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The integer x is positive. What is the remainder when x is divided

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The integer x is positive. What is the remainder when the x is divided by 14?
(1) The remainder when 4x is divided by 28 is 12.
(2) The remainder when x is divided by 21 is 3.
Official Answer

1 Answer

St 1 gives 4x=28k+12 or x=7k+3. I.e x can be 3,10,17,24
St2 gives x=21j+3. So x can be 3,24, 45.
If x = 3, x÷14 r=3 and if x=24, x÷14 r=10. I.e both statement 1 n 2 even together can't give unique answer
answered Dec 27, 2015 by Guru (5,628 points)
Please solve my query.

If we solve above question as:

St1: 4x/28 or 2x/14 gives 12 as remainder. Now, if dividend decreases, remainder also decreases in same proportion. Eg: x= 20 => so (2 * 20)/14 gives 12 as remainder and 20/14 will give 6(12/2) as remainder. So as per this,statement 1 can find out what will be the remainder.

Please tell me the error in my approach.
commented Jan 30, 2016 by Partner (551 points)
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