Number problem

[raushan.ravi]

How many numbers lying between 950 and 1,050 leave a remainder of 6 when divided by 7,8 and 14?

(A) 2
(B) 3
(C) 4
(D) 15

what would be ab efficient way to solve it...

[RB_51273]

Correct if I am wrong

Take the LCM of 7,14,and 8.It is 56.Now the multiples of between 950 and 1050 are
952 and 1008.The number which will give the remainder 6 when divided by the 7,14,and 8 will be 958 and 1014.

IMO:A

Tks

Ram

[imanemekouar]

I dont get after you find the lcm 56. Can you please explain further.
tks

[RB_51273]

sorry,there some typo error my side I missed write 56.I am rewriting full again


Take the LCM of 7,14,and 8.It is 56.Now the multiples of 56 between 950 and 1050 are
952 and 1008.(only multiples of 56 will give remainder zero when it will be divided by the 7,14,and 8). The number which will give the remainder 6 when divided by the 7,14,and 8 will be 958 and 1014.(No will just 6 more than the multiples of 56)

IMO:A

Hope it will be clear now.

Tks

Ram

[RonPurewal]

the posters above have given "nice" solutions.

if you don't get the "nice" solution RIGHT AWAY, you should go in for the "dirty grind" solution.

namely: just MAKE LISTS.

let's divide 950 by 14. if we do, we get a remainder of 12.
this means that 952 is a multiple of 14.
this means that 958 is the first number in the list with the requisite remainder of 6 upon division by 14.
to find more such numbers (that give remainders of 6 upon division by 14), just keep adding 14:
958, 972, 986, 1000, 1014, 1028, 1042
that's the whole list.

now divide them by 8:
958 / 8 --> remainder is 6; keep it
972 / 8 --> remainder is not 6; throw it away
986 / 8 --> remainder is not 6; throw it away
1000 / 8 --> remainder is not 6; throw it away
1014 / 8 --> remainder is 6; keep it
1028 / 8 --> remainder is not 6; throw it away
1042 / 8 --> remainder is not 6; throw it away
all you've got left is 958 and 1014.

there are no answers smaller than two, so you're done. (a).

you can EASILY do this in the requisite amount of time, IF YOU GET STARTED ON IT RIGHT AWAY.
DO NOT STARE AT PROBLEMS.

the end.

--

also note that, if a number has remainder 6 when you divide by 14, then it also MUST have remainder 6 when you divide by 7. (this is so because all multiples of 14 are also multiples of 7.)