Question

When a number is divided by 13, the remainder is 11.

When the same number is divided by 17, the remainder is 9..

What is the number??

Options:
a)339 b) 349
c) 369 d) Data Inadequate

I only need the solution to this problem..
Thanks if anyone can help me with this..

Answer 1

if no. =x
then x = 13n + 11
and x = 17m + 9
3 variables ->2 eqn..
i'd say d)

Answer 2

17m - 13n = 2
is there any way for integral solutions ?
or just hit and trial ? :|
maybe the ans is not d)

Answer 3

There is an answer of this question...
Answer is not d)..

Answer 4

the answer is b because i tried it!

Answer 5

349

Answer 6

I need the solution @eliassaab ..

Answer 7

Can you please explain??

Answer 8

Do not try from the options..
Suppose you don't know the answers,
then tell me how to get to the answer by solving it logically..

Answer 9

349=26(13)+11
349 =20(17)+9

Answer 10

What if I did not the give the choices???
Suppose there is no choice, then is their a method to get the answer by proper solution??

Answer 11

141, 349, 557, 765, 973, etc. i just played around and try things :s

Answer 12

answer is 221m-93
m is 1,2,3,...

Answer 13

let x=13k+11=17y+9

Answer 14

From here:

k = (17y - 2)13..

Answer 15

very well

Answer 16

Find the value of y for which there will be no remainder...

Answer 17

then k=y+(4y-2)/13

Answer 18

How you did this?

Answer 19

k=(13y+4y-2)/13

Answer 20

ok?

Answer 21

How 4y come??

Answer 22

17y=13y+4y

Answer 23

Here is a list of possible answers less than a million
{128, 349, 570, 791, 1012, 1233, 1454, 1675, 1896, 2117, 2338, 2559, \
2780, 3001, 3222, 3443, 3664, 3885, 4106, 4327, 4548, 4769, 4990, \
5211, 5432, 5653, 5874, 6095, 6316, 6537, 6758, 6979, 7200, 7421, \
7642, 7863, 8084, 8305, 8526, 8747, 8968, 9189, 9410, 9631, 9852, \
10073, 10294, 10515, 10736, 10957, 11178, 11399, 11620, 11841, 12062, \
12283, 12504, 12725, 12946, 13167, 13388, 13609, 13830, 14051, 14272, \
14493, 14714, 14935, 15156, 15377, 15598, 15819, 16040, 16261, 16482, \
16703, 16924, 17145, 17366, 17587, 17808, 18029, 18250, 18471, 18692, \
18913, 19134, 19355, 19576, 19797, 20018, 20239, 20460, 20681, 20902, \
21123, 21344, 21565, 21786, 22007, 22228, 22449, 22670, 22891, 23112, \
23333, 23554, 23775, 23996, 24217, 24438, 24659, 24880, 25101, 25322, \
25543, 25764, 25985, 26206, 26427, 26648, 26869, 27090, 27311, 27532, \
27753, 27974, 28195, 28416, 28637, 28858, 29079, 29300, 29521, 29742, \
29963, 30184, 30405, 30626, 30847, 31068, 31289, 31510, 31731, 31952, \
32173, 32394, 32615, 32836, 33057, 33278, 33499, 33720, 33941, 34162, \
34383, 34604, 34825, 35046, 35267, 35488, 35709, 35930, 36151, 36372, \
36593, 36814, 37035, 37256, 37477, 37698, 37919, 38140, 38361, 38582, \
38803, 39024, 39245, 39466, 39687, 39908, 40129, 40350, 40571, 40792, \
41013, 41234, 41455, 41676, 41897, 42118, 42339, 42560, 42781, 43002, \
43223, 43444, 43665, 43886, 44107, 44328, 44549, 44770, 44991, 45212, \
45433, 45654, 45875, 46096, 46317, 46538, 46759, 46980, 47201, 47422, \
47643, 47864, 48085, 48306, 48527, 48748, 48969, 49190, 49411, 49632, \
49853, 50074, 50295, 50516, 50737, 50958, 51179, 51400, 51621, 51842, \
52063, 52284, 52505, 52726, 52947, 53168, 53389, 53610, 53831, 54052, \
54273, 54494, 54715, 54936, 55157, 55378, 55599, 55820, 56041, 56262, \
56483, 56704, 56925, 57146, 57367, 57588, 57809, 58030, 58251, 58472, \
58693, 58914, 59135, 59356, 59577, 59798, 60019, 60240, 60461, 60682, \
60903, 61124, 61345, 61566, 61787, 62008, 62229, 62450, 62671, 62892, \
63113, 63334, 63555, 63776, 63997, 64218, 64439, 64660, 64881, 65102, \
65323, 65544, 65765, 65986, 66207, 66428, 66649, 66870, 67091, 67312, \
67533, 67754, 67975, 68196, 68417, 68638, 68859, 69080, 69301, 69522, \
69743, 69964, 70185, 70406, 70627, 70848, 71069, 71290, 71511, 71732, \
71953, 72174, 72395, 72616, 72837, 73058, 73279, 73500, 73721, 73942, \
74163, 74384, 74605, 74826, 75047, 75268, 75489, 75710, 75931, 76152, \
76373, 76594, 76815, 77036, 77257, 77478, 77699, 77920, 78141, 78362, \
78583, 78804, 79025, 79246, 79467, 79688, 79909, 80130, 80351, 80572, \
80793, 81014, 81235, 81456, 81677, 81898, 82119, 82340, 82561, 82782, \
83003, 83224, 83445, 83666, 83887, 84108, 84329, 84550, 84771, 84992, \
85213, 85434, 85655, 85876, 86097, 86318, 86539, 86760, 86981, 87202, \
87423, 87644, 87865, 88086, 88307, 88528, 88749, 88970, 89191, 89412, \
89633, 89854, 90075, 90296, 90517, 90738, 90959, 91180, 91401, 91622, \
91843, 92064, 92285, 92506, 92727, 92948, 93169, 93390, 93611, 93832, \
94053, 94274, 94495, 94716, 94937, 95158, 95379, 95600, 95821, 96042, \
96263, 96484, 96705, 96926, 97147, 97368, 97589, 97810, 98031, 98252, \
98473, 98694, 98915, 99136, 99357, 99578, 99799}

Answer 24

@waterineyes is that right?

Answer 25

What people are trying to explain to you that 2 equations with three unknown might have an infinite number of solutions.

Answer 26

maybe i just got it..using @eliassaab work..
first no. following the series is 128
LCM(17,13) =221
thus every no is in the form of 221p + 128
p is any integer..
so you might arrive to ans thus..

Answer 27

Ya I got, further.??.

Answer 28

since all options are 300 something,,so you can easily judge that p=1//
following which you have the ans : 349

Answer 29

sorry i lost my connection

Answer 30

I am getting somewhat..
I have tried one more method...

Answer 31

well then
\[k=y+\frac{4y-2}{13} \\ k \ is \ an \ integer \ then \ \frac{4y-2}{13} \ \ must \ be \ an \ integer \\ then \ 4y-2=13t\]

Answer 32

ok?

Answer 33

x = 13p + 11

x = 17q + 9

Just equate:

13p + 11 = 17q + 9

p = (17q - 2)/13

Now at value of q we get p a whole number??

Let us try for q = 7

p = (119 - 2)/13 = 9
So, q = 7 and p = 9

So, the number is : 13p + 11 = 128
As this is not in the choice, so let us try once more..

Put q = 20,

p = (340 - 2)/13 = 26

So, q = 20 and p = 26

So other number will be: 13p + 11 = 338 + 11 = 349...

Answer 34

Thanks guys....
Thanks @mukushla thanks @eliassaab and thanks @shubhamsrg ..

Answer 35

So it all boils down to finding the first number that satisfies the conditions (be it by trial and error) and just keeping on adding the least common multiple to that until the answer is one which is in the choices, right?

Answer 36

\[4y-2=13t \ \ \ \ then \ \ 4y=13t+2 \ \ \ \\ y=3t+\frac{t+2}{4} \ \ y \ is \ an \ integer \ \ \ so \ \ \ \ \ t+2=4m \\ that \ \ results\ \ in \\ t=4m-2 \\ y=13m-6 \\ and \ \ finally \\ x=17y+9=221m-93 \ \]
put m=2 then x=349

Answer 37

@waterineyes your welcome

Answer 38

Go thru the Options.... if not any of three means opntion d is correct

Answer 39

Thanks one again @mukushla

Answer 40

Actually this I am seeing today..