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CAT Standard Multiple-choice Question Papers 03 |
Races
In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race?
150 seconds
165 seconds
135 seconds
66.67 seconds
Ans : C
A gives B a start of 10 metres in a 100 metre race and still beats him by 1.25 seconds. How long does B take to complete the 100 metre race if A runs at the rate of 10 m/sec?
8 seconds
10 seconds
16.67 seconds
12.5 seconds
Ans : D
A predator is chasing its prey. The predator takes 4 leaps for every 6 leaps of the prey and the predator covers as much distance in 2 leaps as 3 leaps of the prey. Will the predator succeed in getting its food?
Yes
In the 6th leap
Never
Cannot determine
Ans : D
A skating champion moves along the circumference of a circle of radius 21 meters in 44 seconds. How many seconds will it take her to move along the perimeter of a hexagon of side 42 meters?
56
84
64
48
Ans : B
A runs 13/5 times as fast as B. If A gives a start of 240m, how far must the post be so that A and B might reach at the same time.
390 m
330 m
600 m
720 m
Ans : A
A gives B a start of 30 seconds in a km race and still beats him by 20 m. However, when he gives B a start of 35 seconds, they finish the race in a dead heat. How long does A take to run the km?
250 seconds
285 seconds
220 seconds
215 seconds
Ans : D
A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?
150
200
100
170
Ans : D
A can give B a start of 50 metres or 10 seconds in a kilometer race. How long does A take to complete the race?
200 seconds
140 seconds
220 seconds
190 seconds
Ans : D
Three runners A, B and C run a race, with runner A finishing 12 meters ahead of runner B and 18 meters ahead of runner C, while runner B finishes 8 meters ahead of runner C. Each runner travels the entire distance at a constant speed.
What was the length of the race?
36 meters
48 meters
60 meters
72 meters
Ans : B
P can give Q a start of 20 seconds in a kilometer race. P can give R a start of 200 meters in the same kilometer race. And Q can give R a start of 20 seconds in the same kilometer race. How long does P take to run the kilometer?
200 seconds
240 seconds
160 seconds
140 seconds
Ans : C
Two numbers when divided by a certain divisor leave remainders of 431 and 379 respectively. When the sum of these two numbers is divided by the same divisor, the remainder is 211. What is the divisor?
599
1021
263
Cannot be determined
Ans : A
How many zeros contained in 100!?
100
24
97
Cannot be determined
Ans : B
Which is greater of the two
2300
3200
Both are equal
Cannot be determined
Ans : B
What is the value of M and N respectively? If M39048458N is divisible by 8 & 11; Where M & N are single digit integers?
7, 8
8, 6
6, 4
5, 4
Ans : C
When 26854 and 27584 are divided by a certain two digit prime number, the remainder obtained is 47. Which of the following choices is a possible value of the divisor?
61
71
73
89
Ans : C
Find the G.C.D of 12x2y3z2, 18x3y2z4, and 24xy4z3
6xy2z2
6x3y4z3
24xy2z2
18x2y2z3
Ans : A
Find the G.C.D of 12x2y3z2, 18x3y2z4, and 24xy4z3
6xy2z2
6x3y4z3
24xy2z2
18x2y2z3
Ans : A
The 7th digit of (202)3is
2
4
8
6
Ans : C
A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge?
Rs. 105 and Rs. 6
Rs. 216 and Rs. 12
Rs. 210 and Rs. 12
Rs. 210 and Rs. 6
Ans : D
Find the range of real values of x satisfying the inequalities 3x - 2 > 7 and 4x - 13 > 15.
x > 3
x > 7
x < 7
x < 3
Ans : B
Number System
How many different factors are there for the number 48, excluding 1 and 48?
12
4
8
None of these
Ans : C
What is the remainder when 9 + 9 2 + 9 3 + .... + 9 8 is divided by 6?
3
2
0
5
Ans : C
The sum of the first 100 numbers, 1 to 100 is divisible by
2, 4 and 8
2 and 4
2 only
None of these
Ans : C
The sum of the first 100 numbers, 1 to 100 is divisible by
2, 4 and 8
2 and 4
2 only
None of these
Ans : C
For what value of 'n' will the remainder of 351 n and 352 n be the same when divided by 7?
2
3
6
4
Ans : B
A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before the will have result that will end with 3 zeroes?
11
10
6
5
Ans : C
What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?
176
187
54043
748
Ans : B
What number should be subtracted from x 3 + 4x 2 - 7x + 12 if it is to be perfectly divisible by x + 3?
42
39
13
None of these
Ans : A
Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?
(x-z) 2 y is even
(x-z)y 2 is odd
(x-z)y is odd
(x-y) 2 z is even
Ans : A
Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?
1050
540
1440
1590
Ans : D
Number System
Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?
144
168
192
None of these
Ans : C
Find the greatest number of five digits, which is exactly divisible by 7, 10, 15, 21 and 28.
99840
99900
99960
99990
Ans : C
When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
11
17
13
23
Ans : C
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
13
59
35
37
Ans : D
Given A = 265 and B = (264+263+262+...+20)
B is 264 larger than A
A and B are equal
B is larger than A by 1
A is larger than B by 1
Ans : D
The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.
44
22
19
None of these
Ans : A
If (x + 2) 2 = 9 and (y + 3) 2 = 25, then the maximum value of x / y is
1 / 2
5 / 2
5 / 8
1 / 8
Ans : C
If p and q are the roots of the equation x 2 - bx + c = 0, then what is the equation if the roots are (pq + p + q) and (pq - p - q)?
x 2 - 2cx + (c 2 - b 2 ) = 0
x 2 - 2bx + (b 2 + c 2 ) = 0
Bcx 2 - 2(b+c)x + c 2 = 0
x 2 + 2bx - (c 2 - b 2 ) = 0
Correct answer- A
A piece of equipment cost a certain factory Rs. 600,000. If it depreciates in value, 15% the first year, 13.5% the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?
2,00,000
1,05,000
4,05,000
6,50,000
Correct answer- B
Solve the inequality 33x-2 > 1
x > 1
x > 3
x > 2/3
x > 1/3
Ans : C
Number System
The largest number amongst the following that will perfectly divide 101100 - 1 is
100
10000
100 100
100000
Ans : 2
What is the highest power of 7 in 5000!? (5000! means factorial 5000)
4998
714
832
816
Ans : C
What is the total number of different divisors including 1 and the number that can divide the number 6400?
24
27
54
68
Ans : B
How many four digit numbers exist which can be formed by using the digits 2, 3, 5 and 7 once only such that they are divisible by 25?
4! - 3!
4
8
6
Ans : B
A certain number when successfully divided by 8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder when the number is divided by the product of 8 and 11, viz 88?
3
21
59
68
Ans : C
'a' and 'b' are the lengths of the base and height of a right angled triangle whose hypotenuse is 'h'. If the values of 'a' and 'b' are positive integers, which of the following cannot be a value of the square of the hypotenuse?
13
23
37
41
Ans : B
What is the reminder when 91 + 92 + 93 + ...... + 99 is divided by 6?
0
3
4
None of these
Ans : B
How many times will the digit '0' appear between 1 and 10,000?
4000
4003
2893
3892
Ans : C
What is the total number of different divisors of the number 7200?
20
4
54
32
Ans : C
What is the least number that should be multiplied to 100! to make it perfectly divisible by 350?
144
72
108
216
Ans : B
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