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Sub 505 (Easy)|   Algebra|   Exponents|      
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Bunuel
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If (400)(6,000) = (240)(100^x), what is the value of x ? 14 Oct 2019, 08:02
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D
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If \((400)(6,000) = (240)(100^x)\), what is the value of x ?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
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D
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If (400)(6,000) = (240)(100^x), what is the value of x ? 01 Sep 2021, 14:28
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Bunuel
If \((400)(6,000) = (240)(100^x)\), what is the value of x ?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
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Here is a different approach:

Given: \((400)(6,000) = (240)(100^x)\)

Divide both sides of the equation by \(40\) to get: \((10)(6,000) = (6)(100^x)\)

Divide both sides of the equation by \(6\) to get: \((10)(1,000) = 100^x\)

Simplify the left side of the equation: \(10,000 = 100^x\)

Since we know that \(100^2 = 10,000\), the correct answer here is \(x = 2\)

Answer: D
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GMAT Focus 1: 735 Q90 V89 DI81
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If (400)(6,000) = (240)(100^x), what is the value of x ? 14 Oct 2019, 08:42
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Bunuel
If \((400)(6,000) = (240)(100^x)\), what is the value of x ?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
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\(400*6000=240*100^x......2400000=240*100^x.....240*100^2=240*100^x...x=2\)

D
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If (400)(6,000) = (240)(100^x), what is the value of x ? 14 Oct 2019, 08:57
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Answer is D. Reason being there would be 5 zeros in the result product out of which 1 zero is taken up by 240. Now remaining 4 zeroes will be adjusted in power of 100 which should be 2 to adjust 4 zeroes.

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If (400)(6,000) = (240)(100^x), what is the value of x ? 14 Oct 2019, 09:26
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Bunuel
If \((400)(6,000) = (240)(100^x)\), what is the value of x ?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Show more
\((400)(6,000) = (240)(100^x)\)

Or, \((240)(100^2) = (240)(100^x)\)

Hence, \(x = 2\), Answer must be (D)
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If (400)(6,000) = (240)(100^x), what is the value of x ? 14 Sep 2020, 08:29
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Method 1

By the Law of exponents, if \(a^x = a^y\), then x = y


\(400 * 6000 = (240) * (100^x)\)

\(240 * 10000 = (240) * (100^x)\)


\(100^2 = 100^x\)


Therefore x = 2


Method 2

400 * 6000 = 24 followed by 5 zeroes.

Since 240 has a zero, then \(100^x\) should have 4 zeroes and therefore x = 2


Option D

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If (400)(6,000) = (240)(100^x), what is the value of x ? 07 Apr 2026, 13:02
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