a number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. when it is successively divided by 5 and 4, then the respective remainders will be;
a 1,2
b 2,3
c 3,2
d 4,1
e. data not sufficient
successive division
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IMO, E.
It's a bit tricky to understand "divided successively". IMO, it means that, number x is divided by 4 first, quotient is n, remainder is 1. Then n is divided by 5, quotient is m, remainder is 4. (m and n are positive ingeters.)
If my understanding is correct, number x
= (5m+4)4n+1
= 20mn+16n+1
= (20mn+15n+5)+(n-4)
When above number is divided by 5, remainder is n-4. Since we don't know value of n, data is not sufficient.
Another way is to use real numbers for (5m+4)4n+1.
When m=1, n=1, x=37, divided by 5, quotient is 7, remainder is 2; 7 divided by 4, remainder is 3.
When m=2, n=2, x=113, divided by 5, quotient 22, remainder 3; 22 divided by 4, remainder 2.
So data not sufficient.
It's a bit tricky to understand "divided successively". IMO, it means that, number x is divided by 4 first, quotient is n, remainder is 1. Then n is divided by 5, quotient is m, remainder is 4. (m and n are positive ingeters.)
If my understanding is correct, number x
= (5m+4)4n+1
= 20mn+16n+1
= (20mn+15n+5)+(n-4)
When above number is divided by 5, remainder is n-4. Since we don't know value of n, data is not sufficient.
Another way is to use real numbers for (5m+4)4n+1.
When m=1, n=1, x=37, divided by 5, quotient is 7, remainder is 2; 7 divided by 4, remainder is 3.
When m=2, n=2, x=113, divided by 5, quotient 22, remainder 3; 22 divided by 4, remainder 2.
So data not sufficient.
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The answer is B
Take a Look:
d1=4 and d2 =5
r1 =1 and r2 =4
so the number is d1*r2+r1 where d1 and d2 are the divisors arranged in increasing order
so number = 4*4 +1 = 17
now question says, this number, 17 divided by 5 remainder =2
and then further divided by 4,so we here divide the quotient left from previous division ie.3
so 3 divided by 4,remainder = 3
answer B
Hope this helps
Take a Look:
d1=4 and d2 =5
r1 =1 and r2 =4
so the number is d1*r2+r1 where d1 and d2 are the divisors arranged in increasing order
so number = 4*4 +1 = 17
now question says, this number, 17 divided by 5 remainder =2
and then further divided by 4,so we here divide the quotient left from previous division ie.3
so 3 divided by 4,remainder = 3
answer B
Hope this helps
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Thanks Karan GMAT740: here is another way to klook at it:
4|x
-----------
5| y -1
-----------
|1 - 4
-----------
SO Y = 5*1 + 4 = 9
X = 4y + 1 = 37
So the number was 37, if we go for reverse division:
5 divides 37 to give quotient of 7 remainder 2
4 divides 7 to give quotient 1 and remainder 3
So 2,3 will be ans
4|x
-----------
5| y -1
-----------
|1 - 4
-----------
SO Y = 5*1 + 4 = 9
X = 4y + 1 = 37
So the number was 37, if we go for reverse division:
5 divides 37 to give quotient of 7 remainder 2
4 divides 7 to give quotient 1 and remainder 3
So 2,3 will be ans