Problem Solving

greatest number which will divide 215,167 and 135 so as to leave same remainder.

a>64
b>32
c>24
d>16


ans-d

bblast wrote:greatest number which will divide 215,167 and 135 so as to leave same remainder.

a>64
b>32
c>24
d>16


ans-d

in this question its best to work with options, as we don't have none as one of the answer options...!!!!

215/64 remainder=23; 167/64 remainder =39; therefore 1 is not an answer.
215/32 remainder=23; 167/32 remainder= 7; therefore 2 is not an answer.
215/24 remainder=23; 167/24 remainder= 23; 135/24 remainder=15; hence 3 is not an answer.
215/16 remainder=7; 167/16 remainder=7; 135/16 remainder =7; hence D is our answer..!!!

An interesting properties of numbers: Lets assume three numbers ax, ay & az such that a is the HCF of these three numbers.

Now, lets consider the differences between these numbers: ax-ay, ay-az & az-ax or a(x-y), a(y-z) & a(z-x)
Thus, we can conclude that the HCF of the differences is also a.

Now, lets go to the question: As here the remainder is common among the three numbers, lets assume it to be x. Now, our question can be reduced to just finding the HCF of (215-x), (167-x) & (135-x). Employing the difference method, explained above, we find the differences to be 48, 32 & 80.
The HCF of these three numbers is 16. Thus, the answer is D

try this folks :

What number leaves a remainder of 1,2 and 4 when divided by 6,7 and 9 respectively.


OA-121

sister link-https://www.beatthegmat.com/remainders-t73139.html

bblast wrote:try this folks :

What number leaves a remainder of 1,2 and 4 when divided by 6,7 and 9 respectively.


OA-121

sister link-https://www.beatthegmat.com/remainders-t73139.html

difference between divisor and quotient is 6-1=7-2=9-4=5;
lcm of 6,7 and 9 is 126; therefore smallest number which will leave remainder 1,2 and 4 when divided by 6,7 and 9 respectively is 126-5=121;
we can also generalize the expression for the numbers as 126k-5; where k is an integer..!!!