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99,998^2 − 2^2 =

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 49968
99,998^2 − 2^2 =  [#permalink]

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New post 19 Sep 2018, 23:36
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (01:06) correct 31% (01:43) wrong based on 71 sessions

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CEO
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Joined: 12 Sep 2015
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Location: Canada
Re: 99,998^2 − 2^2 =  [#permalink]

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New post 20 Sep 2018, 06:50
1
Top Contributor
Bunuel wrote:
\(99,998^2 − 2^2 =\)


(A) \(10^{10} − 4\)

(B) \((10^5 − 4)^2\)

(C) \(10^4(10^5 − 4)\)

(D) \(10^5(10^4 − 4)\)

(E) \(10^5(10^5 − 4)\)


Key concept: x² - y² = (x + y)(x - y)

So, 99,998² - 2² = (99,998 + 2)(99,998 - 2)
= (100,000)(99,996)
= (100,000)(100,000 - 4)
= (10⁵)(10⁵ - 4)

Answer: E

Cheers,
Brent
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Director
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99,998^2 − 2^2 =  [#permalink]

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New post 19 Sep 2018, 23:46
1
Bunuel wrote:
\(99,998^2 − 2^2 =\)


(A) \(10^{10} − 4\)

(B) \((10^5 − 4)^2\)

(C) \(10^4(10^5 − 4)\)

(D) \(10^5(10^4 − 4)\)

(E) \(10^5(10^5 − 4)\)


\(99,998^2 − 2^2\)=\((10^5-2)^2-2^2\)
Applying the formula: \(a^2-b^2=(a+b)(a-b)\), wher \(a=(10^5-2)\) and \(b=2\)

So, \((10^5-2)^2-2^2\)=\((10^5-2+2)*(10^5-2-2)\)=\(10^5(10^5 − 4)\)

Ans. (E)
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Re: 99,998^2 − 2^2 =  [#permalink]

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New post 19 Sep 2018, 23:53
Answer e

Sol: rewrite the expression in the form of (a - b)^2 - c^2. => (10^5 - 2)^2 - 2^2
Simplifying it = (10^5)^2 - ( 2. 10^5. 2)
= 10^5 ( 10^5 - 4 )

Henceforth option E.

Kudos please if you like the solution
Cheers
Hari
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99,998^2 − 2^2 =  [#permalink]

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New post 20 Sep 2018, 02:20
1
Bunuel wrote:
\(99,998^2 − 2^2 =\)


(A) \(10^{10} − 4\)

(B) \((10^5 − 4)^2\)

(C) \(10^4(10^5 − 4)\)

(D) \(10^5(10^4 − 4)\)

(E) \(10^5(10^5 − 4)\)



\(a^2-b^2 = (a+b) (a-b)\)

\(99998^2 - 2^2 = (99998 + 2) ( 99998 - 2)\)

99998 + 2 = 100000 =\(10^5\)

99998 - 2 = 99996 = 100000 - 4 = \(10^5 - 4\)

So,\(10^5(10^5 - 4)\)

The best answer is E.
Math Expert
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Joined: 02 Aug 2009
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Re: 99,998^2 − 2^2 =  [#permalink]

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New post 20 Sep 2018, 07:16
Bunuel wrote:
\(99,998^2 − 2^2 =\)


(A) \(10^{10} − 4\)

(B) \((10^5 − 4)^2\)

(C) \(10^4(10^5 − 4)\)

(D) \(10^5(10^4 − 4)\)

(E) \(10^5(10^5 − 4)\)



\(99,998^2 − 2^2 =\) straightway is in the form of a\(^2-b^2\) which is (a-b)(a+b)
so \(99,998^2 − 2^2 =(99,998-2)(99,998+2)=99,996*100,000=(100,000-4)*100,000=(10^5-4)*10^5\)
E

also 99,998 is just less than \(10^5\), so 99,998^2 will be just less than \(10^{10}\) AND the units digit will be 0 as \(8^2 -2^2\) means \(4-4 =0\)
let us see the choices

(A) \(10^{10} − 4\)... this choice is slightly less than \(10^{10}\) but it changes \(99,998^2\) to \(10^2\) so our answer has to be even lesser.. eliminate

(B) \((10^5 − 4)^2\)..... units digit will be \((10-6)^2=4^2\), so 6...eliminate

(C) \(10^4(10^5 − 4)\)..... \(10^9-4*10^4\).....this is just 1/10th of 10^10, so too less to be correct...eliminate

(D) \(10^5(10^4 − 4)\)..... \(10^9-4*10^5\).....this is just 1/10th of 10^10, so too less to be correct...eliminate

(E) \(10^5(10^5 − 4)\)....10^10-4*10^5..correct

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: 99,998^2 − 2^2 = &nbs [#permalink] 20 Sep 2018, 07:16
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