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Re: When the positive integer A is divided by 5 and 7, the [#permalink]
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mrinal2100
When the positive integer A is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of A-B?

(A) 12
(B) 24
(C) 35
(D) 16
(E) 30

The easiest way to approach these problems is by taking an example

1. The first choice is 18. Take it as B
2. The next choice is 53. Take it as A
3. A-B=35

c is the only choice that is correct.
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When the positive integer A is divided by 5 and 7, the [#permalink]
mrinal2100
When the positive integer A is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of A-B?

(A) 12
(B) 24
(C) 35
(D) 16
(E) 30

if A and B, when divided by the same divisors, leave the same remainders,
then the difference between them will always be a multiple of the product of those divisors
5*7=35
C

Originally posted by gracie on 05 Dec 2017, 17:38.
Last edited by gracie on 26 Jan 2018, 11:44, edited 1 time in total.
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Re: When the positive integer A is divided by 5 and 7, the [#permalink]
SravnaTestPrep
mrinal2100
When the positive integer A is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of A-B?

(A) 12
(B) 24
(C) 35
(D) 16
(E) 30

The easiest way to approach these problems is by taking an example

1. The first choice is 18. Take it as B
2. The next choice is 53. Take it as A
3. A-B=35

c is the only choice that is correct.

I chose the same approach but only a further tip to speed up:
When you found the value of A you can simply try to add every value from the answer choices: if the number obtained satisfy the initial divisibility conditions then you have found the correct answer :grin:
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Re: When the positive integer A is divided by 5 and 7, the [#permalink]
VeritasKarishma

Mam, I did it this way, is this a correct way?

A=5Q+3 & A=7s+4
so equating we get

5Q=7s+1

Which is for both A&B so the numbers derived are 18 and 53 solving for the above, hence the factor of 53-18= 35

C
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Re: When the positive integer A is divided by 5 and 7, the [#permalink]
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BigUD94
VeritasKarishma

Mam, I did it this way, is this a correct way?

A=5Q+3 & A=7s+4
so equating we get

5Q=7s+1

Which is for both A&B so the numbers derived are 18 and 53 solving for the above, hence the factor of 53-18= 35

C

It seems that basically you have found 2 numbers which satisfy both conditions and taken their difference (which would need to be a multiple of at least one of the choices). It is correct. I hope you understand why it is correct. It you are not sure, check out the link I have given above in my post.
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Re: When the positive integer A is divided by 5 and 7, the [#permalink]
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