GMAT Diagnostic Test Question 5

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Re: GMAT Diagnostic Test Question 5 [#permalink]

18 Aug 2010, 04:59

tejal777 wrote:

If you had to compare between 10^36 and 15^20 how would you compare and find which one is greater?This is where I had goten stuck...

Please explain!

you need compare apple with apple, so you try replace 15 with 10^n. Because it it easy to compare 10^36 with 15^20=(10^n)^20=10^(n*20).
So we go like this 15=10^n, what is n ? definitely n<2 because 10^2 is 100, definitely n>1 because 10^1 is only 10.
Let's check the result for 10^1.5 approximately is 10^1*10^0.5=10*sqrt(10)= near 33 (root 10 is around 3.3)
So 10^1.5 is equal near 33 which is more than 15, so for 15=10^n, n will be even less than 1.5. Let's put 1.5 to our original formula 10^(1.5*20)=10^30 which is already less than 10^36, and we remember that n will be even less than 1.5. the answer is 10^36 > 15^20

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Re: GMAT Diagnostic Test Question 5 [#permalink]

11 Sep 2010, 16:09

the way I broke numbers down:
999^36 = approx 1000^36
10^36 = 1000^12
777^36< 1000^36
20^24 = 10^24*2^24 =10^24*2^24*2^24 < 10^24*2^12*5^12(A)
(SQRT15)40 = 15^20=3^20*5^20 < 5^36*2^36 (A)
HENSE A IS AN ANSWER.

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Re: GMAT Diagnostic Test Question 5 [#permalink]

15 Feb 2012, 21:44

on gmat are answers displayed by increasing value?

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Re: GMAT Diagnostic Test Question 5 [#permalink]

16 Feb 2012, 03:50

shawndx wrote:

on gmat are answers displayed by increasing value?

Usually the answer choices in PS are in increasing or decreasing order. But not always, and certainly not for a question such as this one where we should find the greatest value.
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Re: GMAT Diagnostic Test Question 5 [#permalink]

03 Apr 2012, 21:34

how did you get from 2^24 to 2^4 * 10^6?

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Re: GMAT Diagnostic Test Question 5 [#permalink]

04 Apr 2012, 01:45

catty2004 wrote:

how did you get from 2^24 to 2^4 * 10^6?

2^{24} =2^4*2^{20}=2^4*(2^{10})^2. Now, since 2^{10}=1024\approx 10^3 then 2^4*(2^{10})^3\approx{2^2*(10^3)^2}=2^4 * 10^6.

Hope it's clear.
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Re: GMAT Diagnostic Test Question 5 [#permalink]

10 Jun 2012, 23:11

Hi, I'm new to the forum and currently prepping for the GMAT.

For this problem I manipulated all the answers in a similar way but I wanted to focus on the two answer choices that I was left with. I actually manipulated the answer choice D in a different manner and wanted to see if the method was okay. The bold is what I'm speaking about.

A - 999^12 -> 1000^12 -> (10^3)^12 -> 10^36

and

D - (-20)^24 -> ((-2)^24)*(10^24)..here is where I did it differently -> (((-2)^3)^8)*(10^24), which then becomes ((-8)^8)*(10^24).

From here I rounded down (-8)^8 to (-10)^8 and then dropped the negative sign because it becomes positive due to the even power.
My answer then looked like this: (10^8)*(10^24) -> 10^(8+24) = 10^32

From here, 10^36 > 10^32, therefore the answer is A.

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Re: GMAT Diagnostic Test Question 5 [#permalink]

20 Jun 2012, 09:56

Ok..i kinda get the concept.

So, can I safely assume that 2^3==10 and so, 2^24==10^3 and then discard D?

And, can we use this form for other questions as well? Ofcourse, in PS questions only (strictly speaking)
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Re: GMAT Diagnostic Test Question 5 [#permalink] 20 Jun 2012, 09:56

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GMAT Diagnostic Test Question 5

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