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If x = (0.0753)(1856), then x satisfies which of the following

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AnkurGMAT20
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If x = (0.0753)(1856), then x satisfies which of the following [#permalink] If x = (0.0753)(1856), then x satisfies which of the following   14 Jan 2024, 10:36
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If x = (0.0753)(1856), then x satisfies which of the following inequalities?

A. x ≤ 1
B. 1 < x ≤ 10
C. 10 < x ≤ 100
D. 100 < x ≤ 1,000
E. 1,000 < x ≤ 10,000
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D
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gmatophobia
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Re: If x = (0.0753)(1856), then x satisfies which of the following [#permalink] If x = (0.0753)(1856), then x satisfies which of the following   14 Jan 2024, 11:06
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AnkurGMAT20 wrote:
If x = (0.0753)(1856), then x satisfies which of the following inequalities?

a) x ≤ 1
b) 1 <x≤ 10
c) 10 <x≤ 100
d) 100 <x≤ 1,000
e) 1,000 <x ≤ 10,000


\(\frac{753}{10000}*1856\)

\(\approx \frac{750}{10000}*1860\)

\(\approx \frac{75}{100}*186\)

\(\approx \frac{13950}{100}\)

\(\approx 139.50\)

Option D
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Re: If x = (0.0753)(1856), then x satisfies which of the following [#permalink] If x = (0.0753)(1856), then x satisfies which of the following   24 Jan 2024, 19:59
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If x = (0.0753)(1856), then x satisfies which of the following inequalities?

a) x ≤ 1
b) 1 <x≤ 10
c) 10 <x≤ 100
d) 100 <x≤ 1,000
e) 1,000 <x ≤ 10,000

(0.0753)(1856) ≈ 0.75 × 186 ≈ 3 × 46 = 138

Correct answer: (D)

Alternative Approach

Check the high end:

(0.0753)(1856) < (0.08)(1900) = 8 x 19 = 152

Eliminate (E).

Check the low end:

(0.0753)(1856) > (0.07)(1800) = 7 × 18 = 126

Eliminate (A), (B), and (C).

Correct answer: (D)
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Re: If x = (0.0753)(1856), then x satisfies which of the following [#permalink] If x = (0.0753)(1856), then x satisfies which of the following   30 Apr 2024, 14:33
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AnkurGMAT20 wrote:
If x = (0.0753)(1856), then x satisfies which of the following inequalities?

A. x ≤ 1
B. 1 < x ≤ 10
C. 10 < x ≤ 100
D. 100 < x ≤ 1,000
E. 1,000 < x ≤ 10,000

­The ranges here are huge, so we can likely round and approximate aggressively.

It's helpful to think of 0.0753 as about 7.5%, or 7.5 * 1%

We could round 1856 to 2000.

What is 1% of 2,000? We just move the decimal place 2 to the left, and get 20.

Then, 7.5 * 20 = 150, which is significantly more than 100, so we can safely choose D.

 
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Re: If x = (0.0753)(1856), then x satisfies which of the following [#permalink]
30 Apr 2024, 14:33
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