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# If P, Q, R, and S are all integers, is product PQRS even?

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If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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17 Feb 2016, 03:13
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If P, Q, R, and S are all integers, is product PQRS even?

(1) PQ = 42
(2) RS = 35

Kudos for correct solution.

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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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17 Feb 2016, 20:33
Bunuel
I have a little doubt here. Since the question stem says is Product PQRS even?
Case 1:
Shall I assume PQ and RS as product of two numbers ?
or
Case 2:
Shall I assume PQ and RS as two different two digit number?

However ,
If I conceder both the cases , answer can be found
Case 1:

(1) PQ = 42. since product is even , that means either P or Q is Even. Now multiply this product with anything it will stay even. Hence sufficient
(2) RS = 35. Since product is odd , that means both R and S are odd. No that we do not know What is P or Q , we can not infer the final product. Hence Insufficient

Now

Case 2:
(1) PQ = 42 . P=4 Q=2. Both are even. so their product is also even.Now multiply this product with anything it will stay even. Hence sufficient
(2) RS = 35 . R=3 S=5. Both are odd. so their product is also odd.No that we do not know What is P or Q , we can not infer the final product. Hence Insufficient
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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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17 Feb 2016, 20:43
tryambaks wrote:
Bunuel
I have a little doubt here. Since the question stem says is Product PQRS even?
Case 1:
Shall I assume PQ and RS as product of two numbers ?
or
Case 2:
Shall I assume PQ and RS as two different two digit number?

However ,
If I conceder both the cases , answer can be found
Case 1:

(1) PQ = 42. since product is even , that means either P or Q is Even. Now multiply this product with anything it will stay even. Hence sufficient
(2) RS = 35. Since product is odd , that means both R and S are odd. No that we do not know What is P or Q , we can not infer the final product. Hence Insufficient

Now

Case 2:
(1) PQ = 42 . P=4 Q=2. Both are even. so their product is also even.Now multiply this product with anything it will stay even. Hence sufficient
(2) RS = 35 . R=3 S=5. Both are odd. so their product is also odd.No that we do not know What is P or Q , we can not infer the final product. Hence Insufficient

Hi,
you should take this as CASE I, because of three reasons..
1) PQRS is written in the same way and has been told in teh Q to be a product..
2) secondly, P,Q,R,S are all given as integer and not digit, so we cannot take them as digits.
3) If PQ were a two digit number, it would be mentioned as PQ is a two digit number..

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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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18 Feb 2016, 08:25
1
PQRS is even implies atleast one of the integer must be even.
Simplified question form is any one of the P,Q,R,S is even ?
Option 1 given PQ is 42 it implies atleast one of them is even integer. So.A
Option 2: RS is 35, 35 is odd so both R,S are odd we have no information about PQ so B is non.conclusive
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If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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Updated on: 23 Feb 2016, 06:58
We have to find out if P*Q*R*S =X is even?

any thing multiplied by even is even.
Even if one of the combination is even then result will be even
From A
X=42RS
i.e X will be even no matter what.
Now this is true only because we are given that all the numbers are integers.

We can not get anything from B
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Originally posted by mahakmalik on 19 Feb 2016, 00:01.
Last edited by mahakmalik on 23 Feb 2016, 06:58, edited 1 time in total.
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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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23 Feb 2016, 06:16
Bunuel wrote:
If P, Q, R, and S are all integers, is product PQRS even?

(1) PQ = 42
(2) RS = 35

Kudos for correct solution.

Given: P, Q, R, and S are all integers
Required: Is PQRS even?

Statement 1: PQ = 42
We know that PQ = 42. Hence atleast one of P or Q is even.
Therefore the product PQRS will also have an even number and will be even.
SUFFICIENT

Statement 2: RS = 35
We know nothing about P and Q.
If one of P or Q is even, then PQRS would be even
If none of P or Q is even, then PQRS will be odd
INSUFFICIENT

Option A
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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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23 Feb 2016, 09:53
1,PQ=42 = 2*21. PQRS=2*21*RS -> Even -> SUFFICIENT
2,RS= 35. We dont know PQ and RS is odd -> cant conclude the product is even or odd since we dont know about PQ -> Insufficient

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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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23 Feb 2016, 09:54
1,PQ=42 = 2*21. PQRS=2*21*RS -> Even -> SUFFICIENT
2,RS= 35. We dont know PQ and RS is odd -> cant conclude the product is even or odd since we dont know about PQ -> Insufficient

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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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23 Feb 2016, 19:03
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If P, Q, R, and S are all integers, is product PQRS even?

(1) PQ = 42
(2) RS = 35

When you modify the original condition and the question, they become even*odd=even. If a question asks if multiplication is even, an even condition is usually an answer.
Thus, in 1), PQ=42, which is always an even number. So, PQRS is always an even number as well, which is sufficient.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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24 Feb 2016, 10:14
Thank you very much
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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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18 Aug 2017, 13:09
Even if we are given PQ is even, R or S could be 0 (0 is also an integer). In that case, product of PQRS will be 0, which is not even.
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Re: If P, Q, R, and S are all integers, is product PQRS even?  [#permalink]

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18 Aug 2017, 14:04
1
rambani87 wrote:
Even if we are given PQ is even, R or S could be 0 (0 is also an integer). In that case, product of PQRS will be 0, which is not even.

Hello rambani87 - ZERO is indeed an EVEN number

Check out - GMAT Club Quant book - Page No. 3

Hope this helps!
Attachments

Zero.PNG [ 37.14 KiB | Viewed 1628 times ]

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Re: If P, Q, R, and S are all integers, is product PQRS even?   [#permalink] 18 Aug 2017, 14:04
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