integer

[vietst]

If x is an integer, is 3x less than 500?

(1) 4^(x-1) < 4^x - 120

(2) x^2 = 36
CAT 4

OA is C.
However, i think (2) is suff
2. x = +/-6, then 3^x < 36. Suff
B.

[StaceyKoprince]

Can you please doublecheck the above? Is that supposed to be 3^x in the question, not 3x?

[shaan17]

Hi Stacey,
the question asks if 3^x < 500
I worked out this problem in the following manner, please let me know if it is correct.
From (1) => 4^(x-1) < 4^x - 120
4^x /4 = 4^x - 120
120 < 4^x (3/4)
160 < 4^x
hence x< 4
from this we can conclude that 3^x < 500 . therefore (1) is sufficient.

From (2) => x= +/- 6
insufficient.
Am I missing something in the way I worked out this prob ? ! :?

[StaceyKoprince]

Check out your last step:

160 < 4^x
hence x< 4

Actually, no. 4 < x, not x < 4. That changes everything!