A number when divided by a certain divisor left...

[swerve]

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

A. 370
B. 365
C. 380
D. 456
E. 460

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

[ErikaPrepScholar]

We can express any division problem as:

Dividend = Divisor * Quotient + Remainder

We can use this to build equations based on what we know.

We have a number that we are dividing by other numbers - that's our dividend. We'll call it X. When we divide by some other number (our divisor) we're left with a remainder of 241. So we can write this as:

X = DQ+ 241

If we multiply both sides by 2, we get:

2X = 2DQ + 482

We know that when twice our dividend (2X, which we already have in our equation) is divided by the same divisor, we're left with a remainder of 112 (but a different quotient). So we can rewrite our equation as:

2X = 2DQ + 370 + 112

So here, 2X is our dividend, 112 is our remainder, and 2DQ + 370 equals our divisor times our quotient. We know that 2DQ + 370 must be divisible by our divisor, which means both 2DQ and 370 must be divisible by our divisor. So we can check to see which of our answer choices can be divided into 370. Only 370 can be divided into 370 without creating a remainder, so the correct answer is A.

[GMATGuruNY]

A number when divided by a certain divisor left remainder 241, . Find the divisor?

A. 370
B. 365
C. 380
D. 456
E. 460

A number when divided by a certain divisor left remainder 241.
In other words, the number x is a multiple of divisor d plus 241:
x = ad + 241.

When twice the number was divided by the same divisor, the remainder was 112.
In other words, twice number x is a multiple of divisor d plus 112:
2x = bd + 112.

Doubling the first equation, we get:
2x = 2ad + 482.

The blue expressions above are both equal to 2x and thus are equal:
bd + 112 = 2ad + 482
bd - 2ad = 370
d(b - 2a) = 370.

The resulting equation implies that d is a factor of 370.
Of the five answer choices, only A is a factor of 370.

The correct answer is A.

[Scott@TargetTestPrep]

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

A. 370
B. 365
C. 380
D. 456
E. 460

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