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

Question

A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?

A. 0
B. 1
C. 2
D. 3
E. 4

ccooley · Accepted Answer

"A number when divided by 18 leaves a remainder 7." That means the number is 7 greater than a multiple of 18. So, it's equal to 18(0) + 7, 18(1) + 7, 18(2) + 7, 18(3) + 7, etc.

What's the remainder when you start dividing those values by 12?

18(0) + 7 = 7, so the remainder is 7. 
18(1) + 7 = 25, so the remainder is 1. 
18(2) + 7 = 43, so the remainder is 7.
18(3) + 7 = 54 + 7 = 61, so the remainder is 1.

In fact, the pattern keeps repeating back and forth between 7 and 1. Mathematically, that happens because each number we check is 18 greater than the one before it. So, if the remainder is originally 1, then the remainder will now be 18 greater, or 19. However, you can't actually have a remainder greater than 12 when you divide by 12, so we need to subtract 12: 19-12 = 7. The same happens when you go from a remainder of 7 to a remainder of 1.

The answer is (C) 2.

nick1816 · Answer

LCM(12, 18)=36

Given- N= 7 MOD 18
Hence, N= 7 MOD 36 or N= 25 MOD 36

i) When N=7 MOD 36, then N=7 MOD 12
ii) When N=25 MOD 36, then N=1 MOD 12

n can take 2 values (1 or 7).

gracie · Answer

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

pratik2018 · Answer

Great Explanation. Thanks a lot.

Fdambro294 · Answer

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:

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.

MathRevolution · Answer

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

VirenderSingh092 · Answer

There are 2 possible values on n.

Yosemite98 · Answer

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

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

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