A natural number p, when divided by a certain divisor q, gives

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Hi..

Remember..
1) whenever you add two numbers, the remainder they leave gets added..
17 gives a remainder 3 when div by 7 and 22 gives remainder 1 when div by 7..
So 17+22 should give 3+1 when div by 7..
Let's see 17+22=39.. remainder is 4 as 39-35
2) next when you multiply two numbers their remainder gets multiplied..
Say 8 gives a remainder 1 when div by 7 and 2 gives a remainder 2..
So 8*2 should give 1*2 or 2 when div by 7..
Let's see 8*2=16.. leaves a remainder 2, 16-12..

The point (2) I the reason why we multiply 2*11

Now 24 should have been the remainder but it is 2 so 24-2 should be div..
You can see that thru equation also

Hope it helps

Answer must be A.

Let \(p = aq + 12\), where a is any integer
=> \(2p = 2aq + 24\)
=> \(3p = 3aq + 36\)

Statement 1:
2p divided by q leaves 2 as remainder => \(2p = bq + 2\)
from above, \(2p = 2aq + 24\), equating both
=> \(bq + 2 = 2aq + 24\)
=> \(q = 22/(b - 2a)\)
=> q has to be factor of 22, however can't be less than 12, it leaves remainder 12, so only
factor of 22, greater than 12 is 22 itself, so q = 22 -> Sufficient

Statement 2:

3p divided by q leaves 6 as remainder => \(3p = cq + 6\)
from above, \(3p = 3aq + 36\), equating both
=> \(cq + 6 = 3aq + 36\)
=> \(q = 30/(c - 3a)\)
=> q has to be factor of 30, possible values are 15, 30 (which are greater than 12)
=> Not Sufficient.

chetan2u Bunuel But Statement 1 and 2 contradicting each other, statement 1: q -> 12 and statement 2: q -> {15,30}

Hi

Its okay the statements are contradicting each other here, since ONLY one statement is giving us the answer. (statement 1)

We should not have a scenario where the answer is D (from each statement alone) and we get different/contradicting answers from the two statements. Then thats an issue and we need to check whether we have done everything correct or not.

Eg; if our answer is D, and we are getting q=22 from first statement and q=15 from second statement THEN thats a problem.

Hi Chetan

Can you please help in clarifying how did the values 2,11 and 22 (St.1)
10,15 and 30 (St.2) arrive?

Thanks

This is incorrect. It's not ok that the statements contradict each other; each statement must be TRUE, the question is only whether it's enough information to answer. Both statements 1 and 2 cannot be true, and so this question is impossible.

We can find from statement 1 that q=22, which means that we could have p=12. In that case, statement 2 is false: 3p gives a remainder of 14 when divided by q. The two statements MUST be consistent.