### CAT Standard Multiple-choice Question Paper

Directions: In this section you will be given two quantities, one in column A and one in column B. You are to determine a relationship between the two quantities and mark.

1. If the quantity in column A is catater than the quantity in column B.
2. If the quantity in column B is catater than the quantity in column A.
3. If the quantities are equal.
4. If the comparison cannot be determined from the information that is given
# A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cms and its width is increased also by x cms so as to make it a square then its area changes by :

1. 4
2. 144
3. 12
4. 2
5. None of the above.

Ans : A
# A motorcycle stunts man belonging to a fair, rides over the vertical walls of a circular well at an average speed of 54 kph for 5 minutes. If the radius of the well is 5 meters then the distance traveled is:

1. 2.5 kms
2. 3.5 kms
3. 4.5 kms
4. 5.5 kms
5. None of the above

Ans : C
# If 1 cm on a map corresponds to an actual distance of 40 kms. And the distance on the map between Bombay and Calcutta is 37.5 cms., the actual distance between them is :

1. 375 kms
2. 3750 kms
3. 1500 kms
4. 1375 kms
5. None of the above

Ans : C
4. A box contains 90 mts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., then the weight of the empty box is :
1. 10 kg
2. 10.5 kg
3. 11 kg
4. 11.5 kg
5. None of the above

Ans : D
5. If the radius of a circle is increased by 20% then the area is increased by :
1. 44%
2. 120%
3. 144%
4. 40%
5. None of the above

Ans : A
6. Tom, Dick and Harry went for lunch to a restaurant. Tom had \$100 with him, Dick had \$60 and Harry had \$409. They got a bill for \$104 and decided to give a tip of \$16. They further decided to share the total expenses in the ratio of the amounts of money each carried. The amount of money which Tom paid more than what Harry paid is
1. 120
2. 200
3. 60
4. 24
5. 36

Ans : E
7. A plot of land is in the shape of a trapezium whose dimensions are given in the figure below :

Hence the perimeter of the field is
1. 50 m
2. 64 m
3. 72 m
4. 84 m
5. None of the above

Ans : c
8. Four concentric ( having the same center ) circles with radii, x, 2x, 3x and 4x are drawn to form two rings A and B as shown in the figure.

Ratio of the area of inner ring A to the area of outer ring B is
1. 1 : 2
2. 1 : 4
3. 2 : 3
4. 3 : 7
5. None of the above

Ans : D
9. If 3/p = 6 and 3/q = 15 then p – q = ?
1. 1/3
2. 2/5
3. 3/10
4. 5/6
5. None of the above

Ans : C
10. A father is three times as old as his son. After fifteen years the father will be twice as old as his son’s age at that time. Hence the father’s present age is
1. 36
2. 42
3. 45
4. 48
5. None of the above

Ans : C

* (1/4) 3 + (3/4) 3 + 3(1/4)(3/4)(1/4 + 3/4) =?
1. 1/64
2. 27/64
3. 49/64
4. 0
5. 1

Ans : E
* If the area of two circles are in the ratio 169 : 196 then the ratio of their radii is
1. 10 : 11
2. 11 : 12
3. 12 : 13
4. 13 : 14
5. None of the above

Ans : D
* A semi-circle is surmounted on the side of a square. The ratio of the area of the semi-circle to the area of the square is
1. 1 : 2
2. 2 : p
3. p : 8
4. 8 : p
5. None of the above

Ans : C
* Which of the following is the greatest ?
1. 40% of 30
2. 3/5 of 25
3. 6.5% of 200
4. Five more than the square of 3
5. 1/2 -4

Ans : E
* Two identical taps fill 2/5 of a tank in 20 minutes. When one of the taps goes dry in how many minutes will the remaining one tap fill the rest of the tank ?
1. 5 minutes
2. 10 minutes
3. 15 minutes
4. 20 minutes
5. None of the above

Ans : C
* If the value of XYZ Company stock drops from \$25 per share to \$21 per share, what is the percent of the decrease?
1. 4
2. 8
3. 12
4. 16
5. 20

Ans : D
* If a building b feet high casts a shadow f feet long, then, at the same time of day, a tree t feet high will cast a shadow how many feet long?
1. ft/b
2. fb/t
3. b/ft
4. tb/f
5. t/fb

Ans : A
* If x, y, and z are consecutive negative integers, and if x > y > z, which of the following must be a positive odd integer?
1. xyz
2. (x – y) (y – z)
3. x – yz
4. x(y + z)
5. x + y + z

Ans : B
* At a certain ice cream parlor, customers can choose among five different ice cream flavors and can choose either a sugar cone or a waffle cone. Considering both ice cream flavor and cone type, how many distinct triple-scoop cones with three different ice cream flavors are available?
1. 12
2. 16
3. 20
4. 24
5. 30

Ans : C
* What is the greatest value of a positive integer n such that 3n is a factor of 1815?
1. 15
2. 18
3. 30
4. 33
5. 45

Ans : C

1. If .2t = 2.2 – .6s and .5s = .2t + 1.1, then s =
1. 1
2. 3
3. 10
4. 11
5. 30

Ans : B
2. Five years ago, Beth’s age was three times that of Amy. Ten years ago, Beth’s age was one half that of Chelsea. If C repre- sents Chelsea’s current age, which of the following represents Amy’s current age?
1. c/6 + 5
2. 2c
3. (c-10)/3
4. 3c-5
5. 5c/3 – 10

Ans : A
3. A portion of \$7200 is invested at a 4% annual return, while the remainder is invested at a 5% annual return. If the annual income from both portions is the same, what is the total income from the two investments?
1. \$160
2. \$320
3. \$400
4. \$720
5. \$1,600

Ans : B
4. An empty swimming pool can be filled to capacity through an inlet pipe in 3 hours, and it can be completely drained by a drainpipe in 6 hours. If both pipes are fully open at the same time, in how many hours will the empty pool be filled to capacity?
1. 4
2. 4.5
3. 5
4. 5.5
5. 6

Ans : E
5. If r = (3p + q)/2 and s = p – q, for which of the following values of p would r2 = s2?
1. 1q/5
2. 10 – 3q/2
3. q – 1
4. 3q
5. 9q/2 – 9

Ans : A
6. At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?
1. 38
2. 40
3. 44
4. 48
5. 50

Ans : C
7. On the xy-coordinate plane, points A and B both lie on the circumference of a circle whose center is O, and the length of AB equals the circle’s diameter. If the (x,y) coordinates of O are (2,1) and the (x,y) coordinates of B are (4,6), what are the (x,y) coordinates of A?
1. (3, 3/2)
2. (1, 2/2)
3. (0, -4)
4. (2/2, 1)
5. (-1, -2/2)

Ans : C
8. If a rectangle’s length and width are both doubled, by what percent is the rectangle’s area increased?
1. 50
2. 100
3. 200
4. 300
5. 400

Ans : D
9. A rectangular tank 10″ by 8″ by 4″ is filled with water. If all of the water is to be transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smaller tanks are needed?
1. 9
2. 12
3. 16
4. 21
5. 39

Ans : B
10. Point Q lies at the center of the square base (ABCD) of the pyramid pictured above. The pyramid’s height (PQ) measures exactly one half the length of each edge of its base, and point E lies exactly halfway between C and D along one edge of the base. What is the ratio of the surface area of any of the pyramid’s four triangular faces to the surface area of the shaded triangle?
1. 3 :v2
2. v5:1
3. 4v3:3
4. 2v2:1
5. 8:v5

Ans : D

1. The average wages of a worker during a fortnight comprising 15 consecutive working days was Rs.90 per day. During the first 7 days, his average wages was Rs.87/day and the average wages during the last 7 days was Rs.92 /day. What was his wage on the 8th day?
1. 83
2. 92
3. 90
4. 97

Ans : D
2. The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?
1. 6.5
2. 4
3. 3
4. 3.5

Ans : C
3. The average temperature on Wednesday, Thursday and Friday was 250. The average temperature on Thursday, Friday and Saturday was 240. If the temperature on Saturday was 270, what was the temperature on Wednesday?
1. 240
2. 210
3. 270
4. 300

Ans : D
4. The average age of a group of 12 students is 20years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is
1. 24
2. 26
3. 23
4. 22

Ans : A
5. When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?
1. 57 kgs
2. 56.8 kgs
3. 58.2 kgs
4. 52.2 kgs

Ans : A
6. Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.

What is the average for all the three classes?
1. 81
2. 81.5
3. 82
4. 84.5

Ans : B
7. The average weight of a class of 24 students is 36 years. When the weight of the teacher is also included, the average weight increases by 1kg. What is the weight of the teacher?
1. 60 kgs
2. 61 kgs
3. 37 kgs
4. None of these

Ans : B
8. The average of 5 quantities is 10 and the average of 3 of them is 9. What is the average of the remaining 2?
1. 11
2. 12
3. 11.5
4. 12.5

Ans : C
9. The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
1. 13.5
2. 14
3. 15
4. 12.5

Ans : D
10. A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?
1. 8
2. 6
3. 2
4. 4

Ans : C
11. Average cost of 5 apples and 4 mangoes is Rs. 36. The average cost of 7 apples and 8 mangoes is Rs. 48. Find the total cost of 24 apples and 24 mangoes.
1. 1044
2. 2088
3. 720
4. 324

Ans : B

Interest

1. A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
1. Rs. 17.5 lakhs
2. Rs. 21 lakhs
3. Rs. 15 lakhs
4. Rs. 20 lakhs

Ans : B
2. What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
1. 2400
2. 2592
3. 2678
4. 2540

Ans : B
3. If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?
1. 9 years
2. 22 years
3. 18 years
4. 33 years

Ans : B
4. The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?
1. 6000
2. 6400
3. 7200
4. 9600

Ans : B
5. A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year.
1. 5624.32
2. 5630.50
3. 5788.125
4. 5627.20

Ans : A
6. The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?
1. 9000
2. 6250
3. 8530.80
4. 8780.80

Ans : D
7. Vijay invested Rs.50,000 partly at 10% and partly at 15%. His total income after a year was Rs.7000. How much did he invest at the rate of 10%?
1. Rs.40,000
2. Rs.40,000
3. Rs.12,000
4. Rs.20,000

Ans : B
8. A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
1. 25 years
2. 40 years
3. 33 years and 4 months
4. Cannot be determined

Ans : A
9. How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest?
1. 8 years
2. 64 years
3. 72 years
4. 56 years

Ans : D
10. Rs. 5887 is divided between Shyam and Ram, such that Shyam’s share at the end of 9 years is equal to Ram’s share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.
1. 2088
2. 2000
3. 3087
4. None of these

Ans : C
Geometry
# Find the coordinates of the point which divides the line joining (5, -2) and (9, 6) internally in the ratio 1 : 3.

1. (6, 0)
2. (6, 3)
3. (0, 6)
4. (3, 6)

Ans : A
# Find the number of triangles in an octagon.

1. 326
2. 120
3. 56
4. Cannot be determined

Ans : C
# Find the equation of a line whose intercepts are twice of the line 3x – 2y – 12 = 0

1. 3x – 2y = 24
2. 2x – 3y = 12
3. 2x – 3y = 24
4. None of these

Ans : A
# Find the area of the sector covered by the hour hand after it has moved through 3 hours and the length of the hour hand is 7cm.

1. 77 sq.cm
2. 38.5 sq.cm
3. 35 sq.cm
4. 70 sq.cm

Ans : B
5. Find the area of the triangle whose vertices are (-6, -2), (-4, -6), (-2, 5).
1. 36
2. 18
3. 15
4. 30

Ans : C
6. A stairway 10ft high is such that each step accounts for half a foot upward and one-foot forward. What distance will an ant travel if it starts from ground level to reach the top of the stairway?
1. 30 ft
2. 33 ft
3. 10 ft
4. 29 ft

Ans : D
7. Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon?
1. 6
2. 8
3. 12
4. 3

Ans : C
8. What is the area of the largest triangle that can be fitted into a rectangle of length ‘l’ units and width ‘w’ units?
1. lw/3
2. (2lw)/3
3. (3lw)/4
4. (lw)/2

Ans : D
9. Which of the following is inCorrect?
1. An incentre is a point where the angle bisectors meet.
2. The median of any side of a triangle bisects the side at right angle.
3. The point at which the three altitudes of a triangle meet is the orthocentre
4. The point at which the three perpendicular bisectors meet is the centre of the circumcircle.

Ans : B
10. A and B are two points with the co-ordinates (-2, 0) and (0, 5). What is the length of the diagonal AC if AB form one of the sides of the square ABCD?
1. units
2. units
3. units
4. units

Ans : B

Geometry

1. What is the measure of the circum radius of a triangle whose sides are 9, 40 and 41?
1. 6
2. 4
3. 24.5
4. 20.5

Ans : D
2. If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?
1. 10 sides
2. 8 sides
3. 12 sides
4. 9 sides

Ans : A
3. If ABC is a right angle triangle with angle A = 900 and 2s = a + b + c, where a > b > c where notations have their usual meanings, then which one of the following is Correct?
1. (s – b) (s – c) > s (s – a)
2. (s – a) (s – c) > s (s – b)