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M15-21

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M15-21  [#permalink]

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New post 16 Sep 2014, 00:56
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (01:10) correct 61% (00:58) wrong based on 160 sessions

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Re M15-21  [#permalink]

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New post 16 Sep 2014, 00:56
1
1
Official Solution:

If \(x = 80.0127^2\), which of the following is true about \(x\)?

A. \(6400.0 \lt x \lt 6400.5\)
B. \(6400.5 \lt x \lt 6401.0\)
C. \(6401.0 \lt x \lt 6401.5\)
D. \(6401.5 \lt x \lt 6402.0\)
E. \(6402.0 \lt x \lt 6402.5\)


\(80.0127^2\) is slightly larger than \(80.0125^2 = (80 + 0.0125)^2 = 80^2 + 2*80*0.0125 + 0.0125^2 =\)

\(=6400 + 2 + 0.0125^2 = 6402 + 0.0125^2\).

Among the listed choices only in E is \(x\) larger than 6402.


Answer: E
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Re: M15-21  [#permalink]

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New post 22 Jan 2016, 21:29
I love the approach of breaking up the numbers to analyze them, very smart.

I understand how \(80^2\) and \(.0125^2\) are derived, but where does the 2 come from? Thanks
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Re: M15-21  [#permalink]

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New post 22 Jan 2016, 21:43
Anonamy wrote:
I love the approach of breaking up the numbers to analyze them, very smart.

I understand how \(80^2\) and \(.0125^2\) are derived, but where does the 2 come from? Thanks



hi,
the formula for \((a+b)^2 is a^2 + 2ab + b^2\)
so that 2 is of 2ab or 2*80*.0125..
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Re: M15-21  [#permalink]

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New post 22 Jan 2016, 22:09
Ah, thank you chetan2u, got it!
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Re: M15-21  [#permalink]

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New post 17 Sep 2016, 04:50
Question stem has a 80.127^2 whereas the explanation has taken 80.125^2. This changes the answer completely. Please correct the error in the question stem
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M15-21  [#permalink]

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New post 29 Sep 2016, 14:49
ryanoberoi wrote:
Question stem has a 80.127^2 whereas the explanation has taken 80.125^2. This changes the answer completely. Please correct the error in the question stem


I think you misunderstood the question and the explanation.

The explanation took 80.125^2 because it is easier to calculate than 80.127^2.

Since 80.125^2 < 80.127^2

if any of the answer choices are smaller than 80.125^2, then it must be wrong.

Because only E is larger than 80.125^2, it must be the answer.

Hope this helps.
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Re: M15-21  [#permalink]

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New post 25 Jan 2017, 07:50
Thanks for the solution .... this one was a bit tricky ....
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Re: M15-21  [#permalink]

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New post 01 Feb 2017, 07:41
Good question. Thanks for the solution... Much faster than doing long multiplication
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Re M15-21  [#permalink]

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New post 04 Mar 2018, 13:53
I think this is a high-quality question and I agree with explanation.
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Re: M15-21  [#permalink]

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New post 30 Jun 2018, 03:36
Bunuel wrote:
Official Solution:

If \(x = 80.0127^2\), which of the following is true about \(x\)?

A. \(6400.0 \lt x \lt 6400.5\)
B. \(6400.5 \lt x \lt 6401.0\)
C. \(6401.0 \lt x \lt 6401.5\)
D. \(6401.5 \lt x \lt 6402.0\)
E. \(6402.0 \lt x \lt 6402.5\)


\(80.0127^2\) is slightly larger than \(80.0125^2 = (80 + 0.0125)^2 = 80^2 + 2*80*0.0125 + 0.0125^2 =\)

\(=6400 + 2 + 0.0125^2 = 6402 + 0.0125^2\).

Among the listed choices only in E is \(x\) larger than 6402.


Answer: E




Hi Bunuel,

Where is the part highlighted?
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Re: M15-21  [#permalink]

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New post 30 Jun 2018, 10:20
nigina93 wrote:
Bunuel wrote:
Official Solution:

If \(x = 80.0127^2\), which of the following is true about \(x\)?

A. \(6400.0 \lt x \lt 6400.5\)
B. \(6400.5 \lt x \lt 6401.0\)
C. \(6401.0 \lt x \lt 6401.5\)
D. \(6401.5 \lt x \lt 6402.0\)
E. \(6402.0 \lt x \lt 6402.5\)


\(80.0127^2\) is slightly larger than \(80.0125^2 = (80 + 0.0125)^2 = 80^2 + 2*80*0.0125 + 0.0125^2 =\)

\(=6400 + 2 + 0.0125^2 = 6402 + 0.0125^2\).

Among the listed choices only in E is \(x\) larger than 6402.


Answer: E




Hi Bunuel,

Where is the part highlighted?


What do you mean by "where"?
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Re: M15-21  [#permalink]

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New post 02 Sep 2018, 18:34
nigina93 wrote:
Bunuel wrote:
Official Solution:

If \(x = 80.0127^2\), which of the following is true about \(x\)?

A. \(6400.0 \lt x \lt 6400.5\)
B. \(6400.5 \lt x \lt 6401.0\)
C. \(6401.0 \lt x \lt 6401.5\)
D. \(6401.5 \lt x \lt 6402.0\)
E. \(6402.0 \lt x \lt 6402.5\)


\(80.0127^2\) is slightly larger than \(80.0125^2 = (80 + 0.0125)^2 = 80^2 + 2*80*0.0125 + 0.0125^2 =\)

\(=6400 + 2 + 0.0125^2 = 6402 + 0.0125^2\).

Among the listed choices only in E is \(x\) larger than 6402.


Answer: E




Hi Bunuel,

Where is the part highlighted?


2*80*0.0125 = 2
and that's how you arrive at 6400 + 2 + 0.0125^2
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Re: M15-21  [#permalink]

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New post 31 Oct 2018, 23:59
Bunuel wrote:
If \(x = 80.0127^2\), which of the following is true about \(x\)?

A. \(6400.0 \lt x \lt 6400.5\)
B. \(6400.5 \lt x \lt 6401.0\)
C. \(6401.0 \lt x \lt 6401.5\)
D. \(6401.5 \lt x \lt 6402.0\)
E. \(6402.0 \lt x \lt 6402.5\)




Conceptual issues tested and corrected.Suppose I have a number 10.5..and now I want find the square of this number..now what i was thinking is 100.25..but hold on..

see actual is 110.25 so its a big big difference...

Good quality question!!
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Re: M15-21  [#permalink]

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New post 26 Nov 2018, 02:59
I solved it in bit different manner...
80 + 0.0127

What happens that after seeing answer choices so close, I felt rounding off will make things difficult.
for second part - 2*80*0.0127
2*80*127/10000
16 * 127/1000
1270 + 127*6 = 2032
which will give 2 hence option E
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Re: M15-21   [#permalink] 26 Nov 2018, 02:59
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