remainder again

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Mon Apr 25, 2011 8:46 pm

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

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Source: Beat The GMAT — Problem Solving | Mon Apr 25, 2011 8:46 pm

manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Mon Apr 25, 2011 10:08 pm

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..!!!

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pankajks2010: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 12:51 amFollowed by: 1 member; Location: New Delhi, India; Thanked: 12 times

by pankajks2010 » Tue Apr 26, 2011 12:32 am

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

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Tue Apr 26, 2011 4:35 am

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

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Tue Apr 26, 2011 4:53 am

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..!!!

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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