Physics

Maths and Physics

 

Males

Females

Males

Females

Males

Females

A

650/1000

450/800

700/1000

600/800

500/1000

400/800

B

 

 

 

 

 

 

C

 

 

 

 

 

 

 

Question:

Based on above case

Solution:


Question 45

CASE

Following is the table containing Students who appeared and passed in exam of Maths and Physics from three schools A, B and C. The data is written in the form of X/Y where X means number of students who passed the exam and Y represents total number of students who appeared in the exam. There are 1800 students in School A, 1500 students in school B and 1200 students in school C.

 

 

Maths

Physics

Maths and Physics

 

Males

Females

Males

Females

Males

Females

A

650/1000

450/800

700/1000

600/800

500/1000

400/800

B

 

 

 

 

 

 

C

 

 

 

 

 

 

 

Question:

Based on above case

Solution:


Question 46

CASE

Following is the table containing Students who appeared and passed in exam of Maths and Physics from three schools A, B and C. The data is written in the form of X/Y where X means number of students who passed the exam and Y represents total number of students who appeared in the exam. There are 1800 students in School A, 1500 students in school B and 1200 students in school C.

 

 

Maths

Physics

Maths and Physics

 

Males

Females

Males

Females

Males

Females

A

650/1000

450/800

700/1000

600/800

500/1000

400/800

B

 

 

 

 

 

 

C

 

 

 

 

 

 

 

Question:

Based on above case

Solution:


Question 47

CASE

There are four judges J1, J2, J3, J4 who heard 200, 100, 150 and 250 cases. Out of the cases they heard the verdict were as follows:

 

P1

The percentage of people who were sentences Guilty

P2

The percentage of People out of Guilty, where the dependent challenged the decision in SC

P3

The percentage of People out of Not Guilty, where the Prosecution challenged the decision in SC

P4

The percentage of cases out of challenged by defendant and overturned by SC

P5

The percentage of cases out of challenged by Prosecution and overturned by SC

 

Question:

Out of the judgments consider by J4, how many were finally convicted guilty?

Solution:


Question 48

CASE

There are four judges J1, J2, J3, J4 who heard 200, 100, 150 and 250 cases. Out of the cases they heard the verdict were as follows:

 

P1

The percentage of people who were sentences Guilty

P2

The percentage of People out of Guilty, where the dependent challenged the decision in SC

P3

The percentage of People out of Not Guilty, where the Prosecution challenged the decision in SC

P4

The percentage of cases out of challenged by defendant and overturned by SC

P5

The percentage of cases out of challenged by Prosecution and overturned by SC

 

Question:

Among all the cases how many cases were overturned by the Supreme Court?

Solution:


Question 49

CASE

There are four judges J1, J2, J3, J4 who heard 200, 100, 150 and 250 cases. Out of the cases they heard the verdict were as follows:

 

P1

The percentage of people who were sentences Guilty

P2

The percentage of People out of Guilty, where the dependent challenged the decision in SC

P3

The percentage of People out of Not Guilty, where the Prosecution challenged the decision in SC

P4

The percentage of cases out of challenged by defendant and overturned by SC

P5

The percentage of cases out of challenged by Prosecution and overturned by SC

 

Question:

Based on above case

Solution:


Question 50

CASE

There are four judges J1, J2, J3, J4 who heard 200, 100, 150 and 250 cases. Out of the cases they heard the verdict were as follows:

 

P1

The percentage of people who were sentences Guilty

P2

The percentage of People out of Guilty, where the dependent challenged the decision in SC

P3

The percentage of People out of Not Guilty, where the Prosecution challenged the decision in SC

P4

The percentage of cases out of challenged by defendant and overturned by SC

P5

The percentage of cases out of challenged by Prosecution and overturned by SC

 

Question:

Based on above case

Solution:


Verbal Ability & LR
Question 1

CASE

Passage1

Frugal Engineering (Business Today)

To get a handle on what frugal engineering is, it helps to understand what it is not. Frugal engineering is not simply low-cost engineering. It is not a scheme to boost profi t margins by squeezing the marrow out of suppliers' bones. It is not simply the latest take on the decades-long focus on cost cutting.

Instead, frugal engineering is an overarching philosophy that enables a true "clean sheet" approach to product development. Cost discipline is an intrinsic part of the process, but rather than simply cutting existing costs, frugal engineering seeks to avoid needless costs in the fi rst place. It recognises that merely removing features from existing products to sell them cheaper in emerging markets is a losing game. That's because emerging market customers have unique needs that usually aren't addressed by mature-market products, and because the cost base of developed world products, even when stripped down, remains too high.

Mature-market customers continue to accept price premiums for new features, leading companies to over-engineer their product lines – at least from the point of view of emerging-market customers. The virtual extinction of manual car windows in the United States is just one example. Frugal engineering, by contrast, addresses the billions of consumers at the bottom of the pyramid who are quickly moving out of poverty in China, India, Brazil, and other emerging nations. They are enjoying their fi rst taste of modern prosperity, and are shopping for the basics, not for fancy features. According to the late C.K. Prahalad, author of The Fortune at the Bottom of the Pyramid, these potential customers, "unserved or underserved by the large organised private sector, including multinational fi rms," total 4 to 5 billion of the 6.7 billion people on Earth. Although the purchasing power of any of these new consumers as an individual is only a fraction of a consumer's purchasing power in mature markets, in aggregate they represent a market nearly as large as that of the developed world.

However, many may not fully grasp the challenges that competition in emerging markets entails. The prospect of high-volume profi t streams may be enticing, but those profi ts must be earned in the face of lower prices, lower per-unit profi ts, and stringent cost targets.

In addition, too few companies realise how demanding emerging market customers can be. They don't spend easily, because they don't have much to spend. They require a different set of product features and functions than their developedworld counterparts, but still insist on high quality. Global companies, therefore, must change the way they think about product design and engineering. Simply selling the cheapest products on hand or re-using technologies from higher priced products will not cut costs enough and is unlikely to result in the kind of products these new customers will buy.

Question:

Direct question based on above passage

Solution:


Question 2
Question:

Direct question based on above passage

Solution:


Question 3
Question:

Inference based question based on above passage

Solution:


Question 4
Question:

Inference based question based on above passage

Solution:


Question 5

CASE

Star Party

A star party is a gathering of amateur astronomers to observe the night sky. Such parties may last for a night or extend over a week. The larger star parties can attract hundreds or even thousands of participants.

Regional star parties are now held annually and form a part of amateur astronomy. It is important to choose a proper location for a star party. Ideally, the location should offer a dark sky unpolluted with city lights.

The sheer thrill of meeting like-minded enthusiasts with varieties of telescopes and binoculars offering spectacular views of constellations, stars, nebulae, planets, comets and deep sky objects makes a star party worth attending. It is common to organize popular lectures, contests, sight-seeing tours, raffles and exhibitions of home-built telescopes at some of the larger star parties. Such events also attract commercial vendors who use the opportunity to meet potential customers. The ambience is that of fun, camaraderie and learning, all under the magnificent canopy of the enchanting night sky.

Question:

Inference

Solution:


Question 6

CASE

Obesity

Environmental causes of obesity cross community, national, and international lines. Key drivers of the epidemic include technology advances that have cut the cost of processed foods and drinks, in turn, leading to larger portion sizes; relentless marketing of high-calorie, low-nutrient foods and drinks, especially to children; and a dramatic rise in the prices of more nutritious foods, such as fruits, vegetables, lean meats, and low-fat dairy products. Other factors include less time for gym classes and recess at school; limited access to supermarkets in low-income areas; and a built environment that encourages driving rather than walking or biking. Each of these factors is a target for policy change, and those changes can take many forms and work at many levels.

Question:

Inference

Solution:


Question 7

CASE

Effect of fish diet on brain structure (Medical Journal)

Eating fish has long been linked with heart health. Now new research adds to growing evidence that fish is good for the brain as well. Researchers at the University of Pittsburgh found that people who ate baked or broiled fish just once a week had a lower risk of developing Alzheimer’s disease. They were also at lower risk of mild cognitive impairment, a type of memory loss that sometimes leads to Alzheimer’s.

The fish eaters had more brain gray matter, as measured by M.R.I., or magnetic resonance imaging, brain scans, than those who didn’t regularly eat fish. Greater brain volume may indicate intact memory and thinking functions, whereas brain shrinkage has been linked to Alzheimer’s disease and other forms of dementia. “If you eat fish just once a week, your hippocampus—the big memory and learning center—is 14% larger than in people who don’t eat fish that frequently. 14%. That has implications for reducing Alzheimer’s risk,” Raji said. “If you have a stronger hippocampus, your risk of Alzheimer’s is going to go down.”

Question:

Para jumble

Solution:


Question 8

CASE

Germ War

During World War II, Britain prepared anthrax animal food cakes to infect German cattle. They also stockpiled vaccines should the Germans strike first. The Scottish research isle of Gruinard was rendered unsafe as a result of escaped anthrax spores until 1987.

Question:

Para jumble

Solution:


Question 9

CASE

Mental Health

Those who worry about their mental health remain disturbed as they find themselves different from other but as they can feel the fear of worry they have normal mental state. It is only the consciousness of mental state that worries them

 

Question:

Para jumble (odd one out)

Solution:


Question 10

CASE

Steps of  Scuba Diving

Question:

Para jumble

Solution:


Question 11

CASE

Negotiation is an Art

Many people believe that negotiations are "all or nothing", and that there has to be one winner and one loser. Nothing could be farther from the truth. While the goal of negotiation is most certainly getting what you want, the fact is that the best deals (the ones that stick) incorporate terms and ideas from both parties.

Question:

Para jumble (odd one out)

Solution:


Question 12

CASE

What is Theory

The word “theory” implies that something is unproven or speculative. As used in science, however, a theory is an explanation or model based on observation, experimentation, and reasoning, especially one that has been tested and confirmed as a general principle helping to explain and predict natural phenomena.

 

Question:

Para jumble (odd one out)

Solution:


Question 13

CASE

plainchant (also called "Gregorian" chant), the vocal religious practice of the Roman Catholic Church. Plainchant was transmitted by memory until the early 9th century, when the Holy Roman Emperor Charlemagne arranged for it to be notated, and for standardized plainchant books to be distributed to churches and monasteries across Europe. Limited in pitch range and monophonic (i.e., composed of a single melody with no accompaniment), plainchant was sung largely by monks, nuns, and clerics rather than by professional singers. Plainchant was sung in the Divine Offices, eight daily prayer services using Old Testament texts, and in the Mass, a midmorning celebration of the life and death of Jesus Christ. The Alleluia reproduced here was a chant of jubilation ("Alleluia" = "Hallelujah"), sung as part of the Mass.

Passage 2- Evolution of Technology.

A lengthy passage with detailed example of Guntenberg Printing Press

Question:

Inferential based question based on above passage

Solution:


Question 14
Question:

Inferential based question based on above passage

Solution:


Question 15
Question:

Inferential based question based on above passage

Solution:


Question 16
Question:

Inferential based question based on above passage

Solution:


Question 17

Case

Passage 3-Colonial rule in India has undermined the intellectual self-confidence among the people of India.

The passage discusses the impact of colonial rule on the minds and behavior of Indians while gives examples of Aryabhatta and other ancient mathematicians.

Question:

Inferential based question based on above passage

Solution:


Question 18
Question:

Inferential based question based on above passage

Solution:


Question 19
Question:

Inferential based question based on above passage

Solution:


Question 20
Question:

Strengthen the given idea from the passage

Solution:


Question 21

Case

Passage 4- Post independence Kurdistan and its distinction from Iraq in terms of culture, policy etc.

Question:

Direct question based on above passage

Solution:


Question 22
Question:

Inferential based question based on above passage

Solution:


Question 23
Question:

Inferential based question based on above passage

Solution:


Question 24
Question:

Application based question based on above passage

Solution:


Question 25

Case

Effective Branding

Successful branding is not only about the product but also the way it associates to the customer. To become a successful brand one needs to study the trend and follow the role models that customers follow and project the product used by their role models. The customer gets associated to a brand when he receives a sense of satisfaction that the purchase is made was the right choice.

Question:

What can be summarized from the above paragraph? (independent.co.uk)

Solution:


Question 26

Case

Some great authors have published their worst works from beyond the grave. A few though, keep getting better when they’re dead, such as the Chilean novelist and short story writer, Roberto Bolaño. His seminal five-part novel, 2666, came out posthumously, won the National Book Critics Circle Award and convinced the world he was not just a master of the short form but could put out his life’s best work at nearly 900 pages, even after death.

Question:

Which of the following can best summarize the above?

Solution:


Question 27
Question:

Inference- A simple paragraph on change in global climate.

Solution:


Question 28
Question:

Summary- A moderate paragraph on Guayaki Indians and studies done by Vellard.

Solution:


Question 29
Question:

Error-Identification

Solution:


Question 30
Question:

Error-Identification

Solution:


Question 31
Question:

Error-Identification

Solution:


Question 32
Question:
Solution:


Question 33
Question:
Solution:


Question 34
Question:
Solution:


Question 35
Question:
Solution:


Question 36

CASE

138 fruits were to be distributed among four people A, B, C and D. The fruit distributed are Apple, Oranges, Plums and Guava. There were 12 apples to be distributed.

There are four students out of which there are 2 females.

Every student gets at least one of each variety of fruit and no students can have more than 4 of any variety. D got least and it was 5 less than the highest.

A got 4 each of Apple and Guava but he didn’t get the highest. B and C got the same number of fruits which was also one of the females. B got same number of apple, Oranges and Plum while C ha dsame number of Oranges and Guava.

Question:

Which of the following is definitely true?

Solution:


Question 37
Question:

What could be the total number of Oranges?

Solution:


Question 38
Question:

A question based on above case

Solution:


Question 39
Question:

A question based on above case

Solution:


Question 40

CASE

A mobile application has been created which has four consecutive buttons which can have either of the two status on or off. By pressing a button its status changes from on to off and vice versa.

Question:

If the initial arrangement is (on,off,on,off) then how many different combinations are possible by pressing 2 consecutive buttons?

(a) 2

(b) 4

(c) 8

(d) 16


Solution:


Question 41
Question:

Which of the following will give all the possible combinations of the switches?

Solution:


Question 42
Question:

If the application is modified such that you can press any two buttons (not necessarily consecutive buttons) then how many total combinations are possible?

(a) 2

(b) 4

(c) 8

(d) 16


Solution:


Question 43
Question:

There was one more similar question……….

Solution:


Question 44

Case

A, B, C, D, and E are five people who take exactly one of the services from 5 service Provider Sata Sky, Sairtel, Tish, Audicone, Citi.

In the first year

Exactly one of the service provider had none of the subscription.

Tish had 2 of this people as subscriber.

E is the only subscriber of his service provider.

In the second year

Audiocone retain its only subscriber and got one more subscriber from other subscriber.

A changed from its earlier subscriber to Sairtel.

Citi increased its subscriber by 1 from 1st year.

Sata sky retails its only subscriber.

Question:

In the first year which of the following had no subscriber?

Solution:


Question 45
Question:

In the second year which of the following had subscription of Sata sky?

Solution:


Question 46
Question:

A question based on above case

Solution:


Question 47
Question:

A question based on above case

Solution:


Question 48

Case

In a school different students take part in activities like Academics, Sports and Culture. They were given the codes 1 or 0. For example 101 will give 1 in academics, 0 in sports and 1 in culture. By the strange coincidence, the number of boys which is abc is same as number of girls bcd. Here abc and bcd are binary numbers.

Boys

 

Sports

Culture

0

1

1

 

60

 

 

 

 

Girls

 

               Culture

Acad

0

1

0

 

 

1

50

70

 

Question:

How many boys are there in Academics?

Solution:


Question 49
Question:

A question based on above case

Solution:


Question 50
Question:

A question based on above case

Solution:


Note:
These questions are similar in nature to CAT-2014 and are sourced from CHEM question bank.
We do not claim them to be actual CAT questions.