This is GRE math question is driving me crazy!!!!!!!!!!!!!!!!!?

Question

Column A Column B
(0.82)^2 (0.82)^3 (0.82)^6

The question asks if:
the quantity in Column A is greater;
if the quantity in Column B is greater;
if the two quantities are equal;
if the relationship cannot be determined from the information given.

The equation is (.82) squared multiplied by (.82) cubed or (.82) to the power of 6.
I thought the answer was that column B was greater, but the the online GRE test says A. If it is A then why?
I assumed that I could just look at it as similar bases so add the exponents in column A. The equivalent would be (.82) to the 5th. What did I do wrong?

Answer 1

you are correct!
The exponent is 5.
Just because the exponent is bigger, it does not make the number bigger. If the number is less than one, then it gets smaller everytime we multiply.
EXAMPLE base = (1/2)
1/2 ^ 1 = 1/2
1/2 ^ 2 = 1/2* 1/2 = 1/4
1/2 ^ 3 = 1/8

As we take half of half of half.. it gets smaller.

So, since 0.82 is less than one, everytime we multiply by itself, it gets smaller.

good job adding exponents!
:)

Answer 2

The quantity in column A is greater. You are multiplying a number less than 1 by itself 5 times (you are right in adding the exponents)

So you are comparing a number between zero and 1 that is to the 5th power or to the 6th power.

The one to the 6th power will be less than the one to the 5th power.

As an easier-to-see example... what do you get if you take 0.1 to the fifth versus 0.1 to the sixth powers?

0.1 to the fifth is 10 times bigger that 0.1 to the 6th.



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AND a way to figure it out:

(.82)^5 ??? (.82)^6 (where ?? is either =, > or <)
divide by (.82)^5

1 ??? .82

so you can see that 1 > .82
so column A is greater than column B

Answer 3

.82^5 > .82^6

any fraction less than one and greater than zero, multiplied five times is greater than that same fraction multiplied six times. Every time you multiply it, the result gets smaller.

Let's try 1/2
(1/2)^5 = 1*1*1*1*1/(2*2*2*2*2) = 1/32
(1/2)^6 = 1*1*1*1*1*1/(2*2*2*2*2*2) = 1/64
(1/2)^1 > (1/2)^5 > (1/2)^6 > (1/2)^100

Answer 4

The quantity (0.82) being raised to the power of 5 or 6 is less than one.
(0.82)^5 = 0.3707
(0.82)^6 = 0.3040

Answer 5

the key is that .82<1
(.82)^2 = .6724
(.82)^3 = .5514

so .82^2 is larger

Answer 6

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