NUMBERS

[pooja talwar]

Ques: N=2^35*3^15*5^16. Find the number of factors of N which are perfect cubes.

A) 324
B) 200
C) 288
D) 225


Ans is A) 324

Please give me solution.

[pooja talwar]

Ques: Let X be the set of integers {
8,14,20,26,32,.....350,356,362,368,374 } and Y be a subset of X such
that no two elements of Y have a sum of 382. Find the maximum number
of elements Y can have.

A) 29
B) 30
C) 31
D) 32

Ans is c) 31

[pooja talwar]

Ques: N is a natural number between 10 & 1000. P denotes the product
of its digits. If 6P+4S=4N, how many values can P take?

A) 9
B) 10
C) 11
D) 12

Ans is C) 11

[pooja talwar]

Ques: IF x=60^99-58^99/60^98+58^98, which of the following holds true?

A) 0<x<=0.5
B) 0.5<x<=1.0
C) 1<x<=2
D) x>2.0

Ans is D)


Please reply answer.

[Abhilash Chandra]

question 1----------

the series is  8,14,20,26.........188,194...374..

so uptill 188 if u take all the numbers no 2 will have sum =382 .here 188 is 31st no...so answer is 31 

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[Abhilash Chandra]

2)the series is  8,14,20,26.........188,194...374..

so uptill 188 if u take all the numbers no 2 will have sum =382 .here 188 is 31st no...so answer is 31 

On Tue, Feb 11, 2014 at 6:23 PM, pooja talwar <poojatalw...@gmail.com> wrote:

[Abhilash Chandra]

Ques: N is a natural number between 10 & 1000. P denotes the product
of its digits. If 6P+4S=4N, how many values can P take?

answer- 

for two digit nos . let N=10a+b, P=ab, S=a+b

so 6ab+4a+4b=40a+4b=>b =6,

so u can try with 16,26,36,46,56.....96 all of them satisfy . so possible Ps are {6,12,18,24,30.........54}   9 values.

with 3 digit nos u cant get a result..

[Abhilash Chandra]

Ques: N=2^35*3^15*5^16. Find the number of factors of N which are perfect cubes.

answer- 2^35 contains { 2^3 ,2^6 ...............2^33} = 11 perfect cubes

3^15 contains { 3^3,3^6...........3^15} =5 perfect cubes 

5^16 contains { 5^3, 5^6,.....5^15} = 5 perfect cubes 

If u take all perfect cubes u get =11*5*5=275 

also take individual perfect cubes =11+5+5=21

----------------------------------------------------------------------------

                                                             296 so only 1 option remains . other factors are {3^i}*{5^i}=5*5=25. 

[manika kapoor]

I got ans as 288

[Abhilash Chandra]

how?

[Deepesh Arora]

first question 2^35*3^15*5^16=((2^11)(3^5)(5^5))^3(2^2*5)so no. of factors =(11+1)*(5+1)*(5+1)=432

 

why this sol is wrong ?

--
With  Regards
Deepesh Arora

[abhishek chakrobrotty]

isme S kya hai ??

[kajal bindal]

if P is product thn S must be sum...

--
kajal

[pooja talwar]

S denotes the sum of its digits.

[pooja talwar]

Ques: What is the remainder when 347^347 is divided by 100 ?

A) 23
B) 43
C) 63
D) 83

Ans is: C) 63

[pooja talwar]

Ques: The number of digits in the cube root of a 29 digit number is

A) 10
B) 9
C) 8
D) Cannot say


Ans is A)

[pooja talwar]

Actually question is having a mistake. It's 2^25 not 2^35.
correct question is : N=2^25*3^15*5^16, find number of factors of N
which are perfect cubes.

[pooja talwar]

Please tell how many values can N take? N can take 11 values but how i
don't know the explanation for it.

On 2/11/14, Abhilash Chandra <abhi1...@gmail.com> wrote:
> Ques: N is a natural number between 10 & 1000. P denotes the product
> of its digits. If 6P+4S=4N, how many values can P take?
>
> answer-
> for two digit nos . let N=10a+b, P=ab, S=a+b
> so 6ab+4a+4b=40a+4b=>b =6,
>

> *so u can try with 16,26,36,46,56.....96 all of them satisfy . so possible
> Ps are {6,12,18,24,30.........54} 9 values.*

>
>
> with 3 digit nos u cant get a result..
>
>
> On Tue, Feb 11, 2014 at 6:27 PM, Abhilash Chandra
> <abhi1...@gmail.com>wrote:
>

>> 2)the series is 8,14,20,26.........*188,194...*374..