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

Question

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

Kudos for correct  solution .

tryambaks · Answer

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
Answer is (A)

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
Answer is (A)

chetan2u · Answer

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..

Badari · Answer

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
 Final answer A

mahakmalik · Answer

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

TeamGMATIFY · Answer

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

tuandoan92 · Answer

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

-> Answer A

tuandoan92 · Answer

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

-> Answer A

MathRevolution · Answer

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.
Thus, A is the answer.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

tuandoan92 · Answer

Thank you very much

rambani87 · Answer

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.

ydmuley · Answer

Hello  rambani87  -   ZERO is indeed an EVEN number

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

Hope this helps!

kiran120680 · Answer

Offical explanation

Solution: A

If a series of integers are being multiplied together, the only way the product can be odd is if ALL the integers being multiplied are odd; one even integer will force the product to be even. Statement (1) says that PQ = 42, so either P or Q is even; SUFFICIENT. Statement (2) says that RS = 35, so both R and S are odd; INSUFFICIENT, as PQ could be even or PQ could be odd. (A).

CrackverbalGMAT · Answer

This is a question based on the concept of Odds & Evens.

The product of any set of numbers can be made even by taking just one number as even . In other words,  we need a minimum of one even integer to make the product of a set of integers even.

If the product of PQRS has to be even, at least one of P, Q, R and S HAS TO be even . Any data that helps us establish this will be sufficient data.

From statement I alone, PQ = 42. 42 is an even number; also 42 = 2*3*7. This means that one of P and Q will definitely be even. This is sufficient to say that the product PQRS will definitely be even. 
Statement I alone is sufficient. Possible answer options are A or D. Answer options B, C and E can be eliminated.

From statement II alone, RS = 35.  If the product of 2 numbers is odd, it means both numbers HAVE TO be odd . So, we know for sure that both R and S are odd. 
But, we do not have any information about P or Q. If one of these becomes even, the product PQRS will become even. If both P and Q are also odd, then PQRS will become odd. As such, we cannot say conclusively that PQRS is even.
Statement II alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.

Hope that helps!

ishitaz · Answer

Hi, I have one doubt. I chose C for this particular question because what if R or S are 0. Combining both statements together assures the fact that all 4 are non zero integers as well. Isn't it?

Thanks in advance

Bunuel · Answer

I think you are missing that 0 is also an even integer.

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

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GMAT Data Sufficiency (DS) Questions

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

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