ISI 2014

Question

Number of integers $x$ between $1$ and $95$ such that $96$ divides $60x$ is

• A. $0$
• B. $7$
• C. $8$
• D. $11$

Comments

//program for : finding counter value
//for getting multiples
#include<bits/stdc++.h>
using namespace std;
int main(void){
	//counter for final value
	int counter=0;
	for(int i=1;i<96;i++){
		int value=60*i;
		if(value%96==0){
			++counter;
			cout<<i<<endl;
		}
	}
	cout<<counter;
system("pause");
return 0;
}

OUTPUT :

$8 \ 16
\  24
\  32
\  40
\  48
\  56
\  64
\  72
\  80
\  88$

Answer : $11$

Answer 1

$\frac{60x}{96} = \frac{5x}{8}$

Now $5x$ is divisible by $8$ only when $x$ is multiple of $8,$ like $5\cdot(8\cdot1), 5\cdot(8\cdot2), 5\cdot(8\cdot3),$ and so on$...$

Here $x$ can be $8\cdot1 = 8, 8\cdot2 = 16, 8\cdot3 = 24 .......... 8\cdot10 = 80, 8\cdot11 = 88$

Thus$ \#$ of $x E (1,95) = 11$

OPTION (D)