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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b?

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Math Expert V
Joined: 02 Sep 2009
Posts: 58449
If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 91% (01:38) correct 9% (02:44) wrong based on 91 sessions

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If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b?

A. 35
B. 42
C. 45
D. 49
E. 54

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Re: If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b?  [#permalink]

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a=105 = 3* 5 *7
a^3 = 21 × 25 × 45 × b
=> a^3 = (7*3) x (5*5) x ( 3^2 * 5) x b
=> a^3 = 3^3 * 5^3 * 7 x b
=>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x b
b = 7^2 = 49

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Joined: 12 Sep 2015
Posts: 4009
Re: If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b?  [#permalink]

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Bunuel wrote:
If a = 105 and a³ = 21 × 25 × 45 × b, what is the value of b?

A. 35
B. 42
C. 45
D. 49
E. 54

This question calls for some prime factorization

a = 105 = (3)(5)(7)

So, a³ = [(3)(5)(7)]³ = (3)(3)(3)(5)(5)(5)(7)(7)(7)

We're told that a³ = 21 × 25 × 45 × b

Take: a³ = (3)(3)(3)(5)(5)(5)(7)(7)(7)
Rewrite as: a³ = (3)(3)(3)(5)(5)(5)(7)(7)(7) = (3)(3)(21)(5)(5)(5)(7)(7)
Now rewrite as: a³ = (3)(3)(21)(5)(5)(5)(7)(7) = (3)(3)(21)(25)(5)(7)(7)
Now rewrite as: a³ = (3)(3)(21)(25)(9)(7)(7) = (21)(25)(45)(7)(7)

If 21 × 25 × 45 × b = (21)(25)(45)(7)(7), then b = (7)(7) = 49

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_________________ Re: If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b?   [#permalink] 16 Oct 2018, 12:51
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If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b?

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