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If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b? A. 35
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24 Jun 2021, 09:37
24 Jun 2021, 09:37
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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
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? A. 35
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24 Jun 2021, 09:41
24 Jun 2021, 09:41
Carcass wrote:
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
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
Answer: D
gmatclubot
Re: If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b? A. 35 [#permalink]
24 Jun 2021, 09:41
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