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# Of the following answer choices, which is the closest approximation of

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
Of the following answer choices, which is the closest approximation of  [#permalink]

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02 Sep 2016, 04:50
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:38) correct 33% (01:45) wrong based on 309 sessions

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Of the following answer choices, which is the closest approximation of $$\frac{1.97^2*7.199^2}{0.0098}$$

A. 1,447
B. 2,450
C. 20,520
D. 41,040
E. 205,200

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Posts: 592
Re: Of the following answer choices, which is the closest approximation of  [#permalink]

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02 Sep 2016, 05:58
1
Bunuel wrote:
Of the following answer choices, which is the closest approximation of $$\frac{1.97^2*7.199^2}{0.0098}$$

A. 1,447
B. 2,450
C. 20,520
D. 41,040
E. 205,200

This is how I tried.

let me take 1.97 ~ 2 approximately
and 7.199 ~ 7.2

and 98 ~ 100

Now ( 2 * 2 * 72 * 72) * 10000 / 98 * 10 * 10 => ( 2 * 2 * 72 * 72) * 10000 / 100 * 10 * 10

=> 4 *n4 * 72 * 72 => 20776 .
Only option C is close by.

OA please..will correct if I missed anything.
CEO
Joined: 11 Sep 2015
Posts: 3435
Re: Of the following answer choices, which is the closest approximation of  [#permalink]

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02 Sep 2016, 06:58
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Top Contributor
Bunuel wrote:
Of the following answer choices, which is the closest approximation of $$\frac{1.97^2*7.199^2}{0.0098}$$

A. 1,447
B. 2,450
C. 20,520
D. 41,040
E. 205,200

We can use a nice rule that says (a^n)(b^n) = (ab)^n

Also, since the answer choices are VERY spread apart, we can be quite AGGRESSIVE in our approximations.
We'll recognize that 1.97 x 7.199 ≈ 14
And 14² ≈ 200
And 0.0098 ≈ 0.01 ≈ 1/100

[(1.97²)(7.199²)]/0.0098 ≈ [14²]/0.0098
≈ [200]/0.01
≈ 200/(1/100)
≈ (200)(100/1)
≈ (200)(100)
≈ 20,000

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Re: Of the following answer choices, which is the closest approximation of  [#permalink]

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18 Dec 2018, 11:59
Bunuel wrote:
Of the following answer choices, which is the closest approximation of $$\frac{1.97^2*7.199^2}{0.0098}$$

A. 1,447
B. 2,450
C. 20,520
D. 41,040
E. 205,200

Got this wrong on the first attempt, then understood why, so here is another way, Hope this solution helps .

1.97 $$\approx$$ 2 so $$2^2$$= 4
7.199 $$\approx$$ 7 so $$7^2$$=49
So in numerator we have 4*49 =196

Denominator =0.0098 $$\approx$$ .01, so finally we have $$\frac{196}{.01}$$ =19600 which is closest to C.
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Re: Of the following answer choices, which is the closest approximation of   [#permalink] 18 Dec 2018, 11:59
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