Data Sufficiency

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

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

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?"

(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]

HI Sanjeev,

you mean to say by virtue of B we get the highest exponential of 2 which is 7 but we dont know which one carrying that, it may be x,y,z or W, thats way its incorrect ???

In source, the answer is B which I also do agree because I guess q is asking what could be the highest power of 2, the other way round , please shed some light ...

vipulgoyal wrote:HI Sanjeev,

you mean to say by virtue of B we get the highest exponential of 2 which is 7 but we dont know which one carrying that, it may be x,y,z or W, thats way its incorrect ???

In source, the answer is B which I also do agree because I guess q is asking what could be the highest power of 2, the other way round , please shed some light ...

The question is:

If x, y, z, and w are positive integers and all of them are exponents of 2, what is the largest one of them?

The opening line introduces us with x, y, z, and w, which are positive integers and all of them are exponents of 2. the closing line in bold reads "what is the largest one of them?". It has to be specific about the largest 'exponent of 2', otherwise it would imply that they want "the largest one of x, y, z, and w", as I interpreted.