Instructions

For the following questions answer them individually

Question 131

A truck travelling at 70 kilometres per hour uses 30% more diesel to travel a certain distance than it does when it travels at the speed of 50 kilometres per hour. If the truck can travel 19.5 kilometres on a litre of diesel at 50 kilometres per hour, how far can the truck travel on 10 litres of diesel at a speed of 70 kilometres per hour?

[CAT 2000]

Video Solution

Solution

If the truck is being driven at 70 kmph, it takes 1.3 liters of diesel to travel 19.5 km.
Therefore, with 10 liters of diesel, the truck can travel 10/1.3 * 19.5 km = 150 km.

Question 132

Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is:

[CAT 2000]

Video Solution

Solution

The first five numbers could be n-2, n-1, n, n+1, n+2. The next two number would then be, n+3 and n+4, in which case, the average of all the 7 numbers would be $$\frac{(5n+2n+7)}{7}$$ = n+1

Question 133

If x>2 and y>-1,then which of the following statements is necessarily true?

Video Solution

Solution

This kind of questions must be solved using the counter example method.

x = 100 and y = -1/2 rules out option a)
x = 3 and y = 0 rules out options c) and d)
Option b) is correct.

Question 134

One red flag, three white flags and two blue flags are arranged in a line such that,

A. no two adjacent flags are of the same colour

B. the flags at the two ends of the line are of different colours.

In how many different ways can the flags be arranged?

Video Solution

Solution

The three white flags can be arranged in the following two ways:

__ W __ W __ W or W __ W __ W __

In the blanks, the 2 blue and one red flag can be arranged in 3 ways.
So, the total number of arrangements is 2*3 = 6

Question 135

Let S be the set of integers x such that:

1) 100 <= x <= 200

2) x is odd

3) x is divisible by 3 but not by 7.

How many elements does S contain?

Video Solution

Solution

Number of multiples of 3 between 100 and 200 = 66 - 33 = 33
Number of odd multiples = 16
Number of odd multiples of 21 = 3 (105, 147, 189)
So, the required number = 13

Question 136

Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all the elements of S. With how many consecutive zeroes will the product end?

Video Solution

Solution

For number of zeroes we must count number of 2 and 5 in prime numbers below 100.

We have just 1 such pair of 2 and 5.

Hence we have only 1 zero.

Question 137

Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

Video Solution

Solution

In option d), x-y is even. So, the product of the three terms is even. So, d) cannot be true.

Question 138

What is the number of distinct triangles with integral valued sides and perimeter 14?

Video Solution

Solution

Let the sides be x, y and 14-(x+y)
x+y > 14-(x+y) => x+y > 7
x+14-x-y > y => y < 7
Similarly, x < 7
If x = 1, y = 7 (not possible)
So, if x = 2, y = 6
if x = 3, y = 5 if x = 4, y = 4, 5
The cases for x = 5 and 6 are already taken care of by y.
Number of possible cases = 4

Question 139

Let N = 1421 * 1423 * 1425. What is the remainder when N is divided by 12?

Video Solution

Solution

The numbers 1421, 1423 and 1425 when divided by 12 give remainder 5, 7 and 9 respectively.

5*7*9 mod 12 = 11 * 9 mod 12 = 99 mod 12 = 3

Question 140

The integers 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?

Video Solution

Solution

The difference of the numbers = 34041 - 32506 = 1535

The number that divides both these numbers must be a factor of 1535.

307 is the only 3 digit integer that divides 1535.

CAT Content

CAT 2000 Question Paper

Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is:

[CAT 2000]

If x>2 and y>-1,then which of the following statements is necessarily true?

One red flag, three white flags and two blue flags are arranged in a line such that,

A. no two adjacent flags are of the same colour

B. the flags at the two ends of the line are of different colours.

In how many different ways can the flags be arranged?

Let S be the set of integers x such that:

1) 100 <= x <= 200

2) x is odd

3) x is divisible by 3 but not by 7.

How many elements does S contain?

Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all the elements of S. With how many consecutive zeroes will the product end?

Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

What is the number of distinct triangles with integral valued sides and perimeter 14?

Let N = 1421 * 1423 * 1425. What is the remainder when N is divided by 12?

The integers 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?

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CAT Content

CAT 2000 Question Paper

Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is: [CAT 2000]

If x>2 and y>-1,then which of the following statements is necessarily true?

One red flag, three white flags and two blue flags are arranged in a line such that, A. no two adjacent flags are of the same colour B. the flags at the two ends of the line are of different colours. In how many different ways can the flags be arranged?

Let S be the set of integers x such that: 1) 100 <= x <= 200 2) x is odd 3) x is divisible by 3 but not by 7. How many elements does S contain?

Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all the elements of S. With how many consecutive zeroes will the product end?

Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

What is the number of distinct triangles with integral valued sides and perimeter 14?

Let N = 1421 * 1423 * 1425. What is the remainder when N is divided by 12?

The integers 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?

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Also Read

Get Started with 5000+ Free CAT Questions & Mock Tests with Detailed Solutions!

Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is:

[CAT 2000]

One red flag, three white flags and two blue flags are arranged in a line such that,

A. no two adjacent flags are of the same colour

B. the flags at the two ends of the line are of different colours.

In how many different ways can the flags be arranged?

Let S be the set of integers x such that:

1) 100 <= x <= 200

2) x is odd

3) x is divisible by 3 but not by 7.

How many elements does S contain?