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# M15-21

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Math Expert
Joined: 02 Sep 2009
Posts: 55732

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16 Sep 2014, 00:56
00:00

Difficulty:

95% (hard)

Question Stats:

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

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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. $$6402.0 \lt x \lt 6402.5$$

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Math Expert
Joined: 02 Sep 2009
Posts: 55732

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16 Sep 2014, 00:56
1
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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.

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Joined: 01 Aug 2014
Posts: 54
Schools: Rotman '17 (A)
GMAT 1: 710 Q44 V42

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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
Math Expert
Joined: 02 Aug 2009
Posts: 7756

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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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Joined: 01 Aug 2014
Posts: 54
Schools: Rotman '17 (A)
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22 Jan 2016, 22:09
Ah, thank you chetan2u, got it!
Intern
Joined: 16 Dec 2015
Posts: 3

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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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Joined: 28 Aug 2016
Posts: 88
Concentration: Strategy, General Management

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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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Posts: 422
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
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25 Jan 2017, 07:50
Thanks for the solution .... this one was a bit tricky ....
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" The few , the fearless "
Intern
Joined: 31 Oct 2016
Posts: 3
GMAT 1: 460 Q38 V17

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01 Feb 2017, 07:41
Good question. Thanks for the solution... Much faster than doing long multiplication
Intern
Joined: 02 Oct 2017
Posts: 2
Location: United Kingdom
WE: Securities Sales and Trading (Investment Banking)

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04 Mar 2018, 13:53
I think this is a high-quality question and I agree with explanation.
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Joined: 31 Jul 2017
Posts: 211
Location: Tajikistan

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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.

Hi Bunuel,

Where is the part highlighted?
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Math Expert
Joined: 02 Sep 2009
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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.

Hi Bunuel,

Where is the part highlighted?

What do you mean by "where"?
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Joined: 11 Oct 2016
Posts: 12
GMAT 1: 680 Q48 V35
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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.

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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Joined: 09 Jun 2014
Posts: 271
Location: India
Concentration: General Management, Operations
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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!!
Intern
Joined: 17 Aug 2017
Posts: 3
GMAT 1: 620 Q49 V26
GMAT 2: 620 Q47 V28

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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
Re: M15-21   [#permalink] 26 Nov 2018, 02:59
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# M15-21

Moderators: chetan2u, Bunuel