16 . If the sum of three consecutive integers is odd, then the first and the last integers must be -

A. odd, even
B. odd, odd
C. even, odd
D. even, even
E. None of these

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Answer: Option D

Explanation:

For example,

2 + 3 + 4 = 9 ( odd)

but,

3 + 4 + 5 = 12 ( even)

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17 . If X is the difference if the squaresof two consecutive even numbers, which of the following numbers is a divisor of X?

A. 4
B. 7
C. 8
D. 9

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Answer: Option A

Explanation:

Let's consider two consecutive even numbers as 2n and 2n+2, where n is any integer.
The square of 2n is (2n)^2 = 4n^2. The square of 2n+2 is (2n+2)^2 = 4(n+1)^2.
Now, let's find the difference between these squares:
X = (2n+2)^2 - (2n)^2 X = 4(n+1)^2 - 4n^2
Now, factor out 4:
X = 4[(n+1)^2 - n^2]
Now, simplify the expression inside the square brackets:
X = 4[(n^2 + 2n + 1) - n^2]
X = 4(2n + 1)
X = 8n + 4
Now, we can see that X is divisible by 4 because it has a factor of 4. So, the correct answer is 4.

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গ্যাস ট্রান্সমিশন কোম্পানি লিমিটেড | সহকারী ব্যবস্থাপক - 26.11.2021 || 2021

A. y / ( x + y )
B. x / xy
C. x / ( x + y)
D. y / xy
E. None of these

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Answer: Option C

Explanation:

Girls = x

Boys = y

So, Girls + Boys = x + y

Composed of girls = x/(x + y).

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Bangladesh Bank - Assistant Director - 2009

A. 10
B. 12
C. 14
D. 16

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Answer: Option D

Explanation:

ধরি, সংখ্যাগুলো x - 3, x - 2, x - 1, x + 1, x + 2, x + 3, x + 4

শেষ চারটি সংখ্যার যোগফল = 4x + 10

প্রথম চারটি সংখ্যার যোগফল = 4x - 6

( - ) পার্থক্য = 16

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20 . Six consecutive whole numbers are given. The sum of the first three numbers is 27. What is the sum of the last three numbers?

A. 36
B. 33
C. 32
D. 30
E. None of these

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Answer: Option A

Explanation:

Let,

Numbers are n, n + 1, n + 2

ATQ,

n + n + 1 + n + 2 = 27

Or, 3n + 3 = 27

Or, 3n = 24

Or, n = 8

So, the numbers are - 8,9,10

Now, the last 3 consecutive numbers are 11,12,13

Sum of them 11 + 12 + 13 = 36

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21 . Sum of 4 consecutive even number is greater than three consecutive odd numbers by 81.If the sum of the least odd and even numbers is 59 then find the sum of largest odd and even numbers

A. 69
B. 53
C. 65
D. 72

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Answer: Option A

Explanation:

Let 4 consecutive even numbers be x, x + 2, X + 4 and x + 6 respectively.
3 consecutive odd numbers be y, y + 2 and y + 4
According to question,
[x + x + 2 + x + 4 + x + 6]−[y + y + 2 + y + 4] = 81
= > (4x + 12)−(3y + 6) = 81
4x−3y = 81−12 + 6
4x−3y = 75
x + 4 = 59
On solving equations (i) and (ii), we get
X = 36
y = 23
The sum of largest odd and even number = x + 6 + y + 4 = x + y + 10 = 36 + 23 + 10 = 69

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Two Combined Bank Recruitment Test Post: Officer - 28/09/2018

A. -4
B. -6
C. 4
D. 6
E. None

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Answer: Option A

Explanation:

Let two consecutive negetive even numbers -2n and - 2(n+1)

According to to the question we can write that,

(-2n)×{-2(n+1)}=24

Or, - 2n(-2n-2)=24

Or, 4n^2+4n=24

Or, 4(n^2+n)=24

Or, n^2+n=24/4

Or, n^2+n=6

Or, n^2+n-6=0

Or, n^2+3n-2n-6=0

Or, n(n+3)-2(n+3)=0

Or,(n+3)=0 or, (n-2)=0

Or, n=-3 [which is not acceptable]

And n=2

Then, As the first negative even integer is -2n= -2×2= -4

And -2(n+1)=-6

Larger number is - 4 between them.

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23 . The product of two consecutive negative even integers is 24. What is the larger number?

A. -4
B. -6
C. 4
D. 6

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Answer: Option A

Explanation:

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24 . The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 18
B. 10
C. 15
D. 14
E. None of these

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Answer: Option A

Explanation:

Let the integers be x, x + 2 and x + 4

Now, 3 ( x + 4) - 40 = x

2x = 40 - 12 = 28

x = 14

x + 4 = 14 + 4 = 18

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25 . The smallest of three consecutive even integers is 40 less then three times the largest . What is the largest of three integers ?

A. 18
B. 10
C. 15
D. 14
E. none

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Answer: Option A

Explanation:

The smallest of three consecutive even integers is 40 less then three times the largest . What is the largest of three integers ?

Let the integers be, N - 2, N and N + 2. respectively.

Now, (N - 2) = 3 x (N + 2) - 40

or, N - 2 = 3N + 6 - 40

or, 3N - N = 40 - 6 - 2

or, 2N = 32

or, N = 16

So, the largest even integer = N + 2 = 16 + 2 = 18

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Probationary Officer | 31.03.2017 ||

A. 16
B. 19
C. 22
D. 23

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Answer: Option D

Explanation:

ধরি,

সংখ্যা তিনটি যথাক্রমে

x - 1, x, x + 1

x - 1 + x + x + 1 <75

3x <75

x<75/3

x<25

যেহেতু x<25 এবং পূর্ণসংখ্যা সেহেতু x = 24

ছোট সংখ্যাটি = ( 24 - 1 ) = 23

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Assistant Director (General) 06.07.18

A. 19
B. 21
C. 23
D. 17

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Answer: Option A

Explanation:

x , x + 2 , x + 4

x + x + 2 + x + 4 = 57

3x = 51

x = 17

The middle number = x + 2 = 17 + 2 = 19.

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Bangladesh Bank - Assistant Director - 2010

A. 57
B. 72
C. 42
D. 50

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Answer: Option B

Explanation:

Let x represent the smallest number. Then the other number are

x + 2, x + 4, x + 6, x + 8 and x + 10. x + 10 is the largest.

The sum of these is 6x + (2 + 4 + 6 + 8 + 10) = 6x + 30

We are told that this is 38 greater than twice the largest, so

6x + 30 = 2(x + 10) + 38 = 2x + 58.

or, 4x = 28

∴x = 7

Then the sum is 6×7 + 30 = 72.

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29 . The sum of five consecutive integers is equal to 3 times the largest. What is the largest of the integers?

A. 8
B. 7
C. 6
D. 5

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Answer: Option D

Explanation:

Let the integers from smallest to largest be x - 2, x - 1, x, x + 1 & x + 2 respectively.

Then, x - 2 + x - 1 + x + x + 1 + x + 2 = 3(x + 2)

or, 5x = 3x + 6

or, 5x - 2x = 6

or, 2x = 6

or, x = 3

So, the largest intger is 3 + 2 = 5.

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30 . The sum of four consecutive even integers is 60. What is the value of the largest number?

A. 14
B. 24
C. 22
D. 20

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Answer: Option C

Explanation:

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সমন্বিত ৭ ব্যাংক || সিনিয়র অফিসার-05-11-2021 ||

16 . If the sum of three consecutive integers is odd, then the first and the last integers must be -

17 . If X is the difference if the squaresof two consecutive even numbers, which of the following numbers is a divisor of X?

18 . In a class composed of x girls and y boys what part of the class is composed of girls ?

19 . In a sequence of 8 consecutive integers, how much greater is the sum of the last four integers than the sum of the first four integers ?

20 . Six consecutive whole numbers are given. The sum of the first three numbers is 27. What is the sum of the last three numbers?

21 . Sum of 4 consecutive even number is greater than three consecutive odd numbers by 81.If the sum of the least odd and even numbers is 59 then find the sum of largest odd and even numbers

22 . The preduct of two consecutive negative ever integers is 24. What is the larger number ?

23 . The product of two consecutive negative even integers is 24. What is the larger number?

24 . The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

25 . The smallest of three consecutive even integers is 40 less then three times the largest . What is the largest of three integers ?

26 . The sum of 3 consecutive integers is less than 75. what is the greatest possible value of the smallest one?

27 . The sum of 3 consecutive odd numbers is 57. The middle one is

28 . The sum of 6 consecutive odd numbers exceeds twice the largest by 38. Find the sum of the six numbers?

29 . The sum of five consecutive integers is equal to 3 times the largest. What is the largest of the integers?

30 . The sum of four consecutive even integers is 60. What is the value of the largest number?

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