between 1 and 50 ,how many numbers are there which will leave a reminder 1 when divided by 4?

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Solution

$A d d i n g 1 t o t h e m u l t i p l e s o f 4 l e a v e r e m a i n d e r 1 o n d i v i d i n g b y 4 . S o, T h e r e q u i r e d n u m b e r s a r e : 4 + 1, 8 + 1, 12 + 1, 16 + 1, 20 + 1, 24 + 1, 28 + 1, 32 + 1, 36 + 1, 40 + 1, 44 + 1, 48 + 1 = 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49$
So, there are 12 such numbers.

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between 1 and 50 ,how many numbers are there which will leave a reminder 1 when divided by 4?

Adding 1 to the multiples of 4 leave remainder 1 on dividing by 4.So, The required numbers are:4+1,8+1,12+1,16+1,20+1,24+1,28+1,32+1,36+1,40+1,44+1,48+1=5,9,13,17,21,25,29,33,37,41,45,49 So, there are 12 such numbers.