Sum of Consecutive Numbers

Q.

How many times will the digit `7' be written when writing the integers from 1 to 1000?

1. 300

2. 190

3. 210

4. None of these

5. 100

Q. What number comes next in the series?
7, 9, 13, 21, 37, ?

1. 58
2. 63
3. 69
4. 72

Q. The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four members?

1. 41
2. 67
3. 21
4. 25

Q.

One score is equal to ______ entities.

Q.

For a set of 5 true-or-false questions, no student has written all the correct answers, and no 2 students have given the same sequence of answers. What is the maximum number of students in the class, for this to be possible?

1. None of these
2. 31
3. 21
4. 51
5. 41

Q. There are 8436 steel balls, each with a radius of 1cm, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth layer and so on. The number of horizontal layers in the pile is ___.

Q. The integers 1, 2, . . ., 40 are written on a black board. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased, and a new number a + b - 1 is written. What will be the number left on the board at the ends?

1. 820
2. 821
3. 781
4. 780

Q.

$S={100}^2-{99}^2+{98}^2-{97}^2+........................+2^2-1^2;$ what is the value of S?

1. 5050

2. 5024

3. 5000

4. 2020

Q. Find the ${28383}^{rd}$ digit: 123456789101112....

1. 3
2. 4
3. 9
4. 7

Q.

The square root of $\left(7+3\sqrt{5}\right)\left(7-3\sqrt{5}\right)$ is :

1. 4

2. 3 (5) ^(1/2)

3. 1

4. (5) ^(1/2)

5. 2

Q. When the natural numbers 1, 2, 3, ..., 500 are written, then the digit 3 is used n times in this way. The value of n is:

1. 100
2. 200
3. 300
4. 280

Q. Insert the missing number:
5, 8, 12, 17, 23, ___ 38

1. None of the above
2. 29
3. 30
4. 32
5. 25

Q. A number of saplings are lying at a place by the side of a straight road. These are to be planted in a straight line at a distance interval of 10 meters between two consecutive saplings. Mithilesh, the country's greatest forester, can carry only one sapling at a time and has to move back to the original point to get the next sapling. In this manner, he covers a total distance of 1.32 kms. How many saplings does he plant in the process if he ends at the starting point?

1. 13
2. 14
3. 11
4. 12

Q.

Fill in the missing number:
5, 18, 10, 12, 15, ?

1. None of the above
2. 4
3. 8
4. 6
5. 10

Q.

What should come in place of the question mark (?) in the following number series?
4, 6, 12, 30, 90, 315, ?

1. 1102
2. 1260
3. 1417.5
4. None of these
5. 945

Q. (1), (2, 3), (4, 5, 6), (7, 8, 9, 10)…..
Sum of the numbers in the 50th bracket is ___.

Q. The next number in the sequence is – 1458, 486, 162, 54, 18, _____________.

Q. If then, r cannot take any value except :(CAT 2004)

1. 
2. -1
3. ½ or -1
4. -1/2 or -1

Q.

The sale of lipsticks in 2000 was by what percent more than the sales of nail enamels in 2000? (Rounded off to nearest integer)

1. none of these

2. 26%

3. 27%

4. 28%

5. 29%

Q. Chandrabhal adds first N natural numbers and finds the sum to be 1850. However, actually one number was added twice by mistake. Find the difference between N and that number.

1. 40
2. 33
3. 60
4. 17

Q. Find the value of x in the series 2, 6, 30, 210, x, 30030, ...

1. 2310
2. 1890
3. 2520
4. 2730
5. None of the above

Q. 27 13 12 16.5 ? 75

1. 30.5
2. 31.5
3. 39.5
4. None of these
5. 37.5

Q. Show that p*2 will leave reminder 1 when divided by 8 if p is an odd positive integer

Q. A triangular number is defined as a number which has the property of being expressed as a sum of consecutive natural numbers starting with 1. How many triangular numbers less than 1000, have the property that they are the difference of squares of two consecutive natural numbers?

1. 21
2. 20
3. 22
4. 23

Q. 7 20 46 98 202 ?

1. 420
2. 410
3. 310
4. 320
5. None of these

Q.

The square root of a natural number is equal to K times its cube root. The number must be

1. K

2. K

3. k

4. K

Q.

In each of the questions below, a number series has been given followed by five alternatives. One term of the given number series is wrong. Find out the wrong term and spot a number from the alternatives which will replace the wrong term of the series.
7, 14, 56, 168, 336, 1344, 2688, 8064

1. 2680
2. 332
3. 3032
4. 5032
5. 4032

Q. How many different numbers of 2-digits can be formed with the digits 1, 2, 3, 4, 5, 6; no digits being repeated?

1. None of these
2. 45
3. 40
4. 30
5. 35

Q. In a football team, 12 players are divided into three groups of 4 each and are given different jersey numbers numbering from 1 to 12 in such a way that the sum of the jersey numbers of each of the three groups is same. Find the sum of jersey numbers of each group.

1. 26
2. 34
3. 78
4. can’t be determined

Q. For a triangle whose sides are 50 m, 78 m and 112 m, respectively, then the length of the perpendicular from the opposite angle on the side 112 m is _____.

1. 45 m
2. 30 m
3. 95 m
4. 35 m
5. None of these