Is v^2 an even integer? (1) v is an even integer (2) √v is an even

Question

Is v^2 an even integer?

(1) v is an even integer
(2)  \sqrt{v}  is an even integer

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kungfury42 · Answer

(1) If v is an even integer, v² will be v*v or even*even which we know is an even quantity.  Clearly, sufficient.

(2) If √v is an even integer, v² will be √v*√v*√v*√v or even*even*even*even which is know is an even quantity.   Clearly, sufficient.

Hence, both the statements are individually sufficient, option D.

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zhanbo · Answer

Pre-thinking 
"Is v^2 an even integer" is equivalent with "is v an even integer"?

(1)Only
Matches pre-thinking. Sufficient.

(2)Only
So v is an even number squared. 
V is thus an even number. 
Sufficient.

The answer is  (D) .

desertEagle · Answer

Even X Even = Even

1) If v is even then  v^2  is Even X Even = Even. Sufficient
2)  \sqrt{v}  is an even integer -> v^2 = Even X Even X Even X Even = Even. Sufficient

Ans D

ReedArnoldMPREP · Answer

The pre-thinking isn't quite right. For this reason, a reformed version of this question would be significantly harder:

Is v an even integer?

1). v^2 is an even integer

2). √v is an even integer

I do this question in my classes sometimes. In my years of teaching, I honestly think fewer than 15% of my students get this question right. Statement 1 is very, very tempting--but it's not sufficient.

Instead of picking v's and seeing which follow the rule, pick v^2s.

v^2 must be an even integer, so v^2 could be:

2
4
6
8
10
12... etc.

It becomes immediately clear why this statement is not sufficient.

v cold be √2 (not an even integer) or 2 (an even integer).

But it's so easy to assume 'integers' and, since 'fractions' don't work in this instance, think any non-integers aren't in play.

kungfury42 · Answer

Very interesting question, and I must admit I did fall into the trap. Thank you for posting. Also, just to confirm is the answer to this B? I can't think of any case that would make B insufficient, but I wouldn't be surprised if there was one.

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ReedArnoldMPREP · Answer

Yes the correct answer would be B. If √v is an even integer, √v could be:

2
4
6
8
10...

Meaning v is

4
16
36
64
100...

(any even perfect square, which are all even integers).

TarunKumar1234 · Answer

Is v^2 an even integer? Stat1: v is an even integer, then v^2 must be an integer. Sufficient Stat2: √v is an even integer, then v^2 must be an integer. Sufficient So, I think D.

Is v^2 an even integer? (1) v is an even integer (2) √v is an even

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