Number System - Questions & Discussions

MBA CAT 2022
562

How many distinct factors of 3^2*8^2*2^4 are perfect cubes?
a)5 , b)4, c)8 ,d)6

563

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564
How many distinct factors of 3^2*8^2*2^4 are perfect cubes?
a)5 , b)4, c)8 ,d)6

is 4 the answer?
565

566
How many distinct factors of 3^2*8^2*2^4 are perfect cubes?
a)5 , b)4, c)8 ,d)6



I am also getting 4.......

As the value can be written as .........3^2*8^3*2.........

Now in it there is only one perfect cube which is 8 hence no of factors which are perfect cube = 3 +1 = 4
567

Given that 1025/1024=1.0009765625, find the sum of the digits of 510?

(a) 36 (b) 40 (c) 50 (d) 102 (e) 41


I don't have the answer......
568

Hi Puys,

Plzz help me in solving this problem:

If b > 1 and x = ab, then which one of the following is necessarily
true?
a)a xb 0 c)a xb = 0

Thanks,
Mohit.

569
How many distinct factors of 3^2*8^2*2^4 are perfect cubes?
a)5 , b)4, c)8 ,d)6

Answer is 4.
570
Hi Puys,

Plzz help me in solving this problem:

If b > 1 and x = ab, then which one of the following is necessarily
true?
a)a xb 0 c)a xb = 0

Thanks,
Mohit.

Is the answer option c)a xb
571
How many distinct factors of 3^2*8^2*2^4 are perfect cubes?
a)5 , b)4, c)8 ,d)6


wats the oa??
my take is 5..
572

How to solve the question
If 5x+2y+z =81 where x,y,z are distinct positive integers ,then find the difference b/w the maximum and minimum possible value of x+y+z.

I dont know if it was posted here but i could nt find an answer . The issue for me here is that i am not sure of the approach taken to solve such questions. If some one can put some light into it it will be great!!

Thanks in advance

573

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574
max value -> when x and y is min and z is max 1+1+74 =76
min value -> when x=y=z ->10+10+11 =31 -> 45...

u can't take same values as x,y,z are distinct positive integers............

Minimum possible value will be when we'll maximize the value of x.maximum possible of x is 15,y=1,z=4..

so 15+1+4=20

Maximum possible value of x + y + z will be when the value of
z is maximized. Maximum possible value of z will be when y
= 2 and x = 1, i.e. z = 72.
Required difference is 75 - 20 = 55
575
How many distinct factors of 3^2*8^2*2^4 are perfect cubes?
a)5 , b)4, c)8 ,d)6


2^0 2^3 (2^3)^2 (2^3)^3 are the cube factors of the given number....
576
what is the remainder when 11^11^11 is divided by 9?


a)5 ,b)4 , c)3 ,d)2 ,e)none of these? i m getting ans as 2 but it is given as 5 how ?


E(9)= 6 and 11^11 = 6k-5 => 11^11^11 =2^5%9 =5
577
How to solve the question
If 5x+2y+z =81 where x,y,z are distinct positive integers ,then find the difference b/w the maximum and minimum possible value of x+y+z.

I dont know if it was posted here but i could nt find an answer . The issue for me here is that i am not sure of the approach taken to solve such questions. If some one can put some light into it it will be great!!

Thanks in advance

for max value, take 'x' as small as possible
x = 1,y=2, z = 72
max value = 75
for min value, take 'x' as large as possible
x = 15, y = 1, z = 4
min value = 20
difference = 55
hope it's correct.
578
How many distinct factors of 3^2*8^2*2^4 are perfect cubes?
a)5 , b)4, c)8 ,d)6

even I am getting answer as 4 only. But OA is given as 5. So bit confused.
@ madnikhil - can you explain how you got the answer as 5??

Explanation:
If a no a^p*b^q*c^r is a perfect cube then powers are multiple of 3. ie p,q,r are multiples of 3.
So here we can represent the above expression as 3^2*2^10 from which we can get the follow 4 factors that can be perfect cubes = 2^0,2^3,2^6 and 2^9 ...i cant find a 5th one though 😞
579
Hi Puys,

Plzz help me in solving this problem:

If b > 1 and x = ab, then which one of the following is necessarily
true?
a)a xb 0 c)a xb = 0

Thanks,
Mohit.


Is the ans: a)a xb
580
onlinecat Says
Is the ans: a)a xb

a-xb can be zero only for b =1 but b>1 so a-xb
581
How to solve the question
If 5x+2y+z =81 where x,y,z are distinct positive integers ,then find the difference b/w the maximum and minimum possible value of x+y+z.

I dont know if it was posted here but i could nt find an answer . The issue for me here is that i am not sure of the approach taken to solve such questions. If some one can put some light into it it will be great!!

Thanks in advance


Hi

For maximum value of x+y+z, we should try to maximize z and minimize z as in the given expr "5x+2y+z" the coefficient of z is the lowest and x is highest. for our case x = 1, y=2, z= 72 so x+y+z = 75.
Similarly for minimum value, we maximize x. Best value can be x = 15, y = 1, z = 4. so x+y+z = 20.'

Hence the difference is 75 - 20 = 55.