Exponent

[Baten80]

If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?

A -1
B 0
C 1
D 2
E 3

[beatthegmatinsept]

If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?

A -1
B 0
C 1
D 2
E 3

[spoiler]x = 2.
[/spoiler]

[Stuart@KaplanGMAT]

If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?

A -1
B 0
C 1
D 2
E 3

When a question asks you to solve for a variable, a great first step is to isolate that variable. Let's move everything except 5^x to the right side:

(6^2)(44)(5^x)(20) = (8^2)(9)(1375)

5^x = (8^2)(9)(1375)/(6^2)(44)(20)

Now we need to do lots of cancellation; we can either work with the numbers as is, or reduce to primes.

Or, even better, we can think to ourselves: "hey self! Hope you're having a great day. Since the answer choices are all integers, all the factors on the right side of the equation that aren't "5"s must cancel out! Awesome, so I can ignore everything else".

At this point we pat ourselves on the back and/or give ourselves a cookie for our brilliance. Only looking at the numbers that are multiples of 5 on the right side:

1375/20

factoring those out:

275*5/4*5

(we can ignore the 4)

275 = 11*25 = 11*5*5

So, there are two 5s left on the right side, giving us:

5^x = 5^2

x = 2... voila!

[rohit_gmat]

If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?

A -1
B 0
C 1
D 2
E 3

(6^2)(44)(5^x)(20) / (8^2)(9) = 1375

(3^2 x 2^2)(4 x 11)(5^x)(4 x 5) / (2^6)(3^2) = 1375

(3^2 x 2^2)(2^2 x 11)(5^x)(2^2 x 5) / (2^6)(3^2) = 1375

Cancelling off the 2^6 against three 2^2s & 3^2 against 3^2

(11)(5^x)(5) / 1 = 1375

(11)(5^(x+1)) = 1375

We know 1375 is divisible by 11

1375/11 = 125
5^(x+1) = 125

Now we just have to start listing (looking at the answer choices, we know we don't have to go too far, 4 is the max)

5^2 = 25
5^3 = 125 (bingo!)

3 = x+1
x = 3-1 = 2

D is correct