Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60540

Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
11 Nov 2019, 02:26
Question Stats:
37% (01:43) correct 63% (01:42) wrong based on 156 sessions
HideShow timer Statistics
Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level Questions
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5701
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
11 Nov 2019, 07:28
Bunuel wrote: Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level Questions1.002^4 = ~ 1.008 IMO C



VP
Joined: 19 Oct 2018
Posts: 1293
Location: India

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
11 Nov 2019, 09:54
\((1+\frac{1}{500})^4\)= \(1+4C1(1)^3(\frac{1}{500})+ 4C2 (1)^2 (\frac{1}{500})^2+4C3 (1) (\frac{1}{500})^3+4C4 (\frac{1}{500})^4\) \(6*(\frac{1}{500})^2\)= .0000015 This is so small that we can neglect it or any higher power of (1/500) Hence, neglect third, fourth and fifth term of the binomial expansion. \(1.002^4 =\) \(1+\frac{4}{500}\)=1.008 ORIf you're not familiar with the binomial expansion, you can write \((1.002)^4= (1.002)^2 *(1.002)^2\) \((1+0.002)^2= 1+2*1*0.002+(0.002)^2\)= 1.004......as we can neglect \((0.002)^2\) \((1.002)^4= (1.004)^2\) \((1+0.004)^2= 1+2*1*0.004+(0.004)^2\)= 1.008......as we can neglect \((0.004)^2\) Bunuel wrote: Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level Questions



VP
Joined: 20 Jul 2017
Posts: 1240
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
11 Nov 2019, 10:25
Bunuel wrote: Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level Questions\(1.002^4 = (1 + 0.002)^4\) = \( (1 + 0.002)^2*(1 + 0.002)^2 \) = \((1 + 2*0.002 + 0.002^2)* (1 + 2*0.002 + 0.002^2) \) Neglect \( 0.002^2 (= 0.000004) \) = \((1 + 0.004)*(1 + 0.004) \) = \((1 + 0.004)^2 \) = \( 1 + 2*0.004 + 0.004^2 \) = \( 1 + 0.008 + 0.000016 \) = \( 1.008016 \) Rounded to 3 decimal places = 1.008 IMO Option C Posted from my mobile device



Intern
Joined: 16 Apr 2019
Posts: 15
Location: India
GPA: 3.52

Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
14 Nov 2019, 22:03
Bunuel wrote: Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level QuestionsStep 1: calculate (1.002)^2 = 1 + (0.002)^2+ 2*(0.002) = 1.004 (because we want only first 3 digits and square of 0.002 will be 6 digits). Step 2: calculate 1.004^2 = 1 + 0.008 = 1.008 (using the same logic as in step 1). Ans = 0.008, Option C



Manager
Joined: 20 Aug 2017
Posts: 102

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
20 Nov 2019, 02:19
Archit3110 wrote: Bunuel wrote: Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level Questions1.002^4 = ~ 1.008 IMO C Did you use a calculator? or is there some trick to visualize this.



Manager
Joined: 20 Aug 2017
Posts: 102

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
20 Nov 2019, 02:25
We can write this fraction as a binomial  (1+0.002)^4. now applying approximation, we have (1+x)^n = 1 + n*x + \(\frac{n(n1)}{2}\)*x^2 so, our expression becomes = 1 +4*0.002 + \(\frac{4*3}{2}\)*(0.002)^2 The third term is very small and the number can be approximated to 1.008 OA  CBunuel wrote: Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level Questions



Senior Manager
Joined: 21 Jun 2017
Posts: 395
Location: India
Concentration: Finance, Economics
GPA: 3
WE: Corporate Finance (Commercial Banking)

Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
04 Jan 2020, 04:00
nick1816 wrote: \((1+\frac{1}{500})^4\)= \(1+4C1(1)^3(\frac{1}{500})+ 4C2 (1)^2 (\frac{1}{500})^2+4C3 (1) (\frac{1}{500})^3+4C4 (\frac{1}{500})^4\) \(6*(\frac{1}{500})^2\)= .0000015 This is so small that we can neglect it or any higher power of (1/500) Hence, neglect third, fourth and fifth term of the binomial expansion. \(1.002^4 =\) \(1+\frac{4}{500}\)=1.008 ORIf you're not familiar with the binomial expansion, you can write \((1.002)^4= (1.002)^2 *(1.002)^2\) \((1+0.002)^2= 1+2*1*0.002+(0.002)^2\)= 1.004......as we can neglect \((0.002)^2\) \((1.002)^4= (1.004)^2\) \((1+0.004)^2= 1+2*1*0.004+(0.004)^2\)= 1.008......as we can neglect \((0.004)^2\) Bunuel wrote: Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level QuestionsHi nick1816, Have you used nc0 + nc1 + ... ncn = 2^n or you have used ncr (p)^r (q)^nr If not, can you please explain the binomial approch a bit more ? Regards



VP
Joined: 19 Oct 2018
Posts: 1293
Location: India

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
04 Jan 2020, 04:23
\((1+x)^n= 1+ nC1*x + nC2*x^2 +.........+ nC(n1)x^{n1} + nCn* x^n\) second or greater powers of x are so small that they won't affect the third decimal place; hence, you can neglect them. ShankSouljaBoi wrote: nick1816 wrote: \((1+\frac{1}{500})^4\)= \(1+4C1(1)^3(\frac{1}{500})+ 4C2 (1)^2 (\frac{1}{500})^2+4C3 (1) (\frac{1}{500})^3+4C4 (\frac{1}{500})^4\) \(6*(\frac{1}{500})^2\)= .0000015 This is so small that we can neglect it or any higher power of (1/500) Hence, neglect third, fourth and fifth term of the binomial expansion. \(1.002^4 =\) \(1+\frac{4}{500}\)=1.008 ORIf you're not familiar with the binomial expansion, you can write \((1.002)^4= (1.002)^2 *(1.002)^2\) \((1+0.002)^2= 1+2*1*0.002+(0.002)^2\)= 1.004......as we can neglect \((0.002)^2\) \((1.002)^4= (1.004)^2\) \((1+0.004)^2= 1+2*1*0.004+(0.004)^2\)= 1.008......as we can neglect \((0.004)^2\) Bunuel wrote: Rounded to three decimal places, \(1.002^4 =\) (A) 1.004 (B) 1.006 (C) 1.008 (D) 1.012 (E) 1.016 Are You Up For the Challenge: 700 Level QuestionsHi nick, Have you used nc0 + nc1 + ... ncn = 2^n or you have used ncr (p)^r (q)^nr If not, can you please explain the binomial approch a bit more ? Regards



Senior Manager
Joined: 21 Jun 2017
Posts: 395
Location: India
Concentration: Finance, Economics
GPA: 3
WE: Corporate Finance (Commercial Banking)

Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
04 Jan 2020, 04:29
nick1816Would you use the binomial approach for (2.002 )^4 ?



VP
Joined: 19 Oct 2018
Posts: 1293
Location: India

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
04 Jan 2020, 05:00
\((a+x)^n= a^n+ nC1*a^{n1}*x + nC2*a^{n2}*x^2 +.........+ nC(n1)*a*x^{n1} + nCn* x^n\) \((2+0.002)^4 ≈ 2^4+ 4C1*2^3*0.002\) ShankSouljaBoi wrote: nick1816Would you use the binomial approach for (2.002 )^4 ?



Senior Manager
Joined: 12 Dec 2015
Posts: 474

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
04 Jan 2020, 07:41
Rounded to three decimal places, \(1.002^4 =\)
(A) 1.004 (B) 1.006 (C) 1.008 > correct: approximation: \((1+x)^n=1+xn\), if x <<1 i.e. x is very very small. so \(1.002^4 = (1+0.002)^4 = 1+0.002*4=1+0.008=1.008\) (D) 1.012 (E) 1.016



Director
Joined: 30 Sep 2017
Posts: 576
GMAT 1: 720 Q49 V40
GPA: 3.8

Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
Show Tags
06 Jan 2020, 08:09
(1.002)^2 = (1+0.002)^2 = 1 +2*0.002*1 +0.002^2 = ~1.004 (neglect the term 0.002^2 because it is negligibly small)
(1.002)^4 = ((1.002)^2)^2 = (1.004)^2 = (1+0.004)^2 = 1 +2*0.004*1 +0.004^2 = ~1.008 (neglect 0.004^2 because it is negligibly small)
Final answer is (C)
Posted from my mobile device




Re: Rounded to three decimal places, 1.002^4 =
[#permalink]
06 Jan 2020, 08:09






