If x, y, z, and w are positive integers and all of them are exponents of 2, what is the largest one of them?
(1) x*y*z*w=2^16
(2) x+y+z+w=170
B
(1) x*y*z*w=2^16
(2) x+y+z+w=170
B
Let's say that x = 2^a, y = 2^b, z = 2^c, and w = 2^d, where a, b, c, and d are positive-integer-exponents of 2. In other words we have to answer, "What is the largest one of a, b, c, d?"vipulgoyal wrote:If x, y, z, and w are positive integers and all of them are exponents of 2, what is the largest one of them?
(1) x*y*z*w=2^16
(2) x+y+z+w=170
B
(1) It means that a + b + c + d = 16. With this much known, how can we figure out the real values of a, b, c, d in order to answer the question? Insufficient
(2) No four similar exponents of 2 can add up to bring a sum whose units' digit is 0. It could be either of the following combinations of
"¢ integers ending in 2 and 8, or
"¢ integers ending in 4 and 6, or
"¢ integers ending in 2, 4, 6, 8.
Further, even if the proper combination (2, 8, 32, and 128) can be guessed, we cannot assign values with any certainty in order to answer the question? Insufficient
If taken together, the only combination for a, b, c, and d is 1, 3, 5, and 7 in some order we don't know. We cannot figure out the real values of x, y, z, and w in order to answer the question? [spoiler]Hence, it's still insufficient.
Pick E[/spoiler]
