A number when divided by 18 leaves a remainder 7. The same number when

let x=dividend
successive values of x=7,25,43,61,79,97...
successive values of n=7,1,7,1,7,1...
2
C

Great Explanation. Thanks a lot.

when an Integer (let's call it X) is Divided by 18 -----> yields a Remainder = 7

X = 7 + (Multiple of 18)

or

X = 18a + 7 ----- where a = NON-Negative Integer Quotient


This Same Number when Divided by 12 ----> yields a Remainder = n

Since the Answer Choices are not that large, you can easily test some values and see if a Pattern emerges:


X = 7 ------ 7/12 ----- Rem = 7

X = 25 ------- 25/12 ------ Rem = 1

X = 43 -------- 43/12 ------- Rem = 7

X = 61 -------- 61/12 ------ Rem = 1


Answer - n can take 2 Values: Rem of 1 or Rem of 7

-C-


or you can take the Euclidean Remainder Equation above and try Dividing the Unique Integer X by 12


X = 18a + 7

(X/12) = (18a + 7)/(12)

Remainder of: (18a + 7) / (12) =

(18a / 12)Rem of + (7 / 12) Rem of =

(18/12) Rem of * (a/12) Rem of + (7 / 12) Rem of =

6 * (a/12)Rem of + 7 =


----where a = Integer quotient------

---The Unique Remainders that (a/12)Remainder of ---> can yield are: [0 ; 1 ; 2 ; 3 ; .......11]


Remove Excess Remainders that EXCEED the Divisor of 12 by continually Dividing by 12:


6 * 1 + 7 = 13 ----- (13/12) = Rem of 1

6 * 2 + 7 = 19 ------ (19/12) = Rem of 7

6 * 3 + 7 = 25 ------- (25/12) = Rem of 1

6 * 4 + 7 = 31 ------ (31/12) = Rem of 7

6 * 5 + 7 = 37 ------ (37/12) = Rem of 1


.....at this point you should be confident that the Pattern will Repeat. However, you could continue through all the Unique Remainders that the Term ---- (a/12)Remainder of ----- can yield.

A number, when divided by 18, leaves a remainder of 7

Let the number be 7. When divided by 18 will give the remainder as 7.Other possible numbers are:

7, 7+18 = 25, 25 + 18 = 43, 43+18 = 61 and so on.

The same number, when divided by 12, leaves a remainder n.

=> 7 divided by 12 gives remainder as 7
=> 25 divided by 12 gives remainder as 1
=> 43 divided by 12 gives remainder as 7
=> 61 divided by 12 gives remainder as 1

So, there are two values for 'n' which are '7' and '1'.

Answer C

There are 2 possible values on n.

Here is an easy albegra aproach:

We have these two equations:
x = 18 K1 +7
x = 12 K2 +n

Lets equal them and see what n can be:

18 K1 + 7 = 12 K2 + n
n= 18 K1 - 12 K2 + 7 = 6 (3 K1 - 2 K2) + 7

We know that n < 12, so (3 K1 - 2 K2) can only be 0 or -1 so that n will be 7 or 1. For any other value of the parenthesis, n > 12 that is not possible.

IMO C