Bissoy.com
Doctors Medicines MCQs Q&A

What is the greatest integer among the following by which the number 55 + 75 is divisible?

What is the greatest integer among the following by which the number 55 + 75 is divisible? Correct Answer 12

Concept:

Formula used:

  • an + bn = {a + b} × {an-1 - an-2b + an-1b2 – ⋯ – abn-2 + bn-1}


Calculation:

Using an + bn = {a + b} × {an-1 - an-2b + an-1b2 – ⋯ – abn-2 + bn-1}

55 + 75 = {5 + 7} × {54 – 53 × 7 + ⋯ +74}

= 12 × {54 – 53 × 7 + ⋯ +74}

Hence, 55 + 75 is divisible 12.

Related Questions

An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?
A, B, and C are divisible by 2. C, D, and E are divisible by 9. B and D are divisible by 3 Conclusion - I 6C is divisible by 54 Conclusion - II B and D are divisible by 6 Conclusion - III 4B + 2E is divisible by 4 Which of the above conclusions logically follows/follow from the given statements?
A particular BNF definition for a “word” is given by the following rules. ∷ = | | ∷ = |  ∷ = |  ∷ = a | b | c | ….. |y| z  ∷ = 0 |1|2| …… | 9 Which of the following lexical entries can be derived from < word > ? l. pick II. picks lll. c44
Let X is divisible by 2 and Y is divisible by 6 then which of the following statement is correct regarding (X + Y)? Statement 1: It is divisible by 2 Statement 2: It is divisible by 3 Statement 3: It is divisible by 4
Suppliers(Sid: integer, sname:string, city:string, street:string) Parts(pid:integer, pname:string, color:string) Catalog(sid:integer, pid:integer, cost:real) Consider the following relational query on the above database: SELECT S.sname FROM Suppliers S  WHERE S.sid NOT IN (SELECT C.sid FROM Catalog C WHERE C.pid NOT IN (SELECT P.pid FROM Parts P WHERE P.color < > ‘blue’)) Assume that relations corresponding to the above schema are not empty. Which of the following is the correct interpretation of the above query?
Consider the following relational schema. Students(rollno: integer, sname: string) Courses(courseno: integer, cname: string) Registration(rollno: integer, courseno: integer, percent: real) Which of the following queries are equivalent to this query in English? “Find the distinct names of all students who score more than 90% in the course numbered 107” (I) SELECT DISTINCT S.sname FROM Students as S, Registration as R WHERE R.rollno=S.rollno AND R.courseno=107 AND R.percent >90 (II) Πsname (σcourseno = 107∧percent>90 (Registration ⋈ Students)) (III) {T | ∃S ∈ Students, ∃R ∈ Registration (S.rollno = R.rollno ∧R. courseno = 107 ∧ R.percent > 90 ∧ T.sname = S. sname)} (IV) {〈SN〉 | ∃SR∃RP(〈SR, SN〉 ∈ Students ∧ 〈SR, 107, RP〉 ∈ Registration ∧ RP > 90)}
Which of the following statement is not correct about integers? I. There is no integer which can be said as the greatest. Any big integer you think of, there exists an integer greater than that. II. Zero (0) is neither positive nor negative
If (x)2 = [x]2 + 2x then which of the following is true. Where [x] represents greatest integer less than or equal to x. (x) represents integer just greater than or equal to x. I represents Integer.
The sum o three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. what is the product of the three integers?
When a certain positive integer P is divided by another positive integer, the remainder is $${r_{1}}$$ . When a second positive integer Q is divided by the same integer, the remainder is $${r_{2}}$$ and when (P + Q) is divided by the same divisor, the remainder is $${r_{3}}$$ . Then the divisor may be :