# Numbers and Algebra - Numbers and Algebra Section 1

>>>>>>>>>>Numbers and Algebra Section 1

• Option : D
• Explanation : Let HCF be h and LCM be l.
I.  Let, numbers be ah and bh. Then abh = and (a + b)h = m
=> (a — b)h = n
Using these ah and bh can be uniquely determined. Thus, I is true II.
II.  If HCF = LCM, then two numbers are equal and same as HCF or LCM. Thus, II is true.
III. LCM/HCF = prime i.e. l/h =P Then one of the numbers is equal to h and other is equal to E. Thus, III is true.

• Option : D
• Explanation : Number = (555+445)*(555-445)*2+30
= (555+445)*2*110+30
= 220000+30 = 220030

• Option : C
• Explanation : 2050 x 2071 x 2095
=(23x89+3)x(23x90+1)x(23x91+2)
=(23[89 x 90+ 89 + 90 x 3]+ 3)x(23 x 91+2)
=(23 *K+ 3)* (23 * 91 + 2) )
=(23 *[K* 91 + K*  2 + 91 * 3]+ 6)
= 23 * L + 6 (where K and L are constants).
Hence remainder is 6.

• Option : A
• Explanation : y3-4y = y(y2-4)
= y(y-2)(y+2)
4y(y3+8)
=4y(y+2)(y2-2y+4)
∴ HCF = y(y + 2).

• Option : A
• Explanation :

Total distance travelled by the ball before coming to rest
= 12 + 2 (6 + 3 + 1.5 +...to?)
= 12 + 2. ( 6/ (1-1/2))
= 12 + 2(12)
= 36m