prettysmart wrote:
x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^(x-1) - 5^x?
Statement #1: z < 25 and w = 7^x
Statement #2: x = 4
Came across this DS problem during practice test. Can you please help me with the explanation?
Dear
prettysmart,
I'm happy to help.
My friend, you have a LOT to learn about typing exponents. First of all, to denote, say, 2 to the power of 3, we would NOT write
23. We would write
2^3, using the carot symbol (^), which is shift-6 on a standard keyboard. Furthermore, you need to understand the nature of mathematical grouping symbols. Read this blog
very carefully:
https://magoosh.com/gmat/2013/gmat-quant ... g-symbols/I hunted down this question in another thread on GMAT club, and found the real question. I had to make several change to what you posted to correct it.
OK, now we can discuss the question.
Statement #2 tells us nothing about w or z, so by itself, it's
insufficient.
Statement #1 is interesting. From the prompt, "
x is an integer and x raised to any odd integer is greater than zero" is a tricky way to tell us that x is a positive integer, because negative integers raised to odd powers are negative. We know x is a positive integer, but in this statement by itself, we don't know what x is.
The question is
w - z > 5*(7^(x-1) - 5^x)?
which means
7^x - z > 5*(7^(x-1) - 5^x) ?
7^x - z > 5*(7^(x-1)) - 5^(x+1) ?
Re-arrange.
7^x - 5(7^(x-1)) + (5^(x+1)) > z?
Well, as x gets bigger, that left hand side will get bigger. Let's look at the smallest possible positive value for x, x = 1. Then
7 - 5 + 25 = 27 > z
because 25 > z. This means, for all positive integers, the left hand side is bigger, and the inequality is true. Thus, given Statement #1, we can give a definitive answer to the prompt question.
First statement sufficient, second insufficient. Answer =
(A)Does all this make sense?
Mike