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# 2^32 – 2^30 is equivalent to which of the following?

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Math Expert
Joined: 02 Sep 2009
Posts: 58458
2^32 – 2^30 is equivalent to which of the following?  [#permalink]

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22 Jan 2019, 01:54
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15% (low)

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76% (00:45) correct 24% (00:31) wrong based on 58 sessions

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$$2^{32} – 2^{30}$$ is equivalent to which of the following?

A 2^2
B 2^2*3
C 2^10
D 2^30
E 2^30*3

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2^32 – 2^30 is equivalent to which of the following?  [#permalink]

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22 Jan 2019, 01:58
Bunuel wrote:
$$2^{32} – 2^{30}$$ is equivalent to which of the following?

A 2^2
B 2^2*3
C 2^10
D 2^30
E 2^30*3

Given ,

$$2^{32} – 2^{30}$$

$$2^{30} (2^2 - 1)$$

2^30*3

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Re: 2^32 – 2^30 is equivalent to which of the following?  [#permalink]

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22 Jan 2019, 05:01
Bunuel wrote:
$$2^{32} – 2^{30}$$ is equivalent to which of the following?

A 2^2
B 2^2*3
C 2^10
D 2^30
E 2^30*3

simplify given expression
we get
2^30*3
IMO E
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Joined: 26 Dec 2018
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Concentration: Finance, Economics
Re: 2^32 – 2^30 is equivalent to which of the following?  [#permalink]

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22 Jan 2019, 17:34
Bunuel wrote:
$$2^{32} – 2^{30}$$ is equivalent to which of the following?

A 2^2
B 2^2*3
C 2^10
D 2^30
E 2^30*3

(a^n)*(a^m)=a^nm

Here we see an opportunity to factor out a term due to the distributive power of exponents.

(2^32)-(2^30)=(2^30)*((2^2)-1)=(2^30)*(4-1)=(2^30)*3

E

Please critique if you see fit!
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Re: 2^32 – 2^30 is equivalent to which of the following?  [#permalink]

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22 Jan 2019, 18:51
Bunuel wrote:
$$2^{32} – 2^{30}$$ is equivalent to which of the following?

A 2^2
B 2^2*3
C 2^10
D 2^30
E 2^30*3

$$2^{32} – 2^{30}$$
$$2^{30} (4 - 1)$$

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Re: 2^32 – 2^30 is equivalent to which of the following?   [#permalink] 22 Jan 2019, 18:51
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