A number when divided by a certain divisor left remainder 24

Easy solution:

N= Dq1+241
2N = 2Dq1 + 482 - (1)

2N = Dq2 + 112 - (2)

As (1) = (2) = 2N

D*(q2-2q1) = 370

D * Some integer = 370

Checking all options only (A) syncs with it.

Rgds,
TGC !

N = Quotient * Divisor + reminder

As given N = QD + 241
2N = 2QD + 482

Now when 482 divided by one of the answer choice we should get a remainder of 112

Only option A gives us that....
sweet solution brother

VeritasPrepKarishma's posts on remainders taught me how to think about this pretty simply...
's
N/ (some divisor)+241 = a remainder of 0 right? It must be a multiple at this point and since N^2 leaves a remainder of > 241 (112) then when N is squared there must be another "grouping" of the number when divided by our mystery divisor so...241-112=129 which is = to the additional "grouping" and if 129 is the additional "grouping" then 241 + 129 must be = to the divisor which is 370!

- My terminology may be off, but if you've checked VeritasPrepKarishma's posts on divisibility you know what I mean...

(n-241)/a=1 ...... 1 => n-241=a
(2n-112)/a=1.....2 => 2n-112=a

replacing a.... > 2n-112=n-241
=>n=129
241+129=370....uff

Is this a sub-600 level question?

Yes... seems to be.

There is no much calculation in this question

algebraic one;

n=qx+241, where x is divisor
2n=2(qx+241)
2n=sx+112
2qx+482=sx+112
370=sx-2qx => x(s-2q)=370.

Only option A says that x=370, so s-2q=1. We know that quotients are always integers, as well as their products and difference

A

n=241(mod d)
2*n=482(mod d); also 2*n=112(mod d); therefore d = 482-112=370

i have a simple method to solve this problem.

in 1st case , remainder is 241 and in 2nd case remainder is 112. the question says twice the first number, so if we multiply the number in the 1st case, remainder should have been 2*241 = 482, but remainder is given as 112. Since divisor is same, we can get the answer by subtracting 112 from 482 i.e. 482-112 = 370

We can let the number = n and the divisor = d.

Since the remainder is 214 when n is divided by d, we can say:

n/d = q + 241/d

Multiplying both sides by d, we have:

n = qd + 241 [Eq. 1]

Also, since the remainder is 112 when twice n is divided by d, we can say:

2n/d = p + 112/d

Multiplying both sides by d, we have:

2n = pd + 112 [Eq. 2]

Multiplying Eq. 1 by 2, we have:

2n = 2qd + 482

Substituting 2n into Eq. 2 as 2qd + 482, we can say:

2qd + 482 = pd + 112

370 = pd - 2qd

d(p - 2q) = 370

Since (p - 2q) is an integer, d must be a factor of 370. The only number in the answer choices that is a factor of 370 is 370 itself. Thus, answer choice A is correct.

Answer: A

Given: A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was 112.
Asked: Find the divisor?

Let the number be X divisor be D.

X = Dk + 241; where k is an integer
2X = 2Dk + 482 = Dm + 112
2Dk + 482 = Dm + 112
(m-2k)D = 370 = 37*2*5

Since D>241 - > D=370

IMO A

number when divided by a divisor leaves remainder 24 when twice the original number is divided by same divisor it leaves reminder 11

I believe that question is discussed here: https://gmatclub.com/forum/a-number-whe ... 44257.html Hope it helps.