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Is 9 the HCF of p and q?
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23 May 2020, 18:09
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35% (02:11) correct 65% (01:29) wrong based on 71 sessions
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GMATBusters’ Quant Quiz Question 4
For past quiz questions, click here Is 9 the HCF of p and q? 1) LCM of p and q = 75 2) pq = 225
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Re: Is 9 the HCF of p and q?
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23 May 2020, 18:10
Important Concept: LCM is a multiple of HCF1) Since 75 is not a multiple of 9, 9 cannot be HCF Statement 1 is sufficient. 2) pq = 225 if 9 is HCF the number can be 9a or 9b the product pq = 81ab since 225 is not a multiple of 81. Statement 2 is also sufficient. Answer is D
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Re: Is 9 the HCF of p and q?
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23 May 2020, 18:25
Answer :A State 1:sufficient p and q have combination of:5,25 or 1,25 hence hcf of p and q not 15 State 2:not sufficient pq=225 =3*75 hence HCF=3 HENCE NO pq=15*15 hence HCF=15 YES



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Re: Is 9 the HCF of p and q?
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Updated on: 23 May 2020, 23:59
Is 15 the HCF of p and q?
1) LCM of p and q = 25 2) pq = 225 #1 1) LCM of p and q = 25 p,q = 25*1 ; 25*5 ; but HCF wont be 15 ; sufficient #2 p*q =225 we know LCM* HCF = product of any two no 225 = 15*LCM LCM= 15 no info about LCM ; insufficient OPTION A
Originally posted by Archit3110 on 23 May 2020, 18:29.
Last edited by Archit3110 on 23 May 2020, 23:59, edited 1 time in total.



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Re: Is 9 the HCF of p and q?
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23 May 2020, 18:31
1) The highest power of 3 in the LCM is zero. So HCF cannot contain a 3 and thus cannot be 15. Sufficient. 2) We can have different possibilities. p=225, q= 1 and the HCF would be 1 and the answer would be NO. p=15, q=15 and the HCF would be 15 and the answer would be YES. Not sufficient.
Answer: A



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Re: Is 9 the HCF of p and q?
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23 May 2020, 18:31
Asked: Is 15 the HCF of p and q? 1) LCM of p and q = 25 3 is NOT a factor of p or q 15 = 3*5 is not HCF(p,q) SUFFICIENT 2) pq = 225 If (p,q) = (1,225); HCF(p,q) = 1 But if (p,q) = (3,75); HCF(p,q) = 3 NOT SUFFICIENT IMO A
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Re: Is 9 the HCF of p and q?
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23 May 2020, 18:56
Is 15 the HCF of p and q?
1) LCM of p and q = 25 2) pq = 225
ANS: C
1) Statement 1 just proivdes LCM there are many possibilites , hence Not sufficient
2) Pq=225
this will give several values of P and Q . Hence not sufficient.
Combined together. It is sufficinet as we know
product of two numbers = HCF * LCM
225=H*L H=225/25=9.



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Re: Is 9 the HCF of p and q?
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23 May 2020, 19:03
IMO A
Is 15 the HCF of p and q?
1) LCM of p and q = 25 Let, p= k x a (Where k,a & b are distinct prime number) q= k x b LCM = K x a x b HCF= K LCM = HCF X (Some Integer) 25 = 15 x (Some integer) This is not possible for any integer value.
So, 15 not HCF of p & q Sufficient
2) pq = 225 pq= 3x3x5x5 if p=15 & q=15 , HCF=15 but if =3, q=75, HCF= 3 Not Sufficient



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Re: Is 9 the HCF of p and q?
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23 May 2020, 22:07
Is HCF(p,q) = 15 ?
From ST(1), LCM(p,q) = 25
There could be following cases, p = 1, q = 25 p = 5, q = 25 p = 25, q = 25
In all cases, HCF(p,q) can never be 15.
Hence, ST(1) is sufficient.
From ST(2), pq = 225 As we know, pq = LCM(p,q) X HCF(p,q)
So, following values can be options HCF = 1, LCM = 225 HCF = 5, LCM = 45 HCF = 15, LCM = 15
Hence, ST(2) is not sufficient.



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Re: Is 9 the HCF of p and q?
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24 May 2020, 11:19
Answer  A
This is an easy yet a tricky question. People might me tempted to choose the answer option as C . But pay attention to question. It is a Yes/No question. Hence, we don't need to find a definitive answer.
Statement 1 : LCM of p and q = 25
This implies there is no factor of 3 in p & q. Hence , HCF can't be 15 if there is no factor of 3 in p & q.
SUFFICIENT to say NO
Statement 2 : pq = 225
Case 1 : p*q = 225 = 15 * 15 , in this HCF is 15, Answer is Yes.
Case 2 : p*q = 225 = 5 * 45 , in this case HCF is 5, Answer is No.
So , Statement 2 is insufficient.
Hence, Answer is A.
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Re: Is 9 the HCF of p and q?
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24 May 2020, 12:00
(1) LCM of p and q = 25 = \(5^2\) Can HCF be = 15 = 3.5? No it cannot, or else the LCM would have at least one factor of 3. Sufficient
(2) pq = 225 =\( 3^2. 5^2\) So yes here the HCF may or may not be 15. **It would be 15 only when both p and q are 15 Not sufficient
IMO A



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Re: Is 9 the HCF of p and q?
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25 May 2020, 02:25
GMATBustersIt seems to me that there is a discrepancy between the statements St.1  (p,q) can be (1,25) (5,25) or vice versa or (25,25) only In none of these cases can pq be 225 as given in st.2 Posted from my mobile device



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Re: Is 9 the HCF of p and q?
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25 May 2020, 07:18
GMATBustersthe initial question posted was Is 15 the HCF of p and q? 1) LCM of p and q = 25 2) pq = 225 everyone here has solved the same aforementioned question but here the question being shown is Is 9 the HCF of p and q? 1) LCM of p and q = 75 2) pq = 225



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Re: Is 9 the HCF of p and q?
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25 May 2020, 09:36
yes I realized that there was a contradiction in St1 & 2 as pointed out. so it was revised. Learning never stops... Isn't it Archit3110 wrote: GMATBustersthe initial question posted was Is 15 the HCF of p and q? 1) LCM of p and q = 25 2) pq = 225 everyone here has solved the same aforementioned question but here the question being shown is Is 9 the HCF of p and q? 1) LCM of p and q = 75 2) pq = 225
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Is 9 the HCF of p and q?
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09 Jun 2020, 00:17
GMATBusters wrote: GMATBusters’ Quant Quiz Question 4
For past quiz questions, click here Is 9 the HCF of p and q? 1) LCM of p and q = 75 2) pq = 225 The question becomes simple if below important property is noted: The HCF of a group of numbers is always a factor of their LCM.This is true precisely because: 1. HCF is the product of all common prime factors using the least power of each common prime factor 2. LCM is the product of highest powers of all prime factors. Statement 1: LCM of two numbers is 75. Since, 9 is not a factor of 75 (3x5x5), 9 cannot be HCF of the two numbers. (Possible HCF's could be: 3, 5, 15, 25, 75) SufficientStatement 2: HCF should be factor of Product of two numbers. 9(3x3) is factor of 225 (3x3x5x5). But so are 15 (e.g. for p=15 , q=15), 25, 45, 75.. Also, for HCF to be 9, the product of numbers should be divisible by 9 twice i.e. 81. Once as factor of p and then as factor of q. Since, 225 is not divisible by 81. Sufficient




Is 9 the HCF of p and q?
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