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# Is 9 the HCF of p and q?

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Is 9 the HCF of p and q?  [#permalink]

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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

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?  [#permalink]

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23 May 2020, 18:10

Important Concept:

LCM is a multiple of HCF

1) 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.

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Re: Is 9 the HCF of p and q?  [#permalink]

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23 May 2020, 18:25
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?  [#permalink]

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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?  [#permalink]

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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.

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Re: Is 9 the HCF of p and q?  [#permalink]

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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?  [#permalink]

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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?  [#permalink]

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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?  [#permalink]

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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?  [#permalink]

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24 May 2020, 11:19

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.

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Re: Is 9 the HCF of p and q?  [#permalink]

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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?  [#permalink]

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25 May 2020, 02:25
2
GMATBusters

It 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

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Re: Is 9 the HCF of p and q?  [#permalink]

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25 May 2020, 07:18
GMATBusters
the 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?  [#permalink]

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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:
GMATBusters
the 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?  [#permalink]

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09 Jun 2020, 00:17
GMATBusters wrote:

GMATBusters’ Quant Quiz Question -4

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) Sufficient
Statement 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?   [#permalink] 09 Jun 2020, 00:17