pls help in understanding below ques.
1. find the number of divisors of 1080 excluding throughout divisors,which are perfect squares.
ans : 28
2. find the number of divisors of 544 which are greater than 3.
ans: 10
3. find the sum of divisors of 544 excluding 1 and 544.
ans : 589
4. find the sum of divisors of 544 which are perferct squares
ans : 21
.Which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54
sol : lcm of 12,14,21,33 and 54 is 8316.
7249+n = 8316x2 (doubt: why 2 is multiplied)
ans : 9383
2. The least perfect sq. number which is divisible by 3,4,6,8,10 and 11 is
3. find the greatest number of 4 digi number when divided by 10,11,15,22 leaves 3,4,8 and 15 as remainders resp.
sol : first find greatest 4 digits multiple of LCM of 10,11,15 and 22 then subtract 7 from it to give answer(doubt :why subtract 7)
4. what will be the least possible number of planks,if 3 pieces of timber 42 m, 49 m, and 63 m long have to be divided into planks of same length?
a)7 b)8 c)22
5. find the greatest number,which will divide 215,167 and 135 so as to leave the same remainder in each case.
a)64 b)32 c)24 d)16
pls help in understanding below ques.
1. find the number of divisors of 1080 excluding throughout divisors,which are perfect squares.
ans : 28
First break the no into prime factors and then multiply their powers by adding one
N = x^a*y^b*z^c where x,y,z are prime nos
Then no fo divisore = (a+1)(b+1)(c+1)
1080 = 2^3*3^3*5
So total no of divisors expected = 4*4*2 = 32 - 4(excluding perfect square 1,4,9,36) = 28
2. find the number of divisors of 544 which are greater than 3.
ans: 10
544 = 2^5*17
So total no of divisors expected = 6*2 - 2(1,2) = 10
3. find the sum of divisors of 544 excluding 1 and 544.
ans : 589
Divisors are = 1,2,4,8,16,17,32,34,68,136,272,544
Hence the exp sum will be = 589
4. find the sum of divisors of 544 which are perferct squares
ans : 21
1+4+16 = 21
.Which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54
sol : lcm of 12,14,21,33 and 54 is 8316.
7249+n = 8316x2 (doubt: why 2 is multiplied) because largest four digit is asked
case 1 when 7249+n = 8316
case 2 when 7249+n = 8316*2
case 3 when 7249+n = 83136*3(Not possible as n will no longer be four digit no)
ans : 9383
2. The least perfect sq. number which is divisible by 3,4,6,8,10 and 11 is
LCM = 1320 = 2^3*3*5*11
So least multiple to make it a perfect square = 2*3*5*11 = 330
Hence the no will be = 1320 * 330 = 435600
3. find the greatest number of 4 digit umber when divided by 10,11,15,22 leaves 3,4,8 and 15 as remainders resp.
sol : first find greatest 4 digits multiple of LCM of 10,11,15 and 22 then subtract 7 from it to give answer(doubt :why subtract 7)
10 -3 = 11-4 = 15-8 = 22 -15 = 7
To keep this remainder for all the nos u have to subtract 7.
4. what will be the least possible number of planks,if 3 pieces of timber 42 m, 49 m, and 63 m long have to be divided into planks of same length?
a)7 b)8 c)22
HCF = 7
so total nos = 42/7+49/7+63/7 = 22
5. find the greatest number,which will divide 215,167 and 135 so as to leave the same remainder in each case.
a)64 b)32 c)24 d)16
From answer we can easily guess its 16
Hope i am clear.... 😃
pls help in understanding below ques.
1. find the number of divisors of 1080 excluding throughout divisors,which are perfect squares.
ans : 28
2. find the number of divisors of 544 which are greater than 3.
ans: 10
3. find the sum of divisors of 544 excluding 1 and 544.
ans : 589
4. find the sum of divisors of 544 which are perferct squares
ans : 21
.Which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54
sol : lcm of 12,14,21,33 and 54 is 8316.
7249+n = 8316x2 (doubt: why 2 is multiplied)
ans : 9383
2. The least perfect sq. number which is divisible by 3,4,6,8,10 and 11 is
3. find the greatest number of 4 digi number when divided by 10,11,15,22 leaves 3,4,8 and 15 as remainders resp.
sol : first find greatest 4 digits multiple of LCM of 10,11,15 and 22 then subtract 7 from it to give answer(doubt :why subtract 7)
4. what will be the least possible number of planks,if 3 pieces of timber 42 m, 49 m, and 63 m long have to be divided into planks of same length?
a)7 b)8 c)22
5. find the greatest number,which will divide 215,167 and 135 so as to leave the same remainder in each case.
a)64 b)32 c)24 d)16
1)1080=2^3*3^3*5=4*4*2=32 factors
squares can be made of 1,2,3,2*3=4 factors
remaining factors=28
2)544=2*2*2*2*2*17=2^5*17
factors are 12
factors less than 3=2(1,2)
remaining=10
3)factors are 10 except 1 and 544
2,4,8,16,32,17,34,68,136,272
total of 589
4)divisors which are perfect squares are 1,4,16
sum is 21
PART II
1)as four digit number is asked.
2)3,4,6,8,10,11
LCM is 3*2*2*2*5*11=1320
to make square,multiply by 3*2*5*11=330
1320*330=435600
3)as,if we add 7,it would be divisible by all of them.
4)7 each as,LCM is 7.so,22 planks.
5)manually calculate with options=>16 with remainder 7.
[quote=shashank3012;
3)as,if we add 7,it would be divisible by all of them.
4)7 as,LCM is 7.
Hey they asked for least no of planks...so it should be 22.
Correct me if i am wrong.
Hey they asked for least no of planks...so it should be 22.
Correct me if i am wrong.
yeah,a mistake.i calculated the LCM and left it there
thanks.
find the sum of series :1/2+1/6+1/12+1/20+.........+1/156+1/182 what is sum if taken to infinite terms ??
Amit31 Saysfind the sum of series :1/2+1/6+1/12+1/20+.........+1/156+1/182 what is sum if taken to infinite terms ??
series is
1/n+1/(n+4)+1/(n+10)+...1/(n+180)
addition of 4 to first term,6 to second term...
2,6,12,20,30,42,56,72,90,110,132,156,182=>13 terms.
for 2 terms,it is 2/3
for 3 terms,it is 3/4
for 4 terms,it is 4/5
for 13 terms,it is 13/14
for n terms,it is n/(n+1)
Amit31 Saysfind the sum of series :1/2+1/6+1/12+1/20+.........+1/156+1/182 what is sum if taken to infinite terms ??
Dunno how you would calculate it for infinite terms.... 😞
1/2+1/6+1/12+1/20+.........+1/156+1/182
= 1/(1 x 2) + 1/(2 x 3) + 1/(3 x 4) +..............1/(13 x 14)
= 1/1 - 1/2 + 1/2 - 1/3 + ............1/13 - 1/14
= 1 - 1/14 = 13/14
Dunno how you would calculate it for infinite terms.... 😞
1/2+1/6+1/12+1/20+.........+1/156+1/182
= 1/(1 x 2) + 1/(2 x 3) + 1/(3 x 4) +..............1/(13 x 14)
= 1/1 - 1/2 + 1/2 - 1/3 + ............1/13 - 1/14
= 1 - 1/14 = 13/14
What u did is correct, in case of infinity the answer wld be 1, as each term wld be canceled with the succeeding term.
else as shashank found for n terms,it is n/(n+1)
now, Lt n->inf Sigma{n/n+1 }
Lt 1/n -> 0 Sigma{ 1/(1+1/n)} = 1
let bi is the number of birds and br be the number of branches
from the info in the question we can arrive at I and II
solve the two eqns to get br = 3
Can some one explain this answer clearly?? I got confused of this question.Pls. help me
1) Four Bells ring at the intervals of 6,8,12,&18 seconds.They started ringing together at 12'0 Clock.After how many seconds they will ring together again??
a) 72 b) 84 c) 60 d) 48
2)For the above problem, How many times they eill ring together durnig the next 12 mins.
a) 9 b) 10 c) 11 d) none
3)The Product of digits of two digit number is twice as large as the sum of its digits.If we subtract "27" from the number, we get a number consisting of same digits written in reverse order.Find the No.??
4)Find no. of Zero's in the Product 1 X 2^2 X 3^3 X 4^4 X 5^5...............100^100
1) Four Bells ring at the intervals of 6,8,12,&18 seconds.They started ringing together at 12'0 Clock.After how many seconds they will ring together again??
a) 72 b) 84 c) 60 d) 48
2)For the above problem, How many times they eill ring together durnig the next 12 mins.
a) 9 b) 10 c) 11 d) none
3)The Product of digits of two digit number is twice as large as the sum of its digits.If we subtract "27" from the number, we get a number consisting of same digits written in reverse order.Find the No.??
4)Find no. of Zero's in the Product 1 X 2^2 X 3^3 X 4^4 X 5^5...............100^100
1) Take Lcm(6,8,12,18 ) = 72
2)(12*60)/Lcm(6,8,12,18 ) = 720/72 = 10
3)ab = 2(a+b), 10a+b - 27 = 10b+a
9a-9b = 27, a-b = 3
easily we can see the number is 63
4)calculate number of 5's
5 + 15 + 50 + 35 + 45 + 55 + 65 + 150 + 85 + 95 + 700 = 1300
HI,
Pls answer these following qsns......
1) Three numbers are such that second is as much lesser than the third as the first is lesser than the second.If the product of two smaller numbers is 85 and product of two larger numbers is 115.Find the middle no
a) 9 b) 8 c) 10 d) 30
2) AB+XY=2XP where A!=0 all the letters signify different digits from 0 to 9 , then the value of "A" is
a) 6 b) 7 c)9 d)any number more than "6"
3) X-4 + Y-4 = 4 , then how many Integer values can (X,Y) have??
4) A Two digit number is thrice as large as the sum of its digits and square of that sum is equal to trebled of required number,then find the no.??
solve and explain....
Thanks,
HI,
Pls answer these following qsns......
1) Three numbers are such that second is as much lesser than the third as the first is lesser than the second.If the product of two smaller numbers is 85 and product of two larger numbers is 115.Find the middle no
a) 9 b) 8 c) 10 d) 30
2) AB+XY=2XP where A!=0 all the letters signify different digits from 0 to 9 , then the value of "A" is
a) 6 b) 7 c)9 d)any number more than "6"
3) X-4 + Y-4 = 4 , then how many Integer values can (X,Y) have??
4) A Two digit number is thrice as large as the sum of its digits and square of that sum is equal to trebled of required number,then find the no.??
solve and explain....
Thanks,
1)a,b,c
b-a = c-b {Implies they are in AP}
ab = 85, bc = 115
c/a = 115/85 = 23/17{ since they are prime, they can be equated to c & a}
17, b, 23
so,b = 20
2)Its not possible!
two digit numbers when added can't giv a number more than 200,{Max is 99 + 99 = 198}
If the question is AB +XY = 1XP then out of options A can take 9 since A + x = x, so A can be 9 or 0.
3)If we draw a graph, we get a right angle triangle with vertices (0,0),(0,4),(4,0)
Now the integer points which lies with in hte area of triangle are
(1,3)(3,1)
(2,2)
(0,4)(4,0)
4)(10a + b) = 3*(a+b) ..... i
(a+b)^2 = = 3*(10a+b) ... ii
solve we get a+b = 9
so number is 27
hello puy.........my doubt is
The numbers 2,4,6,8...98,100 are multiplied together. The number of zeros at the end of the product must be :
13
12
11
10
9
hello puy.........my doubt is
The numbers 2,4,6,8...98,100 are multiplied together. The number of zeros at the end of the product must be : 13
12
11
10
9
Calculate the no of 5 in that
10,20,30,40,60,70,80,90 - one 5's each
50,100 - two 5's each
So total = 8+4 =12 zeros
Calculate the no of 5 in that
10,20,30,40,60,70,80,90 - one 5's each
50,100 - two 5's each
So total = 10 zeros
from 10 to 90 total 8 zero
and for 50 & 100 total 4 zero
so ans =12
from 10 to 90 total 8 zero
and for 50 & 100 total 4 zero
so ans =12
but the ans given is 11
shona_ne Saysbut the ans given is 11
It is not given factorial to calculate number of 5's
Its just 2*4*6*8*10*.....*100
zeros are contributed by 10,20,30,...100
so will be having 11 zeros at the end
It is not given factorial to calculate number of 5's
Its just 2*4*6*8*10*.....*100
zeros are contributed by 10,20,30,...100
so will be having 11 zeros at the end
but menacebhai 50 and 100 both have 2 times 5