Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 15 Dec 2015
Posts: 120
GPA: 4
WE: Information Technology (Computer Software)

A natural number p, when divided by a certain divisor q, gives [#permalink]
Show Tags
Updated on: 30 Jul 2017, 20:18
Question Stats:
20% (02:13) correct 80% (01:58) wrong based on 123 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
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.



Math Expert
Joined: 02 Aug 2009
Posts: 6217

Re: A natural number p, when divided by a certain divisor q, gives [#permalink]
Show Tags
30 Jul 2017, 10:42
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 242=22 should be div by q.. q can be 2,11,22 but q>12 as the remainder in initial case was 12ans 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..
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



SVP
Joined: 26 Mar 2013
Posts: 1719

Re: A natural number p, when divided by a certain divisor q, gives [#permalink]
Show Tags
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 242=22 should be div by q..q can be 2,11,22 but q>12 as the remainder in initial case was 12ans 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



Math Expert
Joined: 02 Sep 2009
Posts: 47030

Re: A natural number p, when divided by a certain divisor q, gives [#permalink]
Show Tags
30 Jul 2017, 11:23



Math Expert
Joined: 02 Aug 2009
Posts: 6217

A natural number p, when divided by a certain divisor q, gives [#permalink]
Show Tags
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 242=22 should be div by q..q can be 2,11,22 but q>12 as the remainder in initial case was 12ans 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 3935 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, 1612.. The point (2) I the reason why we multiply 2*11 Now 24 should have been the remainder but it is 2 so 242 should be div.. You can see that thru equation also Hope it helps
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Senior Manager
Joined: 02 Apr 2014
Posts: 486

A natural number p, when divided by a certain divisor q, gives [#permalink]
Show Tags
28 Nov 2017, 13:37
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}



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1273
Location: India

Re: A natural number p, when divided by a certain divisor q, gives [#permalink]
Show Tags
28 Nov 2017, 23:47
hellosanthosh2k2 wrote: 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.




Re: A natural number p, when divided by a certain divisor q, gives
[#permalink]
28 Nov 2017, 23:47






