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# Problems on Numbers Questions

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Given n = 1 + x and x is a product of four consecutive integers. Then which of the following is true ?
A. n is an odd integer B. n is prime C. n is a perfect square

Aboth A and C are correct

Bboth A and B are correct

Conly A is correct

Donly C is correct

Explanation:

Take any 4 values, like 2, 3, 4, 5 and get the answer a & c only.

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How many of the numbers x (x being integer) with 10 <= x <= 99 are 18 more than the sum of their digits

A9

B12

C18

D10

Explanation:

Let the number be ab. So given that
=>10a + b = 18 + a + b
=> 9a = 18
=> a = 2
So 20, 21, ... upto 29 there are total 10 numbers possible.

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You are given 87 matchsticks. They are arranged in rectangular manner.Find the number of triangles formed?

A43

B54

C44

D23

Explanation:

1st triangle formed by using 3 sticks.
so remaining sticks are =87-3=84
all other can be formed by just using two sticks =84/2 =42

so total =42(by using two sticks)+1(by using three sticks) =43

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How many Palindrone number are there between 5000 To 67000 . Palindrone no 5335 is palindone no because if u read from first and last the value remains same

A456

B620

C630

D768

Explanation:

5000 To 10000 = Per section 10 Total 5 section S/T = 5*10 = 50
Than
10000 To 67000 = Per Section 10 Total 57 Section S/T = 57*100 = 570
Total is = 50+570 = 620

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If all the numbers between 11 and 100 are written on a piece of paper. How many times will the number 4 be used?

A18

B12

C19

D43

Explanation:

There are total 9 4's in 14, 24, 34...,94 & total 10 4's in 40,41,42....49

thus, 9+10=19.

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The fourteen digits of a credit card are to be written in the boxes shown above. If the sum of every three consecutive digits is 18, then the value of x is:

A3

B2

C1

DCannot be determined

Explanation:

Let us assume right most two squares are a , b

Then Sum of all the squares = 18 x 4 + a + b ------ (1)
Also Sum of the squares before 7 = 18

Sum of the squares between 7, x = 18 and
sum of the squares between x , 8 = 18

So Sum of the 14 squares = (18 + 7 + 18 + x + 18 + 8 + a + b) ------- (2)
By Solving equation 1 and 2
x = 3

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Given that 0 < a < b < c < d, which of the following the largest?

A(c+d) / (a+b)

B(a+d) / (b+c)

C(b+c) / (a+d)

D(b+d) / (a+c)

Explanation:

Take a = 1, b = 2, c = 3, d = 4

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X = 101102103104105106107......146147148149150 (From numbers 101-150). Find out the remainder when this number is divided by 9.

A7

B4

C2

D3

Explanation:

The divisibility rule for 9 is sum of the digits is to be divisible by 9. So

We calculate separately, sum of the digits in hundreds place, tenths place, and units place.

Sum of the digits in hundreds place: 1 * 50 = 50

Sum of the digits in tenths place : 0 * 9 + 1 * 10 + 2 * 10 + 3 * 10 + 4 * 10 + 5 * 1 = 105

Sum of the digits in units place : (1 + 2 + 3 + ...+ 9) * 5 = 225

So total = 380

So remainder = 380 / 9 = 2

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A number is 101102103104...150. As 101 102 103 103.... 150. What is reminder when divided by 3?

A5

B2

C7

D1

Explanation:

Divisibility rule for 3 also same as 9.
so from the above discussion sum of the digits = 380
and remainder = 380/3 = 2

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7^1+7^2+7^3+.......+7^205. Find out how many numbers present which unit place contain 3?

A34

B51

C50

D56

Explanation:

Units digits of first 4 terms are 7, 9, 3, 1. and this pattern repeats.
So for every 4 terms we get one term with 3 in its unit digit.
So there are total of 205/4 = 51 sets and each set contains one terms with 3 in its unit digit.

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