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

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A natural number p, when divided by a certain divisor q, gives  [#permalink]

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Updated on: 30 Jul 2017, 20:18
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Difficulty:

95% (hard)

Question Stats:

24% (03:11) correct 76% (02:17) wrong based on 181 sessions

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A natural number p, when divided by a certain divisor q, gives remainder 12, what is the value of q?

(1) When 2p is divided by q, the remainder is 2.
(2) When 3p is is divided by q, the remainder is 6.

Originally posted by DHAR on 30 Jul 2017, 08:28.
Last edited by DHAR on 30 Jul 2017, 20:18, edited 2 times in total.
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Posts: 7749
Re: A natural number p, when divided by a certain divisor q, gives  [#permalink]

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30 Jul 2017, 10:42
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DH99 wrote:
A natural number p, when divided by a certain divisor q, gives remainder 12, what is the value of q?

Statement 1: When 2p is divided by q, the remainder is 2.
Statement 2: When 3p is is divided by q, the remainder is 6.

Hi..
when p is div by q , remainder is 12..

lets see the statements..

Statement 1: When 2p is divided by q, the remainder is 2.
If p divided by q , 12 is the remainder.
so 2p divided by q should gives us remainder 2*12=24..

but the remainder is 2 so 24-2=22 should be div by q..
q can be 2,11,22 but q>12 as the remainder in initial case was 12
ans q is 22
sufficient

Statement 2: When 3p is is divided by q, the remainder is 6.
so remainder should have been 3*12=36..
so 30 is div by q..
so q could be 10,15,30..
but q>12, so possible values 15 or 30...
so two values possible
Insuff..

A..

the problem with the Q is that it does not give the value 22 in statement II, which is not possible in actual gmat. each statement has to point towards the actual value..
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Re: A natural number p, when divided by a certain divisor q, gives  [#permalink]

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30 Jul 2017, 11:16
chetan2u wrote:
DH99 wrote:
A natural number p, when divided by a certain divisor q, gives remainder 12, what is the value of q?

Statement 1: When 2p is divided by q, the remainder is 2.
Statement 2: When 3p is is divided by q, the remainder is 6.

Hi..
when p is div by q , remainder is 12..

lets see the statements..

Statement 1: When 2p is divided by q, the remainder is 2.
If p divided by q , 12 is the remainder.
so 2p divided by q should gives us remainder 2*12=24..
but the remainder is 2 so 24-2=22 should be div by q..

q can be 2,11,22 but q>12 as the remainder in initial case was 12
ans q is 22
sufficient

Dear chetan2u,

Can you please elaborate the above highlighted? Why should it divided by 'q' after subtracting 2 from 24?

Thanks
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Re: A natural number p, when divided by a certain divisor q, gives  [#permalink]

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30 Jul 2017, 11:23
DH99 wrote:
A natural number p, when divided by a certain divisor q, gives remainder 12, what is the value of q?

(1) When 2p is divided by q, the remainder is 2.
(2) When 3p is is divided by q, the remainder is 6.

Please name topics properly. Read rule 3 in our RULES OF POSTING. Thank you.
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A natural number p, when divided by a certain divisor q, gives  [#permalink]

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30 Jul 2017, 21:56
Mo2men wrote:
chetan2u wrote:
DH99 wrote:
A natural number p, when divided by a certain divisor q, gives remainder 12, what is the value of q?

Statement 1: When 2p is divided by q, the remainder is 2.
Statement 2: When 3p is is divided by q, the remainder is 6.

Hi..
when p is div by q , remainder is 12..

lets see the statements..

Statement 1: When 2p is divided by q, the remainder is 2.
If p divided by q , 12 is the remainder.
so 2p divided by q should gives us remainder 2*12=24..
but the remainder is 2 so 24-2=22 should be div by q..

q can be 2,11,22 but q>12 as the remainder in initial case was 12
ans q is 22
sufficient

Dear chetan2u,

Can you please elaborate the above highlighted? Why should it divided by 'q' after subtracting 2 from 24?

Thanks

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
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A natural number p, when divided by a certain divisor q, gives  [#permalink]

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28 Nov 2017, 13:37
2

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}
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Re: A natural number p, when divided by a certain divisor q, gives  [#permalink]

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28 Nov 2017, 23:47
hellosanthosh2k2 wrote:

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.
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Re: A natural number p, when divided by a certain divisor q, gives  [#permalink]

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02 Dec 2018, 04:08
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Re: A natural number p, when divided by a certain divisor q, gives   [#permalink] 02 Dec 2018, 04:08
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