Marcab wrote:
If x is an integer, can the number (5/28)(3.02)(90%)(x) be represented by a finite number of non-zero decimal digits?
(1) x is greater than 100
(2) x is divisible by 21
Source: Jamboree
\(\frac{5}{28} * \frac{302}{100} * \frac{90}{100} * x\)
for this to be a terminating decimal the denominator must be in the form of \(\frac{x}{2^a * 5^b}\)
Re-writing the question stem numbers to be \(\frac{5}{7*2^2} * \frac{302}{2^2 * 5^2} * \frac{90}{2^2 * 2^5} * x\)
from statement 1) if we x > 100 it might include a multiple of 7 and it might not. so insufficient.
2) x is divisible by 21, meaning it could be 21,42,63 etc.. it is a multiple of 21 and 21 = 7 * 3
This will cancel the 7 in the denominator and will lead to the terminating decimal form, sufficient.
Answer choice B