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HiteshPunjabi
Updated on: 16 Jul 2013, 22:22
Originally posted by HiteshPunjabi on 02 Jan 2013, 18:58.
Last edited by Bunuel on 16 Jul 2013, 22:22, edited 4 times in total.
Last edited by Bunuel on 16 Jul 2013, 22:22, edited 4 times in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
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Question Stats:
76% (01:33) correct
24%
(01:26)
wrong
based on 331
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Which of the following is equal to 0.9998^2 ?
A. 0.99950014
B. 0.99950234
C. 0.99960004
D. 0.99960064
E. 0.99961024
M15-07
A. 0.99950014
B. 0.99950234
C. 0.99960004
D. 0.99960064
E. 0.99961024
M15-07
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17 Apr 2023, 02:45
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Official Solution:
What is the value of \(0.9998^2\)?
A. 0.99950014
B. 0.99950234
C. 0.99960004
D. 0.99960064
E. 0.99961024
APROACH 1:
Observe that the last two digits in the answer choices are different. Therefore, if we can find the last two digits of the required expression, we can identify the correct answer. The last two digits of \(0.9998*0.9998\) will be determined by the last two digits of their multiples. Next, \(98^2 = (100 - 2)^2 = 100^2 - 400 + 4 = 9604\). Therefore, the last two digits of \((0.9998)^2\) must be 04. Only option C fits.
APROACH 2:
Notice that 0.9998 is just 0.0002 away from 1: \(0.9998 + 0.0002 = 1\). How can we exploit this to simplify the calculation? If we had \(0.9998^2 - 0.0002^2\), we could apply the difference of squares formula (\(a^2 - b^2 = (a + b)(a - b)\)) and obtain \(0.9998^2 - 0.0002^2 = (0.9998 - 0.0002)(0.9998 + 0.0002) = 1*0.9996\). We don't have that, however, we could rewrite \(0.9998^2\) as \(0.9998^2 - 0.0002^2 + 0.0002^2\), which would be equal to:
Answer: C
What is the value of \(0.9998^2\)?
A. 0.99950014
B. 0.99950234
C. 0.99960004
D. 0.99960064
E. 0.99961024
APROACH 1:
Observe that the last two digits in the answer choices are different. Therefore, if we can find the last two digits of the required expression, we can identify the correct answer. The last two digits of \(0.9998*0.9998\) will be determined by the last two digits of their multiples. Next, \(98^2 = (100 - 2)^2 = 100^2 - 400 + 4 = 9604\). Therefore, the last two digits of \((0.9998)^2\) must be 04. Only option C fits.
APROACH 2:
Notice that 0.9998 is just 0.0002 away from 1: \(0.9998 + 0.0002 = 1\). How can we exploit this to simplify the calculation? If we had \(0.9998^2 - 0.0002^2\), we could apply the difference of squares formula (\(a^2 - b^2 = (a + b)(a - b)\)) and obtain \(0.9998^2 - 0.0002^2 = (0.9998 - 0.0002)(0.9998 + 0.0002) = 1*0.9996\). We don't have that, however, we could rewrite \(0.9998^2\) as \(0.9998^2 - 0.0002^2 + 0.0002^2\), which would be equal to:
\((0.9998^2 - 0.0002^2) + 0.0002^2 = \).
\(=(0.9998 - 0.0002)(0.9998 + 0.0002) + 0.0002^2 =\)
\(=1*0.9996 + 0.0002^2\) =
\(=0.9996 + 0.00000004 = 0.99960004\)
\(=(0.9998 - 0.0002)(0.9998 + 0.0002) + 0.0002^2 =\)
\(=1*0.9996 + 0.0002^2\) =
\(=0.9996 + 0.00000004 = 0.99960004\)
Answer: C
General Discussion
PrashantPonde
Joined: 27 Jun 2012
Last visit: 29 Jan 2025
Posts: 322
Given Kudos: 185
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
02 Jan 2013, 19:58
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Below is the easier way to solve:
Remember: \((a-b)^2 = a^2 - 2ab + b^2\)
Apply that to your problem:
\((0.9998) ^2 = (1 -0.0002)^2 = 1^2 - 2 (1) (0.0002) + (0.0002)^2 = 1 - 0.0004 + (0.0002)^2 = 0.9996 + 0.0000004 = 0.99960004\)
Hence choice (C) is the correct answer. (OA - choice (D) is incorrect. Verify using your calculator.)
Remember: \((a-b)^2 = a^2 - 2ab + b^2\)
Apply that to your problem:
\((0.9998) ^2 = (1 -0.0002)^2 = 1^2 - 2 (1) (0.0002) + (0.0002)^2 = 1 - 0.0004 + (0.0002)^2 = 0.9996 + 0.0000004 = 0.99960004\)
Hence choice (C) is the correct answer. (OA - choice (D) is incorrect. Verify using your calculator.)
