2311 . If x is an integer, then which of the following statements about $x^{2} - x - 1$ is true?

A. It is always odd.
B. It is always even.
C. It is always positive.
D. It is even when x is even and odd when x is odd.

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Answer: Option A

Explanation:

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Janata Bank PLC || Officer (Rural Credit) (27-10-2023) || 2023

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2312 . If x is an integer and y = 7x + 5, which o fthe following CANNOT be a divisor of y?

A. 10
B. 11
C. 12
D. 14

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Answer: Option D

Explanation:

এখানে, y = 7x + 5 যেখানে x একটি পূর্ণসংখ্যা এখন,

x =1 হলে y =12 যা 12 দ্বারা বিভাজ্য

x= 2 হলে y =19

x=3 হলে y=26

x=4 হলে y=33 যা 11 দ্বারা বিভাজ্য

x=5 হলে y=40 যা 10 দ্বারা বিভাজ্য

যেহেতু ১৪ দ্বারা কোন সংখ্যাই বিভাজ্য নয়, সেহেতু 14 উত্তর হবে।

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First Security Islami Bank Ltd | Probationary Officer | 19-02-2021

A. -9
B. -8
C. -7
D. -6

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Answer: Option B

Explanation:

To find the least value of x for which y is less than 9, we can solve the inequality:

y < 9

Given that y = -2x - 8, we can substitute this expression into the inequality:

-2x - 8 < 9

Now, let's solve for x:

-2x - 8 < 9

First, add 8 to both sides of the inequality:

-2x - 8 + 8 < 9 + 8

-2x < 17

Next, divide both sides by -2. Remember that when dividing by a negative number, the inequality sign flips:

x > -17/2

Now, we want to find the least integer value of x that satisfies this inequality. Since x is an integer, we round up to the nearest integer:

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অফিসার (সাধারণ) ২৭.১২. ২০১৯

A. -9
B. -8
C. -7
D. -6

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Answer: Option B

Explanation:

To find the least value of x for which y is less than 9, we can solve the inequality:

y < 9

Given that y = -2x - 8, we can substitute this expression into the inequality:

-2x - 8 < 9

Now, let's solve for x:

-2x - 8 < 9

First, add 8 to both sides of the inequality:

-2x - 8 + 8 < 9 + 8

-2x < 17

Next, divide both sides by -2. Remember that when dividing by a negative number, the inequality sign flips:

x > -17/2

Now, we want to find the least integer value of x that satisfies this inequality. Since x is an integer, we round up to the nearest integer:

x > -17/2 rounded up to the nearest integer is -8

So, the least integer value of x for which y is less than 9 is -8. Therefore, the answer is -8.

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Sonali Bank Ltd. Senior Officer Recruitment 01.06.2018

A. 2x-1
B. (x-1)/2
C. 5x+1
D. x-2

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Answer: Option C

Explanation:

let, x is an odd integer i.e. x=1,3,5,…

now if x=1, 5x+1=5*+1=6 is an even integer

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2316 . If x is an odd integer and y an even integer which of the following statements is (are) alwayes true? 1. x+y is odd 2. xy is odd 3. 2x+y is even

A. 1 only
B. 2 and 3 only
C. 3 only
D. 1 and 3 only

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Answer: Option D

Explanation:

We know,

odd+even=odd [i is correct]

odd×even=even [ii is incorrect]

2×(odd)+even=even [iii is correct]

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2317 . If X is an odd integer and Y is an even integer, which of the following statements is(are) always true? I. X + Y is odd II. XY is odd III. X + 2Y is even

A. I only
B. II and III only
C. I and III only
D. III only

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Answer: Option A

Explanation:

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2318 . If x is an odd integer and y is an even integer which of the statements is(are) always true? I. x + y is odd II. xy is odd III. 2x + y is even.

A. I only
B. II and III only
C. I and III only
D. III only

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Answer: Option C

Explanation:

1. Addition of odd and even integers yields odd intgers. Example: 4 + 3 = 7. So, statement 1 is true.

2. Multiplication of odd and even integers yields even integers. Example: 4x3 = 12. So, statement 2 is false.

3. 2x is even and y is also even. So, 2x + y is even. Therefore, statement 3 is true.

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2319 . If X is brother of son of Y's son, then how is X related to Y ?

A. Cousin
B. Grandson
C. Son
D. Brother

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Answer: Option B

Explanation:

son of Y's son is Y's Grandson

brother of grandson is also a grandson.

so, X is Y's grandson.

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Bangladesh Bank - Officer(Cash) - 2016

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. R is the same color as Y
B. W is a different color from any other country
C. X is the same color as Y
D. S is the same color as X

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Answer: Option B

Explanation:

R,S, X and Y each are adjacent to W, so W can not be the same color as X, as x is the same color as Z, So W can not be the same color as Z too. So W is different from any other country.

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Bangladesh Bank - Officer - 2015

A. y-4
B. (x+40)/xy
C. xy/(x+4)
D. (xy+4y)/x

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Answer: Option C

Explanation:

Hints:

x men কাজটি করে y দিনে

1 man কাজটি করে xy দিনে

x + 4 men কাজটি করে xy/ (x + 4) দিনে

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2323 . If $(x - y) = 10,$ and $x y = 75$ what is the value of x?

A. $15$
B. $5$
C. $10$
D. $20$
E. $25$

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Answer: Option A

Explanation:

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Bangladesh Bank - Officer(Cash) - 2011

2324 . If x-y=3 then what is the value of $x^{3} - y^{3} - 9 x y ?$

A. $12$
B. $18$
C. $20$
D. $27$

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Answer: Option D

Explanation:

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Probashi Kallyan Bank-Officer (Cash)-25-09-2021

A. x + y ≥ 3
B. x + y ≤ 7
C. x - y ≤ 3
D. x - y ≤ 10

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Answer: Option C

Explanation:

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2312 . If x is an integer and y = 7x + 5, which o fthe following CANNOT be a divisor of y?

2313 . If x is an integer and y=-2x-8 , what is the least value of x for which y is less than 9?

2314 . if x is an integer and y=-2x-8 what is the least value of x for which y is less than 9

2315 . If x is an odd integer, which of the following must be an even integer?

2316 . If x is an odd integer and y an even integer which of the following statements is (are) alwayes true? 1. x+y is odd 2. xy is odd 3. 2x+y is even

2317 . If X is an odd integer and Y is an even integer, which of the following statements is(are) always true? I. X + Y is odd II. XY is odd III. X + 2Y is even

2318 . If x is an odd integer and y is an even integer which of the statements is(are) always true? I. x + y is odd II. xy is odd III. 2x + y is even.

2319 . If X is brother of son of Y's son, then how is X related to Y ?

2320 . If X is the difference if the squaresof two consecutive even numbers, which of the following numbers is a divisor of X?

2321 . If X is the same color as Z, then it must be true that-

2322 . If x men can do a work in y days, how many days will it take (x+4) men to do the same work?

2325 . If x ≥ 10 and y ≤ 7, which of the following must be true?

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