# Math-_Class_10th_-_Number_System_with_Solutions

Apr 30th, 2015
Studypool Tutor
Price: \$10 USD

Tutor description

Numbers are intellectual witnesses that belong only to mankind. 1. If the H C F of 657 and 963 is expressible in the form of 657x + 963x - 15 find x. (Ans:x=22)

Word Count: 623
Showing Page: 1/6
Math- Class 10th - Number System with SolutionsNUMBER SYSTEMSNumbers are intellectual witnesses that belong only to mankind. 1. If the H C F of 657 and 963 is expressible in the form of 657x + 963x - 15 find x. (Ans:x=22) Ans: Using Euclids Division Lemma a= bq+r , o r < b 963=6571+306 657=3062+45 306=456+36 45=361+9 36=94+0 HCF (657, 963) = 9 now 9 = 657x + 963 (-15) 657x=9+96315 =9+14445 657x=14454 x=14454/657 2. Express the GCD of 48 and 18 as a linear combination. (Ans: Not unique) A=bq+r, where o r < b 48=18x2+12 18=12x1+6 12=6x2+0 HCF (18,48) = 6 now 6= 18-12x1 6= 18-(48-18x2) 6= 18-48x1+18x2 6= 18x3-48x1 6= 18x3+48x(-1) i.e. 6= 18x +48y x =22 x=3 , y=-1 76= 183 +48(-1) =183 +48(-1) + 1848-1848 =18(3+48)+48(-1-18) =1851+48(-19) 6=18x+48y Hence, x and y are not unique. 3. Prove that one of every three consecutive integers is divisible by 3. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1, 3q + 2 So we have the following cases Case I when n = 3q In the this case, n is divisible by 3 but n + 1 and n + 2 are not divisible by 3 Case - II When n = 3q + 1 Sub n = 2 = 3q +1 +2 = 3(q +1) is divisible by 3. but n and n+1 are not divisible by 3 Case III When n = 3q +2 Sub n = 2 = 3q +1 +2 = 3(q +1) is divisible by 3. but n and n+1 are not divisible by 3 Hence one of n, n + 1 and n + 2 is divisible by 3 4. Find the lar

## Review from student

Studypool Student
" Awesome! Exactly what I wanted. "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1828 tutors are online

### Other Documents

04/30/2015
04/30/2015
04/30/2015

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors