Unit-2:Pure Arithematic
(a) Factors and multiples, divisibility, H.C.F. and L.C.M.
(b) Fractions and decimals
Q1.
H.C.F of 585 and 819 is 117, find the L.C.M.
Solution.
Product of two numbers = L.C.M and H.C.F
Let L.C.M is a
585 x 819 = 117 x (a)
a = 4095
Solution
Q2.
If x is HCF of two numbers a and b . y is LCM of these two numbers then y/x gives remainder.
(a)0 (b)1 (c)2 (d)3
Solution.
HCF of two numbers always divides their LCM exactly (then remainder will be zero).
Solution
Q3.
If two numbers a and b are co-prime , then product of these two numbers will be
(a)their LCM (b)their HCF (c)2 (d)none of these
Solution.
The product of a and b will be their L.C.M.
If given numbers are co-prime then their HCF will be 1.(product of two numbers = LCM x HCF)
Solution
Q4.
If a/b is the lowest term of a fraction then HCF of a and b is
(a)0 (b)1 (c)2 (d)3
Solution.
If a fraction is in lowest term, HCF of its numerator and denominator will be equal to 1.
Solution
Q5.
Which fraction is improper.
(a)12/7 (b)7/12 (c)3/5 (d)3/4
Solution.
Improper fraction is 12/7.
In improper fractions numerators are greater than or equal to denominator.
Solution
Q6.
Which fraction is largest.
(a)4/5 (b)6/15 (c)7/20 (d)6/14
Solution.
4/5
Solution
Q7.
Which number is divisible by 16.
(a)548962 (b)435698 (c)356214 (d)734064
Solution.
Ans.734064
The number whose last 4-digit number is divisible by 16, whole number will also divisible by 16.
Solution
Q8.
Which number is divisible by 9.
(a)78925 (b)56912 (c)56124 (d)68912
Solution.
Ans.56124
If the sum of all digits of a number is divisible 9,the number is divisible by 9.
Solution
Q9.
The expression 34n - 52n has a factor
(a)60 (b)56 (c)18 (d)10
Solution.
Ans.56
As we known that xn - an is exactly divisible by x-a (when x is odd or even)
Solution
Q10.
The expresion 26n - 32n has a factor
(a)11 (b)9 (c)7 (d)6
Solution.
(23)2n - (3)2n = 82n - 32n
2n is an even integer {xn - an is
exactly divisible by x+a when n is even.}
Solution
