Im still confused abt this question

[tvtt2010]

if n and k are integers whose product is 400, which of the following statements must be true?
A. n+k>0
B. n#k
C. either n or k is multiple of 10
D. if n is even, then k is odd
E. if n is odd, then k is even

what is the different between D and E? They both indicate the same thing that: one of each is odd or even

Thanks

[vineeshp]

You cant say that. D and E are specifically different numbers here. So n is n and k is k. You cannot interchange. Hence if n is odd, then they dont meant one of the numbers is odd, they mean n specifically is odd.

[Anurag@Gurome]

what is the different between D and E? They both indicate the same thing that: one of each is odd or even

In fact they are completely opposite as n and k are different integers.

If n and k are integers whose product is 400, which of the following statements must be true?
A. n+k>0
B. n#k
C. either n or k is multiple of 10
D. if n is even, then k is odd
E. if n is odd, then k is even

A. n = k = -20 --> (n +k) = -40 < 0 ----> FALSE
2. n = k = 20 ---------------------------> FALSE
3. n = 16 and k = 25 --------------------> FALSE
4. n = 2 and k = 400 --------------------> FALSE
5. If n is odd then k must be even as their product is even ---> TRUE

The correct answer is E.

[Maciek]

Hi

I like the way the problem was explained by the expert.

Moreover, it is worth to remember about the roles of antecedent and consequent of a conditional.
The antecedent of a conditional is a sufficient condition for the consequent.
The consequent of a conditional is a necessary condition for the antecedent.
Thus:

D)
Antecedent: n is even
Consequent: k is odd

E)
Antecedent: n is odd
Consequent: k is even

You cannot interchange the sentences D) and E).

If you want to read more about necessary and sufficient conditions, you may check Critical Reasoning: A User's Manual: www.ou.edu/ouphil/faculty/chris/crmscreen.pdf

Hope it helps!

Best,
Maciek

[Scott@TargetTestPrep]

if n and k are integers whose product is 400, which of the following statements must be true?
A. n+k>0
B. n#k
C. either n or k is multiple of 10
D. if n is even, then k is odd
E. if n is odd, then k is even

Let's go through the choices.

Since n can be -20 and k can be -20, we see that choice A is not true.

Since n can be 20 and k can be 20, we see that choice B is not true.

Since 400 = 16 x 25, we see that choice C is not true.

Since 400 = 20 x 20, we see that choice D is not true.

So choice E must be true. We can also show that it must be true because if n is odd, then k must be even, in order to produce an even product (400 is an even number). For example, if n is 25 (odd), then k must be even, which it is, since k must be 16.

Answer: E