## superhelp101 one year ago SAT Question:

1. superhelp101

2. superhelp101

I feel like the first and the last one could be the answer

3. GreenCat

root w over 2 is an odd INTEGER

4. GreenCat

so that means root w is even

5. GreenCat

so w is the square of an even number

6. acxbox22

|dw:1434403835527:dw|

7. GreenCat

|dw:1434403901094:dw| remember x is odd so w is 4 times the square of an odd number

8. GreenCat

divide the answer chices by 4 and see which is the square of an odd number

9. acxbox22

you can just plug all the answer choices and check

10. GreenCat

anything that is not divisible by 4 is wrong cross out 49, 81, and 225

11. GreenCat

Divide by 4: 144/4=36 196/4=49

12. superhelp101

but 7.5 is also odd

13. GreenCat

7.5 is not an integer.

14. acxbox22

no it isn't odd or even is only defined for numbers

15. superhelp101

ohh so $\sqrt{w}$ has to be even?

16. acxbox22

yea then only it can be divided by 2

17. superhelp101

ohh cool let me work it out

18. superhelp101

144 and 196 could work

19. superhelp101

no it is 196 right?

20. freckles

$\frac{\sqrt{w}}{2}=2k+1 \\ \text{ multiply 2 on both sides } \\ \sqrt{w}=2(2k+1) \\ \text{ \square both sides } w=2^2(2k+1)^2$

21. freckles

this says w is divisble by 4 and some other odd number square

22. freckles

is 49,81,225 divisible by 4?

23. superhelp101

no

24. freckles

so your choices are narrowed down to either 144 or 196 write the prime factorization both of these

25. superhelp101

|dw:1434404702547:dw|

26. GreenCat

According to what I had earlier shown, yes 196 works as you said.

27. superhelp101

|dw:1434404755390:dw|

28. freckles

$144=2^4 \cdot 3^2 \\ 196=2^2 \cdot 7^2$ and $w=2^2(2k+1)^2$ which fits the w form?

29. freckles

notice the 2 has a square on it in the w factorization both satisfy the odd^2 part but only one of them satisfy the 2 raised to the second power part

30. superhelp101

oh okayyy

31. superhelp101

thank you all for the help! :)