Q: x and y are integers x + y 6 What is the smallest possible value of x - y ?

The smallest value will be obtained by giving x the smallest possible value while y gets the largest possible value. The smallest value for x = 7. This means that y will have to be less than or equal to 3 (so that x + y <11), but we want the largest value of y which is 3. The difference, x - y will be 4.

Question 1

(3x + 2) (2x - 5) = ax² + kx + n . What is the value of a - n + k ?

Accepted Answer

This is a quadratic equation. To find n we multiply the last terms in each bracket together (2 times -5) = -10 To find ‘a’ we multiply the first terms in each bracket together (3x times 2x) = 6x2, So a = 6. Thus a - n = 16 To find k we multiply the first term in the first bracket by the second term in the second bracket and add the result to the product of the second term in the first bracket and the first term in the second. (-15x + 4x) = -11x. So k = -11 16 - 11 = 5

Question 2

A person in a bet 40 shots taken. 50p for a hit, 10p for a miss.(he have to give). Finally he has Rs.5. How many hits he have ?

Accepted Answer

Let number of hit shots be 'X' Let number of miss shots be 'Y' Given X + Y = 40....(1) 50X - 10Y = 500.....(2) Solving 1 and 2, we get X = 15 and Y = 25 Therefore, number of hits = 15

Question 3

The sum of the two digits of a number is 8. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number ?

Accepted Answer

Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place. P + Q = 8 ----- (1) (10Q + P) - (10P + Q) = 54 9(Q - P) = 54 (Q - P) = 6 ----- (2) Solve (1) and (2) P = 1 and Q = 7 The required number is = 17

Question 4

One number is 25% of another number. The larger number is 12 more than the smaller. The large number is

Accepted Answer

16

Question 5

How many numbers are there from 2000 to 7000 which are both perfect squares and perfect cubes?

Accepted Answer

1

Question 6

If in a two digit number, the digit at unit place is z and the digit at tens place is 8, then the number is

Accepted Answer

80 + z

Question 7

The sum of three numbers is 2, the 1st number is 1/2 times the 2nd number and the 3rd number is 1/4 times the 2nd number. The 2nd number is

Accepted Answer

8/7

Question 8

The smallest number, which should be added to 756896 so as to obtain a multiple of 11, is

Accepted Answer

3

Question 9

Of the 3 numbers whose average is 22, the first is 3/8th the sum of other 2. What is the first number?

Accepted Answer

18

Question 10

How many natural numbers are there between √261 and √45109?

Accepted Answer

196

Question 11

What is that least number that must be added to the product 684 × 686 to make it a perfect square?

Accepted Answer

1

Question 12

Determine the largest 4 digit number which is a perfect square.

Accepted Answer

9801

Question 13

The largest 5 digit number exactly divisible by 89 is:

Accepted Answer

99947

Question 14

The sum of all prime numbers between 58 and 68 is

Accepted Answer

187

Question 15

The average of 25 consecutive odd integers is 55. The highest of these integers is

Accepted Answer

79

Question 16

N is the largest two digit number, which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively. What is the remainder when N is divided by 5?

Accepted Answer

4

Question 17

The difference between a number and its three-iflh is 50. What is the number ?

Accepted Answer

Let the number be x. Then, x - 3x/5 = 50 <=> x = (50 * 5) / 2 = 125..

Question 18

The total weight of a tin and the cookies it contains is 2 pounds. After ¾ of the cookies are eaten, the tin and the remaining cookies weigh 0.8 pounds. What is the weight of the empty tin in pounds?

Accepted Answer

Let the weight of the empty tin = w (2 - w) = weight of the cookies; and one quarter of the cookies weigh (2 - w)/4 One quarter of the cookies + tin = 0.8 = w + (2 - w)/4 Multiply through by 4; 3.2 = 4w + 2 - w 1.2 = 3w; w = 0.4

Question 19

If two painters can complete two rooms in two hours, how many painters would it take to do 18 rooms in 6 hours?

Accepted Answer

Two painters can complete two rooms in two hours.So 18 rooms can be painted in 6 hrs by 6 painters

Question 20

x and y are integers x + y < 11 , and x > 6 What is the smallest possible value of x - y ?

Accepted Answer

The smallest value will be obtained by giving x the smallest possible value while y gets the largest possible value. The smallest value for x = 7. This means that y will have to be less than or equal to 3 (so that x + y <11), but we want the largest value of y which is 3. The difference, x - y will be 4.

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