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# If p and q are integers greater than zero, what is the value of pq?

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Math Expert
Joined: 02 Sep 2009
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If p and q are integers greater than zero, what is the value of pq?  [#permalink]

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23 Sep 2015, 22:47
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If p and q are integers greater than zero, what is the value of pq?

(1) The least common multiple of p and q is 240.

(2) The greatest common factor of p and q is 8.

Kudos for a correct solution.

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If p and q are integers greater than zero, what is the value of pq?  [#permalink]

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23 Sep 2015, 23:25
Bunuel wrote:
If p and q are integers greater than zero, what is the value of pq?

(1) The least common multiple of p and q is 240.

(2) The greatest common factor of p and q is 8.

Kudos for a correct solution.

St 1:

LCM of P & Q = 240,
P=60, Q=80 , or vice versa, LCM 240, PQ = 4800
P=30, Q=80 or vice versa, LCM 240, PQ = 2400
P=10, Q=240 or vice versa,LCM 240, PQ = 2400
P=8, Q=240 or vice versa, LCM 240, PQ = 1920
P=6, Q=240 or vice versa, LCM 240, PQ = 1440 ......

So many values. Not sufficient.

St 2:

GCF of P & Q = 8

P=8, Q=16 , GCF 8, PQ = 128
P=24, Q=40, GCF 8, PQ = 960
P=240, Q=8, GCF 8, PQ = 1920.....

Same here. Not sufficient.

Combine 1 & 2,
LCM of P * Q is 240, GCF is 8 only when P=240, Q=8 or vice versa
There PQ = 1920.

Ans C.
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Joined: 12 Sep 2015
Posts: 4017
Re: If p and q are integers greater than zero, what is the value of pq?  [#permalink]

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24 Sep 2015, 07:41
Bunuel wrote:
If p and q are integers greater than zero, what is the value of pq?

(1) The least common multiple of p and q is 240.

(2) The greatest common factor of p and q is 8.

Kudos for a correct solution.

Target question: What is the value of pq?

Statement 1: The least common multiple of p and q is 240.
This statement doesn't FEEL sufficient, so I'm going to TEST some values.There are several values of p and q that satisfy statement 1. Here are two:
Case a: p = 1 and q = 240, in which case pq = 240
Case b: p = 240 and q = 240, in which case pq = 240^2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: The greatest common factor of p and q is 8
This statement doesn't FEEL sufficient either, so I'm going to TEST some values.
Case a: p = 8 and q = 8, in which case pq = 64
Case b: p = 8 and q = 16, in which case pq = 128
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There's a nice rule that says (greatest common factor of y and x )(least common multiple of x and y) = xy
So, (8)(240) = pq
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: If p and q are integers greater than zero, what is the value of pq?  [#permalink]

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24 Sep 2015, 14:42
Bunuel wrote:
If p and q are integers greater than zero, what is the value of pq?

(1) The least common multiple of p and q is 240.

(2) The greatest common factor of p and q is 8.

Kudos for a correct solution.

Statement 1:
Doesn't provide any concrete values for p and q.
INSUFFICIENT

Statement 2:
Again, doesn't tell much about p and q.
INSUFFICIENT

Combining 1 and 2:
HCF*LCM= Product of the two given numbers.

or pq = 240*8 =1920
SUFFICIENT

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Re: If p and q are integers greater than zero, what is the value of pq?  [#permalink]

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24 Sep 2015, 20:39
Individual statements are not sufficient. coz 240 LCM and 8 GCM can have multiple possibilities
hence
IMO C
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Re: If p and q are integers greater than zero, what is the value of pq?  [#permalink]

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27 Sep 2015, 08:43
For any two numbers a and b:
$$a*b = gcd(a, b) * lcm(a, b)$$

$$p*q = 240 * 8 = 1920$$

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Re: If p and q are integers greater than zero, what is the value of pq?  [#permalink]

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17 Jul 2017, 19:37
Bunuel wrote:
If p and q are integers greater than zero, what is the value of pq?

(1) The least common multiple of p and q is 240.

(2) The greatest common factor of p and q is 8.

Kudos for a correct solution.

Out of curiosity - has anybody actually seen this on an actually GMAT exam?

Anyways if you have the lcm and gcf of x and y then you have enough to know the product of x and y
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Re: If p and q are integers greater than zero, what is the value of pq?  [#permalink]

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22 Nov 2017, 12:53
I learned a really helpful formula from a Magoosh lesson...
For any two integers, P & Q:
LCM = (P*Q)/GCF [where LCM = Lowest Common Multiple; GCF = Greatest Common Factor]

Using the above formula you can quickly deduce that Statements 1 and 2 are insufficient on their own, but sufficient together.
Re: If p and q are integers greater than zero, what is the value of pq?   [#permalink] 22 Nov 2017, 12:53
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# If p and q are integers greater than zero, what is the value of pq?

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