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Which of the following is the greatest?

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Which of the following is the greatest?  [#permalink]

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New post Updated on: 28 Mar 2018, 01:00
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[GMAT math practice question]

Which of the following is the greatest?

\(A. (1+2)^5\)
\(B. 10^3\)
\(C. (1^2+2^2)^4\)
\(D. (2^2+2^2+2^2)^3\)
\(E. (2^2+2^2+2^2+2^2)^2\)

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Originally posted by MathRevolution on 25 Mar 2018, 23:56.
Last edited by MathRevolution on 28 Mar 2018, 01:00, edited 2 times in total.
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Re: Which of the following is the greatest?  [#permalink]

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New post Updated on: 26 Mar 2018, 03:53
1
MathRevolution wrote:
[GMAT math practice question]

Which of the following is the greatest?

\(A. (1+2)^5\)
\(B. 10^3\)
\(C. (1^2+2^2)^4\)
\(D. (2^2+2^2+2^2)^3\)
\(E. (2^2+2^2+2^2+2^2)^2\)


Hi MathRevolution,

I think the OA provided is incorrect.

\(A. (1+2)^5 = 3^5 = (3^3)*(3^2) = 27*9 <1000\)
\(B. 10^3 = 1000\)
\(C. (1^2+2^2)^4 = ( 1 + 4)^4 = 5^4 = 625 < 1000\)
\(D. (2^2+2^2+2^2)^3 = ( 4 + 4 + 4)^3 = 12^3 = (12^2)*12 = 144*12 > 1000\)
\(E. (2^2+2^2+2^2+2^2)^2 = ( 4 + 4 + 4 + 4)^2 = 16^2 = 256\)

Hence Option (D) seems to be the greatest, whereas OA = C.

Please look into it...

Best,
Gladi
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Originally posted by Gladiator59 on 26 Mar 2018, 00:15.
Last edited by Gladiator59 on 26 Mar 2018, 03:53, edited 1 time in total.
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Re: Which of the following is the greatest?  [#permalink]

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New post 26 Mar 2018, 02:20
MathRevolution wrote:
[GMAT math practice question]

Which of the following is the greatest?

\(A. (1+2)^5\)
\(B. 10^3\)
\(C. (1^2+2^2)^4\)
\(D. (2^2+2^2+2^2)^3\)
\(E. (2^2+2^2+2^2+2^2)^2\)


\(A. (1+2)^5 = 3^5\)
\(B. 10^3= 5^3*2^3 = 8*5^3\)
\(C. (1^2+2^2)^4 = 5^4\)
\(D. (2^2+2^2+2^2)^3= 12^3\)
\(E. (2^2+2^2+2^2+2^2)^2 = 16^2 = 4^4\)
4^4 <5^4 < 8*5^3 = 10^3 < 12^3
Also 3^5 = 243 < 4^4 = 256
A. < E. < C. < B. < D.

Answer D
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Re: Which of the following is the greatest?  [#permalink]

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New post 26 Mar 2018, 03:22
MathRevolution wrote:
[GMAT math practice question]

Which of the following is the greatest?

\(A. (1+2)^5\)
\(B. 10^3\)
\(C. (1^2+2^2)^4\)
\(D. (2^2+2^2+2^2)^3\)
\(E. (2^2+2^2+2^2+2^2)^2\)


OA should be D.
MathRevolution Please correct it.

Option A : \((1+2)^5\) = 3^5 =243
Option B : \(10^3\) = 1000
Option C :\((1^2+2^2)^4\) = \(5^4\)=625
Option D :\((2^2+2^2+2^2)^3\) = \(12^3\)=1728
Option E :\((2^2+2^2+2^2+2^2)^2\) = \(16^2\) = 256

We can put it more clearly
Option A: 243
Option B: 1000
Option C: 625
Option D: 1728
Option E: 256
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Re: Which of the following is the greatest?  [#permalink]

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New post 26 Mar 2018, 03:34
1
Gladiator59 wrote:
MathRevolution wrote:
[GMAT math practice question]

Which of the following is the greatest?

\(A. (1+2)^5\)
\(B. 10^3\)
\(C. (1^2+2^2)^4\)
\(D. (2^2+2^2+2^2)^3\)
\(E. (2^2+2^2+2^2+2^2)^2\)


Hi MathRevolution,

I think the OA provided is incorrect.

\(A. (1+2)^5 = 3^5 = (3^3)^2 = 27^2 <1000\)

\(B. 10^3 = 1000\)
\(C. (1^2+2^2)^4 = ( 1 + 4)^4 = 5^4 = 625 < 1000\)
\(D. (2^2+2^2+2^2)^3 = ( 4 + 4 + 4)^3 = 12^3 = (12^2)*12 = 144*12 > 1000\)
\(E. (2^2+2^2+2^2+2^2)^2 = ( 4 + 4 + 4 + 4)^2 = 16^2 = 256\)

Hence Option (D) seems to be the greatest, whereas OA = C.

Please look into it...

Best,
Gladi


Gladiator59
Hi Gladi

I think that there is a mistake in calculation of option A.

\(3^5\) should be equal to \(3^3*3^2\)
as \((3^3)^2\)= \(3^3\)*\(3^3\)=\(3^6\)

regards for pointing out mistake in OA
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Re: Which of the following is the greatest?  [#permalink]

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New post 26 Mar 2018, 03:54
Princ wrote:
Gladiator59 wrote:
MathRevolution wrote:
[GMAT math practice question]

Which of the following is the greatest?

\(A. (1+2)^5\)
\(B. 10^3\)
\(C. (1^2+2^2)^4\)
\(D. (2^2+2^2+2^2)^3\)
\(E. (2^2+2^2+2^2+2^2)^2\)


Hi MathRevolution,

I think the OA provided is incorrect.

\(A. (1+2)^5 = 3^5 = (3^3)^2 = 27^2 <1000\)

\(B. 10^3 = 1000\)
\(C. (1^2+2^2)^4 = ( 1 + 4)^4 = 5^4 = 625 < 1000\)
\(D. (2^2+2^2+2^2)^3 = ( 4 + 4 + 4)^3 = 12^3 = (12^2)*12 = 144*12 > 1000\)
\(E. (2^2+2^2+2^2+2^2)^2 = ( 4 + 4 + 4 + 4)^2 = 16^2 = 256\)

Hence Option (D) seems to be the greatest, whereas OA = C.

Please look into it...

Best,
Gladi


Gladiator59
Hi Gladi

I think that there is a mistake in calculation of option A.

\(3^5\) should be equal to \(3^3*3^2\)
as \((3^3)^2\)= \(3^3\)*\(3^3\)=\(3^6\)

regards for pointing out mistake in OA


Thanks for pointing out Princ,

Edited the post.

Best,
Gladi
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Re: Which of the following is the greatest?  [#permalink]

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New post 26 Mar 2018, 08:59
Top Contributor
MathRevolution wrote:
[GMAT math practice question]

Which of the following is the greatest?

\(A. (1+2)^5\)
\(B. 10^3\)
\(C. (1^2+2^2)^4\)
\(D. (2^2+2^2+2^2)^3\)
\(E. (2^2+2^2+2^2+2^2)^2\)


A. (1 + 2)^5 = (3)^5 = 243
B. 10^3 = 1,000
C. (1^2 + 2^2)^4 = (1 + 4)^4 = (5)^4 = 625
D. (2^2 + 2^2 + 2^2)^3 = (4 + 4 + 4)^3 = (12)^3
ASIDE: I won't bother evaluating this right now. We can already see that 12^3 is greater than 10^3 so, at the moment, D is the greatest value.

E. (2^2 + 2^2 + 2^2 + 2^2)^2 = (4 + 4 + 4 + 4)^2 = (16)^2 = 256

Answer: D

Cheers,
Brent
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Re: Which of the following is the greatest?  [#permalink]

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New post 28 Mar 2018, 01:01
=>

\(A. (1+2)^5 = 3^5 = 243\)
\(B. 10^3 = 1000\)
\(C. (1^2+2^2)^4 = 5^4 = 625\)
\(D. (2^2+2^2+2^2)^3 = 12^3 = 1728\)
\(E. (2^2+2^2+2^2+2^2)^2 = 16^2 = 256\)

Therefore, D is the answer.

Answer: D
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Re: Which of the following is the greatest?   [#permalink] 28 Mar 2018, 01:01

Which of the following is the greatest?

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