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99,999^2 - 1^2......

by Vincen » Wed Jan 24, 2018 8:42 am
$$99,999^2-1^2=$$

A. 10^10 - 2
B. (10^5 - 2)^2
C. 10^4(10^5 - 2)
D. 10^5(10^4 - 2)
E. 10^5(10^5 - 2)

The OA is the option E.

How can I solve this PS question fast? Is there a fast way? Thanks in advanced.
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Difference of two squares

by GMATGuruNY » Wed Jan 24, 2018 9:12 am
Vincen wrote:$$99,999^2-1^2=$$

A. 10^10 - 2
B. (10^5 - 2)^2
C. 10^4(10^5 - 2)
D. 10^5(10^4 - 2)
E. 10^5(10^5 - 2)
One approach:
99,999 = 100,000 - 1 = 10� - 1.

Thus:
99,999² - 1²

= (10� - 1)² - 1²

= (10�)² - 2(10�)(1) + 1² - 1²

= (10�)² - 2(10�)

= 10�(10� - 2).

The correct answer is E.

Alternate approach:
a² - b² = (a+b)(a-b).

Thus:
99,999² - 1²

= (99,999 + 1)(99,999 - 1)

= (100,000)(99,998)

= (10�)(10� - 2).
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by Jeff@TargetTestPrep » Mon Jan 29, 2018 9:49 am
Vincen wrote:$$99,999^2-1^2=$$

A. 10^10 - 2
B. (10^5 - 2)^2
C. 10^4(10^5 - 2)
D. 10^5(10^4 - 2)
E. 10^5(10^5 - 2)
We can use the difference of squares, and we have:

(99,999 + 1)(99,999 - 1)

100,000 x 99,998

10^5 x 99,998

10^5(10^5 - 2)

Answer: E

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[email protected]

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