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15 February 2007

AskMeCha: I need math help... →[More:]I'm studying for the GMAT test and this question stumped me:

3(2¹³) = 2^x - 2^(x-2)

No calculators on this test.

I happened to get this question right (x=15), but only because that was the only answer that resulted in x-2=13. But I'm really not sure why that's right.

Can someone explain to me the proper method when approaching this question?

post by: mullacc at: 19:12 | 13 comments

*runs away screaming*

posted by mudpuppie 15 February | 19:17

Reasoning it out goes like this for me:

1. Given: n^x * n^y = n^x+y
2. 3(2¹³) = 4(2¹³) - 1(2¹³)
3. 4(2¹³) = 2² * 2¹³
4. From (1), 2² * 2¹³ = 2²⁺¹³ = 2¹⁵
4. So back to (2), 3(2¹³) = 2¹⁵ - (2^15-2)

posted by cortex 15 February | 19:20

That second step four should be step 5, obviously.

posted by cortex 15 February | 19:20

The important property to remember is that a^(n-m)=(aⁿ)(a^m), so

2^(x-2) = (2^x)(2^-2) = (1/2²)(2^x) = (1/4)(2^x)

So, 3(2¹³) = 2^x - (2^x)/4
3(2¹³) = (3/4)(2^x)

multiply both sides by (4/3), and you get
4(2¹³) = (2^x)

of course, 2 = 2², so

(2²)(2¹³) = (2^x)
do the reverse of the first step I showed you, and you'll get

13+2 = x, so x = 15.

Or what cortex said. Let me know if you want me to expand any further. Of course, your reasoning got the answer much quicker.

posted by muddgirl 15 February | 19:27

Oh! I got it...

3(2¹³) = (2¹³)(2²)-2¹³

3(2¹³) = 2¹³ * (2²-1)

3 = (2²-1)

(On preview, I need a minute to look at cortex's answer..)

posted by mullacc 15 February | 19:28

Thanks, muddgirl and cortex!

posted by mullacc 15 February | 19:31

Math!

posted by cortex 15 February | 19:33

I've been studying for the GRE, and I made a dumb mistake on my math bit, and came up with the wrong answer the first time I worked it out. Just for full disclosure.

posted by muddgirl 15 February | 19:42

*head explodes*

posted by mlis 15 February | 23:28

This thread makes me so horny.

posted by Eideteker 16 February | 06:40

Head hurts.

posted by deborah 16 February | 14:22

a^(n-m)=(aⁿ)(a^m)
This is wrong, of course. It should be
a^(n+m)=(aⁿ)(a^m)

posted by muddgirl 16 February | 14:32

Boy, you can tell you're old when the math problem is trivial but you don't know how to code the superscripts in HTML.

posted by ikkyu2 16 February | 16:30

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