The post LRDI of the Day #2 appeared first on Learningroots.

]]>#LRDIoftheDay #2

The following table provides partial details about the number of Twenty20s (T20) and One Day Internationals (ODIs) played by 6 players of the Indian cricket team against five nations viz. Australia, South Africa, England, Pakistan and the West Indies in the year 2017. Assume that the Indian cricket team played only against these nations in the year 2017, and also, they played no form of matches other than the T20s and the ODIs. India played 25% of its total matches against Australia, 20% of its total matches against South Africa, 10% of its total matches against Pakistan, 15% of its total matches against England, and 30% of its total matches against West Indies.

1. The total number of matches played by the Indian cricket team in 2017 could not be less than

2. Out of the matches played by the Indian cricket team against the West Indies in 2017, the number of matches not played by Jasprit could at least be

3. If Hardik played all the “ODIs” and Virat played all the “T20s” that the Indian cricket team played against England in 2017, then what could be the minimum number of T20s played by the Indian cricket team against England in the year 2017?

4. What is the minimum number of matches played by Shikhar throughout the season if he played all T20 matches against England, Pakistan and West Indies?

The solution will be up tomorrow. Enjoy!

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]]>The post LRDI of the Day #1 appeared first on Learningroots.

]]>#LRDIoftheDay #1

The six members of the Justice League were ranked by a group of friends – Leonard, Sheldon, Raj and Howard. From every friend, each character received a distinct integral rating ranging from 1 to 6, depending on how much the character was liked by that friend, i.e. the character he liked most, was given a rating of 6 and the character he liked least was given a rating of 1 and so on. The six characters were named Batman, Superman, Wonder Woman, Aquaman, Cyborg and Flash. The judges were named Leonard, Sheldon, Raj and Howard.

Further information is given below:

I. Batman received a different rating from each friend. This holds true for the other five characters as well.

II. For each of Batman, Wonder Woman and Cyborg the ratings received from the four friends were in A.P.

III. The sums of four ratings received by Batman, Wonder Woman and Cyborg were also in A.P., with a common difference of 4, not necessarily in that order.

IV. The sums of four ratings received by Superman, Aquaman and Flash were also in A.P., with a common difference of 1, not necessarily in that order.

V. The ratings received by Batman from Sheldon, Wonder Woman from Howard and Cyborg from Raj were the same.

VI. Wonder Woman received a higher rating from Raj as compared to what she received from Sheldon.

The attached table provides partial information about the ratings received by the six characters from the four friends.

1. What was the maximum possible sum of the four ratings received by any of the six characters?

(a) 14 (b) 16 (c) 17 (d) 18

2. What was the sum of the four ratings received by Flash?

(a) 12 (b) 18 (c) 14 (d) None of these

3. What was the rating received by Wonder Woman from Howard?

(a) 2 (b) 3 (c) 4 (d) None of these

4. What was the rating received by Superman from Sheldon?

(a) 1 (b) 3 (c) 6 (d) Cannot be determined

The solution to the set:

You may go through our popular courses here (at discounted prices): Full LRDI course for CAT 2017 (Rs. 1750 only) | Full VARC course for CAT 2017 (Rs. 1750 only) | Full Quant course for CAT 2017 (Rs. 3500 only) | CAT 2017 full course (Rs. 6000 only) | Current affairs and GK (Rs. 299 only)

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]]>The post Geometry and Mensuration Question Bank – CAT 2017 appeared first on Learningroots.

]]>Together, we learn more! So here we go: Geometry and Mensuration Question Bank – CAT 2017

You may go through our other question banks here: CAT 2017 Question Banks

**1st edition: 17 September 2017 (Q.1 to Q.43)**

1. A ladder is inclined to a wall making an angle of 30° with it. A man is ascending the ladder at the rate of 2 m/s. How fast is he approaching the wall?

https://www.facebook.com/groups/crackingcat/permalink/671330656354802/

2. A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are natural numbers. What is the perimeter of the triangle?

https://www.facebook.com/groups/crackingcat/permalink/875216012632931/

3. P (-sqrt3, 1) and Q (s, t) lie on the circumference of the circle with center O. What is the value of s?

https://www.facebook.com/groups/crackingcat/permalink/620820044739197/

4. The coordinates of the vertices of the triangle ΔABC are A(0, 1), B(4, 4) and C(5, 3). From which vertex the length of the median drawn to the opposite side is the minimum?

(1) A (2) B (3) C (4) All medians are of equal length

https://www.facebook.com/groups/crackingcat/permalink/659050780916123/

5. A point on a circle inscribed in a square is 1 and 2 units from the closest side of the square. What is the area of the square?

https://www.facebook.com/groups/crackingcat/permalink/624682161019652/

6. ABCD is a trapezium with AB parallel to CD. M is the midpoint of AD. Angle MCB = 150 degrees, BC = 4, MC = 12. Area of the trapezium ABCD will be?

https://www.facebook.com/groups/crackingcat/permalink/624685024352699/

7. A right circular cone of height h is cut by a plane parallel to its base and at a distance of h/3 from the base, then the volume of the resulting cone and the frustum are in the ratio?

https://www.facebook.com/groups/crackingcat/permalink/625210044300197/

8. ABC is an equilateral triangle with side length = 1 cm. P is any point on the circumcircle of this triangle. What is the value of AP^2 + BP^2 + CP^2 ?

https://www.facebook.com/groups/crackingcat/permalink/627591137395421/

9. The radii of the ends of a bucket 45 cm high, which is of the form of a frustum of a cone, are 28 cm and 7 cm. Determine its capacity.

1) 48510 cu.cm

2) 30400 cu.cm

3) 5610 cu.cm

4) 21020 cu.cm

https://www.facebook.com/groups/crackingcat/permalink/629469800540888/

10. The sides of a triangle are 5, 12 and 13 units respectively. A rectangle is constructed which is equal in area to the triangle and has a width of 10 units. Then the perimeter of the rectangle isTop of Form

https://www.facebook.com/groups/crackingcat/permalink/629904700497398/

11. A rhombus is drawn on the x-y plane by joining the points having coordinates A (0, 0), B (x1, y1), C (4, 6), D (x2, y2). What is the equation of the diagonal BD?

(1) 3x – 4y = 3

(2) 2y + 3x = 1

(3) 3y + 2x = 13

(4) 6x – 2y = 1

https://www.facebook.com/groups/crackingcat/permalink/659045514249983/

12. ABC is a triangle with AB = 14, BC = 10 and CA = 6. D and E are points on BC and CA respectively such that CD = 3 and CE = 2.5. A line passing through C and the point of intersection of AD and BE cut the side AB at F. Then AF = ?

(a) 5

(b) 5.25

(c) 6

(d) 6.25

(e) 7.5

https://www.facebook.com/groups/crackingcat/permalink/626830337471501/

13. Given points P1, P2, P3, … P7 on a straight line, in the order stated (not necessarily evenly spaced). Let P be an arbitrary point selected on the line and let s be the sum of undirected lengths PP1, PP2, PP3, … PP7. Then s is smallest if and only if the point P is

1. Midway between P1 and P7

2. Midway between P2 and P6

3. Midway between P3 and P5

4. At P4

5. At P1

https://www.facebook.com/groups/crackingcat/permalink/626907917463743/

14. Find the number of distinct integer-sided triangles with perimeter 1001.

https://www.facebook.com/groups/crackingcat/permalink/626909787463556/

15. The coordinates of the vertices of the triangle ΔABC are A(0, 1), B(4, 4) and C(5, 3). From which vertex the length of the median drawn to the opposite side is the minimum?

(1) A (2) B (3) C (4) All medians are of equal length

https://www.facebook.com/groups/crackingcat/permalink/659050780916123/

16. In a quadrilateral ABCD, E is a point on AB. If ∠ADE =∠DEC = ∠ECB= 30°, AD = 2 units and BC = 4 units, then what is the area of the ΔDEC?

https://www.facebook.com/groups/crackingcat/permalink/661444237343444/

17. Refer to the figure in the link. ABC, DEF and GHI are three equilateral triangles having the same area. BD = DG = GC. Find the ratio of EJKL to AKHIB.

https://www.facebook.com/groups/crackingcat/permalink/662754627212405/

18. The area of a right-angled triangle is 40 sq. cm and its perimeter is 40 cm. The length of its hypotenuse is

https://www.facebook.com/groups/crackingcat/permalink/663902447097623/

19. Find the equation of circle with center (2, 4) and equation of tangent as 3x + 4y = 12.

https://www.facebook.com/groups/crackingcat/permalink/663908967096971/

20. The area of the quadrilateral (in sq. units) formed by the points (1,8), (3,4), (5,8) and (–3,4) is

https://www.facebook.com/groups/crackingcat/permalink/666584430162758/

21. A farmer has a land in the shape of a triangle, the sides of which are 50 m, 120 m and 130 m. As it is a hilly area, the farmer can use only some portion in the middle of the field. To maximise his area of cultivation he draws a circle touching all the three sides. Now he plans to use the area covered inside the circle, only because it is more fertile and there exists a tube well in the centre. He draws perpendicular lines on the three sides from the tube well and divides the total cultivable area into three parts. He fixes the smallest portion for vegetables, the largest portion for wheat and the third portion for rice. Find the area (in sq.m.) in which vegetables are cultivated.

(a) 100pi

(b) 90pi

(c) 120pi

(d) Cannot be determined

https://www.facebook.com/groups/crackingcat/permalink/671266533027881/

22. A rectangular piece of paper is folded in such a way that one pair of diagonally opposite vertices coincide. If the dimensions of the rectangle is 40 cm * 30 cm, then find the length of the crease (fold) in cm.

1) sqrt(2100)

2) 75 sqrt(3)

3) 37.5 cm

4) 60 sqrt(3)

https://www.facebook.com/groups/crackingcat/permalink/620147434806458/

23. A right angled triangle with sides 3 cm, 4 cm and 5 cm is drawn. Semicircles are drawn on all three sides with the side-length as the diameters. Find area of the shaded region (figure in the link)

https://www.facebook.com/groups/crackingcat/permalink/671382303016304/

24. A couple of questions on properties of intersecting chords and bisectors of chords

https://www.facebook.com/groups/crackingcat/permalink/671509086336959/

25. What is the maximum possible value of (21 Sin X + 72 Cos X)?

https://www.facebook.com/groups/crackingcat/permalink/673001616187706/

26. The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is 3/2 times that of the side of the square, then the side of the square is :

(a) 15 cm

(b) 20 cm

(c) 30 cm

(d) 60 cm

https://www.facebook.com/groups/crackingcat/permalink/863763463778186/

27. The exterior angles of a quadrilateral are in the ratio 1:3:4:7. What is the sum of the largest and the smallest interior angles of the quadrilateral?

https://www.facebook.com/groups/crackingcat/permalink/864716903682842/

28. As a cone rolls on the surface of a table, it traces a circular arc centered on the vertex. While making a full circle, it rotates 17 times. Find the ratio of the height of the cone to its radius.

https://www.facebook.com/groups/crackingcat/permalink/873865509434648/

29. Isosceles trapezium is inscribed in a circle of radius 10 cm such that the non-parallel sides are 10 cm each. If one of the sides is the diameter of the circle that circumscribes the trapezium, what is the area of the trapezium?

https://www.facebook.com/groups/crackingcat/permalink/874718332682699/

30. Data Sufficiency – Geometry

https://www.facebook.com/groups/crackingcat/permalink/620745231413345/

31. Eight identical octagons are placed edge to edge to form a symmetrical star shaped figure. Find the area of the star shaped figure (figure in the link)

https://www.facebook.com/groups/crackingcat/permalink/879181322236400/

32. PQRS is a square, U and V are the midpoints of PS and SR. PV and UR meet at T. Find A(PQRS):A(PQRT).

https://www.facebook.com/groups/crackingcat/permalink/879188348902364/

33. D, E, F are the mid points of the sides BC, CA and AB respectively of a triangle ABC. What is the ratio of the circumradii of triangles DEF and ABC respectively?

https://www.facebook.com/groups/crackingcat/permalink/880195918801607/

34. The minimum number of straight lines required to obtain 16 non-overlapping parallelograms are

https://www.facebook.com/groups/crackingcat/permalink/883421188479080/

35. Consider a square ABCD of side 60 cm. lt contains arcs BD and AC drawn with centres at A and D respectively. A circle is drawn such that it is tangent to side AB, and the arcs BD and AC. What

is the radius of the circle?

A. 9 cm

B. 10 cm

C. 12 cm

D. 15 cm

E. None of the above

https://www.facebook.com/groups/crackingcat/permalink/674195982734936/

36. If you have a 4*6*8 cuboid from which the largest possible cube is cut out, what would be the minimum number of cubes into which the remaining figure could be divided assuming that there is no piece left over and the all the smaller cubes are of equal dimension?

https://www.facebook.com/groups/crackingcat/permalink/846431102178089/

37. A sphere is inscribed in a cube with an edge 10. What is the shortest distance from one of the vertices of the cube to the surface of the sphere?

https://www.facebook.com/groups/crackingcat/permalink/884121635075702/

38. In ABC, AB < AC < BC. CA is extended to a point P such that AP = AB. Point R is selected on CP such that CR = BC. If RP is equal to the diameter of the biggest circle that can be drawn inside ABC, and all angles are integers, which of the options is definitely true?

a. Angle B < 90 degrees

b. Angle C > 90 degrees

c. Angle A is not equal to 90 degrees

d. Angle C is 90 degrees

https://www.facebook.com/groups/crackingcat/permalink/884611535026712/

39. Find the difference between the lengths of the inradius and circumradius of a triangle with sides 11 units, 60 units and 61 units.Top of Form

https://www.facebook.com/groups/crackingcat/permalink/885916921562840/

40. Two tangents from an external point P touch a circle with center O at points A and B such that A is to the north of B. M(angle APB) is 70 degrees. Also, X and Y are points on the circumference of the circle such that A-Y-B-X-A in a clockwise manner and Y lies to the east of X. Find the measure of arc(AXB).

https://www.facebook.com/groups/crackingcat/permalink/885919551562577/

41. In a right-angled triangle, the sum of the squares of the three side lengths is 1800. The length of its hypotenuse is

https://www.facebook.com/groups/crackingcat/permalink/886015088219690/

42. A circle with center O and radius 8 cm is drawn, BD is a chord and A is a point on the minor arc BD. C is a point on BD such that AC is perpendicular to BD. AC = 4 cm and BC = 12 cm. Find CD. Figure in the link.

https://www.facebook.com/groups/crackingcat/permalink/886816041472928/

43. How many values of the integer k will make the triangle with sides 6, 8 and k obtuse?

https://www.facebook.com/groups/crackingcat/permalink/886821258139073/

This post will be updated every now and then to add new questions. In case you spot some issue with the links, let us know.

The post Geometry and Mensuration Question Bank – CAT 2017 appeared first on Learningroots.

]]>The post Common idioms for CAT, XAT, IIFT, SNAP, NMAT, TISS, MICAT (Part 2) appeared first on Learningroots.

]]>31. Barking Up The Wrong Tree:

A mistake made in something you are trying to achieve.

32. Beat A Dead Horse:

To force an issue that has already ended.

33. Beating Around The Bush:

Avoiding the main topic. Not speaking directly about the issue.

34. Bend Over Backwards:

Do whatever it takes to help. Willing to do anything.

35. Between A Rock And A Hard Place:

Stuck between two very bad options.

36. Bite Off More Than You Can Chew:

To take on a task that is way to big.

37. Bite Your Tongue:

To avoid talking.

38. Blood Is Thicker Than Water:

The family bond is closer than anything else.

39. Blue Moon:

A rare event or occurance.

40. Break A Leg:

A superstitious way to say ‘good luck’ without saying ‘good luck’, but rather the opposite.

41. Buy A Lemon:

To purchase an item (commonly a vehicle/second hand car) that constantly gives problems or stops running after you drive it away.

42. Can’t Cut The Mustard :

Someone who isn’t adequate enough to compete or participate.

43. Cast Iron Stomach:

Someone who has no problems, complications or ill effects with eating anything or drinking anything.

44. Charley Horse:

Stiffness in the leg / A leg cramp.

45. Chew someone out:

Verbally scold someone.

46. Chip on his Shoulder:

Angry today about something that occured in the past.

47. Chow Down:

To eat.

48. Close but no Cigar:

To be very near and almost accomplish a goal, but fall short.

49. Cock and Bull Story:

An unbelievable tale.

50. Come Hell Or High Water:

Any difficult situation or obstacle.

51. Crack Someone Up:

To make someone laugh.

52. Cross Your Fingers:

To hope that something happens the way you want it to.

53. Cry Over Spilt Milk:

When you complain about a loss from the past.

54. Cry Wolf:

Intentionally raise a false alarm.

55. Cup Of Joe:

A cup of coffee.

56. Curiosity Killed The Cat:

Being Inquisitive can lead you into a dangerous situation.

57. Cut to the Chase:

Leave out all the unnecessary details and just get to the point.

58. Dark Horse:

One who was previously unknown and is now prominent.

59. Dead Ringer:

100% identical. A duplicate.

60. Devil’s Advocate:

Someone who takes a position for the sake of argument without believing in that particular side of the argument. It can also mean one who presents a counter argument for a position they do believe in, to another debater.

Stay tuned for more such quality content!

You may have a look at our courses here: CAT 2017 Verbal Course | CAT 2017 LRDI Course | CAT 2017 QA Course | GK course for TISSNET, MICAT, SNAP, IIFT, MAT, CMAT, ATMA

The post Common idioms for CAT, XAT, IIFT, SNAP, NMAT, TISS, MICAT (Part 2) appeared first on Learningroots.

]]>The post Numbers Question Bank – CAT 2017 appeared first on Learningroots.

]]>Together, we learn more! So here we go: Numbers Question Bank – CAT 2017

You may go through our other question banks here: CAT 2017 Question Banks

**1st edition: 13 September 2017 (Q.1 to Q.54)**

1. All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?

https://www.facebook.com/groups/crackingcat/permalink/791637407657459/

2. What is the product of all the factors of 1800 that have 5 as unit’s digit. Give your answer as a^x*b^y*c^z where a b c are primes

https://www.facebook.com/groups/crackingcat/permalink/782016098619590/

3. M is a two digit number such that the product of the factorials of its individual digits is greater than the sum of the factorials of its individual digits. How many values of M exist?

https://www.facebook.com/groups/crackingcat/permalink/627476624073539/

4. If n is a positive prime number, and n^4 + 3(n^3) is a perfect cube, what is the sum of the lowest two possible values of n?

https://www.facebook.com/groups/crackingcat/permalink/627475897406945/

5. When 6 is affixed at the end of a five-digit number and the resultant number is quadrupled, the result is 6 followed by the original five-digit number. What was the original 5-digit number?

https://www.facebook.com/groups/crackingcat/permalink/627475074073694/

6. Find the greatest number which when divides 378, 2079 and 1890 leaves the same remainder.

https://www.facebook.com/groups/crackingcat/permalink/798940680260465/

7. 120 blue marbles, 180 green marbles and 240 red marbles are to be arranged in rows in such a manner that each row contains an equal number of marbles. Also, each row should have marbles of the same colour. What is the minimum number of rows required?

https://www.facebook.com/groups/crackingcat/permalink/798941046927095/

8. What is the greatest power of 5 which can divide 80! exactly?

https://www.facebook.com/groups/crackingcat/permalink/798941190260414/

9. Simplify 2^73 – 2^72 – 2^71

https://www.facebook.com/groups/crackingcat/permalink/798941626927037/

10. How many 3-digit even numbers can you form such that if one of the digits is 5 then the following digit must be 7?

https://www.facebook.com/groups/crackingcat/permalink/798941923593674/

11. Ria has three types of boxes viz. red, blue and green. She plays a game in which she placed 9 red boxes on the table. She puts 5 blue boxes each, in a few of the red boxes then she puts 5 green boxes each, in few of the blue boxes. If the number of boxes that have been left empty in the game is 41, then how many boxes were used in the game by Ria?

https://www.facebook.com/groups/crackingcat/permalink/878072595680606/

12. Three friends are playing a card game. They start with sums of money in the ratio 7 : 6 : 5 and finish with sums of money in the ratio 6 : 5 : 4, in the same order as before. One of them won Rs. 12. How many rupees did he start with? [The three friends gambled amongst each other only]

https://www.facebook.com/groups/crackingcat/permalink/878073889013810/

13. Atul has exactly six sealed bags containing 15, 31, 19, 20, 16 and 18 candies. Out of the six bags with Atul, there are exactly five bags that contained chocolate candies whereas one box contained orange candies. He distributed all the six bags among his three sons in such a manner that his eldest son got the only box with orange candies and the other bags were distributed in such a manner so that other two brothers received the chocolate candies in the ratio of 2 : 1. How many orange candies were there with Atul? (Assume no candies were taken out of the bags)

https://www.facebook.com/groups/crackingcat/permalink/878366812317851/

14. For how many integers m, is (5m+23)/(m-7) also an integer?

https://www.facebook.com/groups/crackingcat/permalink/878431165644749/

15. A six-digit number is formed by writing 3 consecutive two-digit number side by side in ascending order. If the number so formed is divisible by 2, 3, 4, 5, 6, 8, then what is the hundreds digit of the number?

https://www.facebook.com/groups/crackingcat/permalink/878557495632116/

16. The year 1789 has three and no more than three adjacent digits (7, 8 and 9) which are consecutive integers in increasing order. How many years between 1000 and 9999 have this property?

https://www.facebook.com/groups/crackingcat/permalink/879158285572037/

17. A survey of 104 students, who study Physics or Mathematics or Chemistry, revealed that 38 did not study Physics, 30 did not study Mathematics and 40 did not study Chemistry. Also 40 studied Chemistry and Physics, 50 studied Chemistry and Mathematics and 44 studied Physics and Mathematics. What is the difference between the number of students who studied Mathematics and the number of students who studied exactly two of the three subjects?

https://www.facebook.com/groups/crackingcat/permalink/879179768903222/

18. At the FMS Alumni meet of 2017, each alumnus brought either 1 or 2 family members. If the ratio of the number of alumni to the number of family members is 3 : 5, what fraction of the alumni brought 2 guests?

https://www.facebook.com/groups/crackingcat/permalink/879198412234691/

19. Diophantus’s youth lasted one sixth of his life. He grew a beard after one twelfth more. After one seventh more of his life, he married. 5 years later, he and his wife had a son. The son lived exactly one half as long as his father, and Diophantus died four years after his son. How many years did Diophantus live?

https://www.facebook.com/groups/crackingcat/permalink/879200218901177/

20. Mr. X went to the C-Mart near his house and purchased four chocolates from there. The first one cost Rs. 1.5, the second one cost Rs. 3, and the third one cost Rs. 4. When Mr. X multiplied the prices of the four chocolates he got a product which was the same as the bill amount in Rupees he paid at C-Mart. We know that he paid a Rs. 50 note at the counter and got back some money. If the billing executive gave him the minimum number of notes/coins, then Mr. X has surely got which of the following notes/coins back from the billing executive?

https://www.facebook.com/groups/crackingcat/permalink/879204822234050/

21. The sum of a two-digit number and the number formed by interchanging the two digits is 45 more than twice the original number. If the sum of the digits of the number is 9, what is the original number?

https://www.facebook.com/groups/crackingcat/permalink/880194815468384/

22. How many three digit numbers are of the form xyz with x < y, z < y and x ≠ 0?

https://www.facebook.com/groups/crackingcat/permalink/880595435428322/

23. There is a staircase of 10 steps. In how many ways can Amit climb the staircase if he can take a maximum of 3 steps at a time?

https://www.facebook.com/groups/crackingcat/permalink/880604118760787/

24. What is the sum of factors of each factor of 1024?

https://www.facebook.com/groups/crackingcat/permalink/881050572049475/

25. Find the number of ordered pairs (x, y) where both x and y are non-negative integers such that,

x – (1/y) = (x/y) + 1?

https://www.facebook.com/groups/crackingcat/permalink/881052542049278/

26. A boy is asked to take a 2-digit number; multiply its digits and keep repeating the process until he gets a single digit number. What is the probability that this single digit is zero?

https://www.facebook.com/groups/crackingcat/permalink/881054962049036/

27. In how many ways can 720 be expressed as product of 2 co-primes?

https://www.facebook.com/groups/crackingcat/permalink/881058178715381/

28. How many pairs of factors of 720 exist such that the factors are co-prime to each other?

https://www.facebook.com/groups/crackingcat/permalink/881058178715381/

29. A set N is formed by selecting some of the numbers from the first 110 natural numbers such that the GCD of any two numbers in the set is 5. What is the maximum number of elements that set N can have?

https://www.facebook.com/groups/crackingcat/permalink/881305085357357/

30. The number of 6-digit numbers of the form ababab (where a and b are distinct, non-negative integers) each of which is a product of exactly 6 district primes is

https://www.facebook.com/groups/crackingcat/permalink/881422505345615/

31. The population of cattle in a farm increases so that the difference between the population in year n + 2 and that in year n is proportional to the population in year n + 1. If the populations in year 2014, 2015 and 2017 were 39, 60 and 123, respectively, then the population in 2016 was

https://www.facebook.com/groups/crackingcat/permalink/881699818651217/

32. MTNL has a waiting list of 5005 applicants for its recently launched mobile phone scheme. The list shows that there are at least 5 males between any two females. The largest possible number of females in the waiting list is:

https://www.facebook.com/groups/crackingcat/permalink/881709568650242/

33. During a parade 289 soldiers are standing in a square formation with 17 ranks and 17 files. Bullets were handed out to each of these soldiers for target practice. The number of bullets with the soldiers in each rank, as well as in each file, were in an arithmetic progression. If the number of bullets with the 4^{th} and the 14^{th} soldiers in the first rank were 831 and 861 respectively, while the number of bullets with the 2^{nd} and the 16^{th} soldiers in the 16^{th} rank were 60 and 102 respectively, find the average number of bullets with all the soldiers.

https://www.facebook.com/groups/crackingcat/permalink/882063668614832/

34. Given that 2^x^y + x^2^y = 3, how many integral solutions are there for the equation?

https://www.facebook.com/groups/crackingcat/permalink/882543631900169/

35. There are 5 distinct real numbers out of which all possible triplets are selected and for each triplet the three numbers are added. The different sums that are generated are: (– 8, 1, 3, 5, 7, 8, 10, 16, 19 and 23).

The smallest among the 5 numbers is

https://www.facebook.com/groups/crackingcat/permalink/882548231899709/

36. There are 5 distinct real numbers out of which all possible triplets are selected and for each triplet the three numbers are added. The different sums that are generated are: (– 8, 1, 3, 5, 7, 8, 10, 16, 19 and 23).

The third largest number is

https://www.facebook.com/groups/crackingcat/permalink/882548231899709/

37. There are 98 given points on a circle. Amar, Akbar and Anthony start playing a game by drawing a chord one by one between two of the points which have not yet been joined together. The game ends when all such points have been joined exhaustively. The winner is the one who draws the last chord. If Anthony starts the game, followed by Akbar, and then Amar, then who will win?

https://www.facebook.com/groups/crackingcat/permalink/882719045215961/

38. A, B, C, D, E and F are six single-digit non-negative integers such that A < B < C < D < E < F. Three-digit number CFC is a perfect square, BE is a two-digit prime number and A + D + F = B + C + E.

What is the value of D?

a. 4

b. 5

c. 6

d. Cannot be determined

https://www.facebook.com/groups/crackingcat/permalink/882722305215635/

39. A, B, C, D, E and F are six single-digit non-negative integers such that A < B < C < D < E < F. Three-digit number CFC is a perfect square, BE is a two-digit prime number and A + D + F = B + C + E.

The four-digit natural number BEFC is definitely not divisible by which of the following two-digit numbers?

a. CB

b. AA

c. CC

d. CE

https://www.facebook.com/groups/crackingcat/permalink/882722305215635/

40. An instruction was sent to all the railway stations across the country that, workers above the age of 47 years must retire. Five workers with different ages at the Kazipet railway station managed to tamper their records. However, the station master knew that the sums of the ages (in years) of all the possible pairs of workers (from out of the five) are 102, 105, 107, 107, 109, 109, 111, 112, 114, 116. Find the age of the oldest of the five workers.

https://www.facebook.com/groups/crackingcat/permalink/883435218477677/

41. X toffees can be distributed equally among Y children, where X > Y. What is the number of Values that X can assume such that Y > 1 and 2 < X + Y < 110?

https://www.facebook.com/groups/crackingcat/permalink/883451448476054/

42. If x^2 < 81 and y^2 < 25, what is the largest prime number that can be equal to x – 2y?

https://www.facebook.com/groups/crackingcat/permalink/883805238440675/

43. A password on Mr. Marsellus Wallace’s briefcase consists of 5 digits. What is the probability that the password contains exactly three sixes?

https://www.facebook.com/groups/crackingcat/permalink/883823825105483/

44. x, y and z are positive integers such that when x is divided by y the remainder is 3 and when y is divided by z the remainder is 8. What is the smallest possible value of x+y+z?

https://www.facebook.com/groups/crackingcat/permalink/883882715099594/

45. What is the smallest positive integer k such that 126*sqrt(k) is the square of a positive integer?

https://www.facebook.com/groups/crackingcat/permalink/883916675096198/

46. Of the applicants passes a certain test, 15 applied to both college X and Y. If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y, how many applicants applied only college X or college Y?

https://www.facebook.com/groups/crackingcat/permalink/884136978407501/

47. The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is prime, then f(p) = ?

(A) P-1

(B) P-2

(C) (P+1)/2

(D) (P-1)/2

https://www.facebook.com/groups/crackingcat/permalink/884150685072797/

48. N is an eight digit number and S(N) is the sum of the digits of N. If N + S(N) = 100,000,000 what would be N?

https://www.facebook.com/groups/crackingcat/permalink/884605891693943/

49. N represents a series in which all the terms are consecutive integers and the sum of all the terms of N is 100. If the number of terms of N is greater than one, find the difference between the maximum and the minimum possible number of terms.

https://www.facebook.com/groups/crackingcat/permalink/884607745027091/

50. If a_{1} = 2, a_{2} = 3 and a_{n+2 }+ a_{n} = 2a_{n+1 }+ 1 for every positive integer n, then a_{51 }equals?

https://www.facebook.com/groups/crackingcat/permalink/884609945026871/

51. If [log1] + [log2] + [log3] + [log4] … + [logn] = n where [x] denotes the greatest integer less than or equal to x, then which of the following is an acceptable range for n? (all logs are in base 10)

a. 96 < n < 104

b. 104 < n < 107

c. 107 < n < 111

d. 111 < n < 116

https://www.facebook.com/groups/crackingcat/permalink/884617405026125/

52. M/30! = 1/30! + 1/29! + 1/2!28! + 1/3!27! + … + 1/28!2! + 1/29! + 1/30!. Find the quotient when M – 1 is divided by 1023.

https://www.facebook.com/groups/crackingcat/permalink/884667498354449/

53. If n is a natural number and n! = n(n – 1)(n – 2)…3.2.1, find the remainder when summation of n(n!) is divided by n^{2} – 2n (n > 2)

a. 0

b. n

c. n^{2} – 2n – 1

d. (n – 1)^{2}

https://www.facebook.com/groups/crackingcat/permalink/884849041669628/

54. The sum of all positive integers n for which (1^{3 }+ 2^{3 }+ 3^{3} … (2n)^{3})/(1^{2} + 2^{2} + 3^{2 }… n^{2}) is also an integer is?

https://www.facebook.com/groups/crackingcat/permalink/884870135000852/

This post will be updated every now and then to add new questions. In case you spot some issue with the links, let us know.

The post Numbers Question Bank – CAT 2017 appeared first on Learningroots.

]]>The post Common idioms for CAT, XAT, IIFT, SNAP, NMAT, TISS, MICAT (Part 1) appeared first on Learningroots.

]]>1. A Bird In The Hand Is Worth Two In The Bush:

Having something that is certain is much better than taking a risk for more, because chances are you might lose everything.

2. A Blessing In Disguise:

Something good that isn’t recognized at first.

3. A Chip On Your Shoulder:

Being upset for something that happened in the past.

4. A Dime A Dozen:

Anything that is common and easy to get.

5. A Doubting Thomas:

A skeptic who needs physical or personal evidence in order to believe something.

6. A Drop in the Bucket:

A very small part of something big or whole.

7. A Fool And His Money Are Easily Parted:

It’s easy for a foolish person to lose his/her money.

8. A House Divided Against Itself Cannot Stand:

Everyone involved must unify and function together or it will not work out.

9. A Leopard Can’t Change His Spots:

You cannot change who you are.

10. A Penny Saved Is A Penny Earned:

By not spending money, you are saving money (little by little).

11. A Picture Paints a Thousand Words:

A visual presentation is far more descriptive than words.

12. A Piece of Cake:

A task that can be accomplished very easily.

13. A Slap on the Wrist:

A very mild punishment.

14. A Taste Of Your Own Medicine:

When you are mistreated the same way you mistreat others.

15. A Toss-Up:

A result that is still unclear and can go either way.

16. Actions Speak Louder Than Words:

It’s better to actually do something than just talk about it.

17. Add Fuel To The Fire:

Whenever something is done to make a bad situation even worse than it is.

18. Against The Clock:

Rushed and short on time.

19. All Bark And No Bite:

When someone is threatening and/or aggressive but not willing to engage in a fight.

20. All Greek to me:

Meaningless and incomprehensible like someone who cannot read, speak, or understand any of the Greek language would be.

21. All In The Same Boat:

When everyone is facing the same challenges.

22. An Arm And A Leg:

Very expensive. A large amount of money.

23. An Axe To Grind:

To have a dispute with someone.

24. Apple of My Eye:

Someone who is cherished above all others.

25. As High As A Kite:

To behave in a silly/uninhibited manner under the influence of drugs/alcohol.

26. At The Drop Of A Hat:

Willing to do something immediately.

27. Back Seat Driver:

People who criticize from the sidelines, much like someone giving unwanted advice from the back seat of a vehicle to the driver.

28. Back To Square One:

Having to start all over again.

29. Back To The Drawing Board:

When an attempt fails and it’s time to start all over.

30. Baker’s Dozen:

A group of Thirteen items

Stay tuned for more such quality content!

You may have a look at our courses here: CAT 2017 Verbal Course | CAT 2017 LRDI Course | CAT 2017 QA Course | GK course for TISSNET, MICAT, SNAP, IIFT, MAT, CMAT, ATMA

The post Common idioms for CAT, XAT, IIFT, SNAP, NMAT, TISS, MICAT (Part 1) appeared first on Learningroots.

]]>The post Learningroots MBA CET 2018 Online Course appeared first on Learningroots.

]]>**Why choose the course?**

Here are a few features of the batch to help you make up your mind:

- 50 sessions covering all topics (Quant/DI, LR, Verbal, Abstract/Visual Reasoning)
- All sessions delivered live online. Aspirants will have the opportunity to ask their doubts during the session
- If you are a working professional, you need not worry. The sessions will be late into the evening and you will be able to participate easily
- All sessions will be recorded. If you miss a live session, you can simply login and view the sessions any time you like
- Doubts will be cleared within 24 hours through a dedicated WhatsApp group
- Online question bank for practice

**Tentative Schedule**

**Who will conduct the sessions?**

We have an unparalleled advantage when it comes to the credentials of our faculty. All sessions will be conducted by:

Shashank Prabhu (CET 2016 – Rank 1, CET 2010 – Rank 1, 100%iler CAT, 100%iler IIFT)

Sriram Krishnan (CET 2017 – Rank 3, CAT 4 time 99.5+, GMAT 760)

Prasad Sawant (CET 2009 – Rank 9, CAT 99.92, MAT 99.99 with 800/800)

The only institute in the country that has **only CET 99.99%ilers** as faculty!

**Still not convinced? Have a look at our result and testimonials**

From our MBA CET 2017 courses (Classroom, Online, and Mocks) we had **17 students above 99 percentile, 30 above 98 percentile and 76 above the 90 percentile mark** (which is about 70% of the students we trained this year).

1) Nireeh Desai – 99.9

2) Arpan Katkoria – 99.87

3) Nikhil Tanawade – 99.87

4) Vishwas Sawant – 99.79

5) Danish Arshad – 99.76

6) Kunj Thakkar – 99.76

7) Viki Gandhi – 99.72

8) Adil Jain – 99.72

9) Debabrata Pal – 99.57

10) Vishal More – 99.52

11) Aakash Chawla – 99.43

12) Rahhel Kadri – 99.36

13) Kiran Mane – 99.36

14) Milind Sukhtankar – 99.29

15) Shivsubramani Sankaranarayanan – 99.29

16) Vinay Rajupalepu – 99.22

17) Amod Tamaskar – 99.02

18) Biswadip Roy – 98.89 (With A 99.98 in CMAT)

19) Sharayu Joshi – 98.89

20) Rahul Mahajan – 98.74

21) Mithila Salvi – 98.74

22) Prathamesh Chilweri – 98.74

23) Jerin Shaji – 98.59 (with a 99.9 in CMAT)

24) Sanket Joshi – 98.44

25) Rohit Saraf – 98.44

26) Uday Wagh – 98.27

27) Mohammed Sayyed – 98.27

28) Viraj Khetle – 98.27

29) Parag Utekar – 98.1

30) Purva Koregave – 98.1

Enrolling for Learningroots test series was one of the best decisions that I took for my CET preparation. In order to get a good score in any competitive exam you need just 2 things: Sound guidance and good material. Learningroots provided me with both. It always helps to talk to people who have ‘been there and done that’. In my case I had considerable trouble dealing with the Visual Reasoning (VR) section. The tricks and hacks that Team Learningroots shared with me for handling the VR section were nothing but KICK ASS. I believe that my score in VR section was what propelled me to the perfect score of 99.99! The content is well organized and extremely useful. I would like to thank Learningroots for providing me with all the necessary tools to ace the CET!

Jaideep Mehendale – CET 2016 99.99 percentile, JBIMS (2016-18)

The best part about Learningroots is that you directly get guidance and support from people who have been there and done that. Career guidance, how to crack interviews, help with SOP, free sessions before exams, they help you with each and everything. I strongly recommend all serious aspirants to join Learningroots and be a part of their legacy. Again, a hearty thanks to the three brilliant founders and their team!

Jayesh Bohra – CET 2016 99.98 percentile, JBIMS (2016-18)

You can read a few more of our students’ testimonials here.

**Fees?**

INR 7,500 only! (Register before 20th of September to get early bird discount of 1,000 Rs)

**Registration**

Only registered participants can attend the webinars. Also, there is a limit on the number of attendees. So ensure that you register yourself for the Learningroots MBA CET 2018 Online Course at the earliest!

Registration Link: Register for Learningroots MBA CET 2018 Online Course

P.S.: Ensure that you have joined our CET group for updates, discussions and much more. Here is the link – Learningroots CET group

The post Learningroots MBA CET 2018 Online Course appeared first on Learningroots.

]]>The post Announcing the Learningroots GMAT Online Batch 2 appeared first on Learningroots.

]]>The first GMAT online batch concluded in the 1st week of July. There were a total of 13 participants in the batch. Some of the reviews that I received at the end of the course:

The sessions were good and has helped me a lot. But the best thing was approachability of Sriram. He is always there no matter what time it is. He gave me very beneficial tips and one of the most important was how to maintain error log.

Individual attention and speedy doubt solving

Number of questions, the pace of the session & the brevity were perfect.

Concepts were covered very well. Even though i had started my preparation long before, this sessions were refreshing.

I also received a few suggestions on improving the course. So incorporating those suggestions, I have come up with a bigger and a better version of the course. All details are mentioned below:

The sessions will be held live at 9 pm Indian Standard Time (IST) everyday. The average length of the session will be 1.5 hours. The tentative schedule is given below:

The first session will be held on 14th August 2017. All classes will be recorded and will be uploaded on a restricted site to which only registered aspirants will have access (for a period of 6 months). You can view the recordings any number of times.

Before certain sessions, I’ll share a pre-session reading assignment. Ensure that you read the material before the session starts. Also, post the session, I’ll share some questions pertaining to the topic that I discussed. Ensure that you solve these questions before the next session.

I take all GMAT sessions at Learningroots. I have a 760 on the GMAT with a 50 in Quant and a 44 in Verbal (Debrief here – http://learningroots.in/gmat/gmat-debrief-760/). I have also scored a perfect 170 in Quant on the GRE.

The price for the complete course is Rs. 18,000. The price for individual courses (either Quant or Verbal) is Rs. 12,000. If you are residing outside India and wish to make the payment in other currencies, then do reach out to me.

***Registration Link (complete)** – https://imjo.in/2vufSY

***Registration Link (Quant/Verbal)** – https://imjo.in/2vufSY

If you have any queries, please write back to me at contact@learningroots.in. Will be happy to resolve any doubts that you may have.

The post Announcing the Learningroots GMAT Online Batch 2 appeared first on Learningroots.

]]>The post CAT 2017: Geometry Theorems #2 appeared first on Learningroots.

]]>**Theorem 6: If three sides of one triangle are respectively equal to the three sides of another triangle, then the two triangles are congruent.**

This is also known as SSS theorem.

For example, if AB = PQ, BC = QR, and AC = PR, then by SSS theorem, triangles ABC and PQR are said to be congruent.

**Theorem 7: If in two right angled triangles, the hypotenuse and a side of on triangle are respectively equal to the hypotenuse and a side of the other, then the two triangles are congruent.**

In triangles ABC and PQR, let angle B and Q be 90º.

If AC = PR and BC = QR, then the two triangles are congruent. This is quite simple to understand as in both the triangles, by Pythagoras theorem, square of the hypotenuse = sum of the squares of the other two sides. Hence, by both SSS and SAS tests, we will get the triangles to be congruent. This is also known as the RHS theorem.

**Theorem 8: If two sides of a triangle are not equal, then the greater side has the greater angle opposite to it.**

In triangle ABC, if AC > BC > AB. Therefore, ∠ ABC > ∠ BAC > ∠ ACB.

Whenever AC > AB, ∠ B > ∠ C.

This also gives us another theorem: If two angles of a triangle are unequal, the greater angle has the greater side opposite to it.

Another point to be noted: In a right angled triangle, the two angles other than the right angle are acute and hence the hypotenuse is the largest side.

**Theorem 9: The locus of a point equidistant from two fixed points is the perpendicular bisector of the line segment joining the two points.**

If B and C are two points and let D be the midpoint of BC. (DB = DC)

If A perpendicular is drawn to line BC from point A, triangles ADB and ADC can be proved to be congruent. Hence, any point on the perpendicular bisector of BC will be equidistant from B and C. Thus, the locus of A which is equidistant from B and C is the perpendicular bisector of the line segment BC.

**Theorem 10: Suppose two straight lines are cut by a transversal and any one of the following three conditions hold, namely,**

**a pair of alternate angles are equal****a pair of corresponding angles are equal****a pair of interior angles on the same side of the transversal add up to 180º**

**then the two straight lines are parallel.**

Using this theorem, if p is transversal and l and m are two straight lines, if any one of the following three conditions hold, namely,

- a pair of alternate angles are equal (say ∠ C and ∠ F)
- a pair of corresponding angles are equal (say ∠ B and ∠ F)
- a pair of interior angles on the same side of the transversal add up to 180º (say ∠ D and ∠ F)

then, these two straight lines are parallel. This also means that if two parallel straight lines l and m are cut by a transversal, then the alternate angles are equal, the corresponding angles are equal, and the sum of the interior angles on the same side of the transversal is equal to 180º.

∠ A = ∠ D = ∠ E = ∠ H

∠ B = ∠ C = ∠ F = ∠ G

∠ C + ∠ E = ∠ D + ∠ F = 180º

Hope you found this post useful. Stay tuned for the next article in this series and join our Facebook group for daily CAT questions. If you are looking at joining any of our online course, visit us here.

The post CAT 2017: Geometry Theorems #2 appeared first on Learningroots.

]]>The post CAT 2017 – 4 Months 99 percentile preparation plan appeared first on Learningroots.

]]>“The three great essentials to achieve anything worthwhile are, first, hard work; second, stick-to-itiveness; third, common sense.”

– Thomas A. Edison

**CAT 2017 – 4 Months 99 percentile preparation plan** is an effort to give aspirants a tool that they can use to achieve their dreams. What does this plan contain?

This daily plan has topic-wise and section-wise data. So, for example:

**Day 1:** Number systems concepts + LOD 1 questions; 1 LR and 1 DI set; 1 RC + 30 minutes of reading

**Day 2:** 1 LR and 1 DI set; 1 RC + 20 questions on parajumbles

**Day 3:** Number System Concepts + LOD 1 questions; 1 LR set and 1 DI set; 1 RC + 30 minutes of reading

**Day 4:** 1 LR and 1 DI set; 1 RC + 20 questions on critical reasoning

**Day 5:** SI CI Concepts + LOD 1 questions; 1 LR set and 1 DI set; 1 RC + 30 minutes of reading

Over these five days, you will also solve questions from past CAT papers that you can download here: Download past CAT papers

Whether you are just starting or have already taken CAT before, this plan should help you structure your preparation. One can also modify this plan to suit one’s needs, for example, if one is good at verbal, one may want to reduce the number of questions and focus more on quant. On any given day, the preparation doesn’t exceed four hours. Number of questions on non-mock days should be around 50-60. In total, the plan should help you hit around 9,000 questions. LOD refers to Level of difficulty (Easy-Moderate-Advanced).

**Download the CAT 2017 – 4 months 99 percentile preparation plan**

We believe this will help aspirants who don’t have access to quality strategic guidance. Do share your thoughts on this with us by commenting on this post or via our Facebook CAT preparation group for serious aspirants. If you are looking at joining any of our online courses, you will find all the details here. As always, for any queries, contact us contact [at] learningroots [dot] in or call us on 9969789521.

The post CAT 2017 – 4 Months 99 percentile preparation plan appeared first on Learningroots.

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