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Operations on Rational Numbers OG-13, Q199

This topic has 3 expert replies and 0 member replies
AkiB Junior | Next Rank: 30 Posts Default Avatar
Joined
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Posted:
16 messages

Operations on Rational Numbers OG-13, Q199

Post Sat Jun 14, 2014 6:23 am

Timer

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Your Answer

A

B

C

D

E

Global Stats

Difficult



0.99999999/ 1.0001 - 0.99999991 /1.0003 =
(A) 10^-8
(B) 3(10^-8)
(C) 3(10^-4)
(D) 2(10^-4)
(E) 10^-4

What is the Easiest way to solve this

OA D

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GMAT/MBA Expert

Post Sat Jun 14, 2014 6:38 am
Quote:
0.99999999/1.0001 - 0.99999991/1.0003 =

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4
One approach is to recognize that both 9999.9999 and 9999.9991 can be rewritten as differences of squares.

First, 0.99999999 = 1 - 0.00000001
= (1 - 0.0001)(1 + 0.0001)

Similarly, 9999.9991 = 1 - 0.00000009
= (1 - 0.0003)(1 + 0.0003)

Original question: 0.99999999/1.0001 - 0.99999991/1.0003
= (1 - 0.0001)(1 + 0.0001)/(1.0001) - (1 - 0.0003)(1 + 0.0003)/(1.0003)
= (1 - 0.0001)(1.0001)/(1.0001) - (1 - 0.0003)(1.0003)/(1.0003)
= (1 - 0.0001) - (1 - 0.0003)
= 1 - 0.0001 - 1 + 0.0003
= 0.0002
= 2 x 10^(-4) = D

Cheers,
Brent

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GMAT/MBA Expert

Post Sat Jun 14, 2014 6:40 am
Quote:
0.99999999/1.0001 - 0.99999991/1.0003=

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4
Another approach is to combine the fractions and then use some APPROXIMATION.

First combine the fractions by finding a common denominator.
(9999.9999)/(10001) - (9999.9991)/(10003)
= (9999.9999)(10003)/(10001)(10003) - (9999.9991)(10001) /(10003)(10001)
= [(10003)(9999.9999) - (10001)(9999.9991)] / (10001)(10003)
≈ [(10003)(10^4) - (10001)(10^4)] / (10^4)(10^4) ... (approximately)
≈ [(10003) - (10001)] / (10^4) ... (divided top and bottom by 10^4)
≈ 2/(10^4)
≈ 2(10^-4)
= D

Cheers,
Brent

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GMAT/MBA Expert

Post Sun Jun 15, 2014 2:57 am
AkiB wrote:
0.99999999/ 1.0001 - 0.99999991 /1.0003 =
(A) 10^-8
(B) 3(10^-8)
(C) 3(10^-4)
(D) 2(10^-4)
(E) 10^-4
Alternate approach:
The answer choices imply that 1.0001 must divide easily into 0.99999999 and that 1.0003 must divide easily into 0.99999991.

x = 0.99999999/1.0001.
1.0001x = 0.99999999.
Notice the values in red.
For the product on the left to yield 0.99999999 -- a value with a rightmost digit of 9 -- the rightmost digit of x must be 9.

y = 0.99999991/1.0003.
1.0003y = 0.99999991.
Notice the values in red.
For the product on the left to yield 0.99999991 -- a value with a rightmost digit of 1 -- the rightmost digit of y must be 7.

Thus:
x-y = (value with a rightmost digit of 9) - (value with a rightmost digit of 7) = (value with a rightmost digit of 2).

Only one answer choice includes a digit of 2:
D: 2(10^-4) = 0.0002.

The correct answer is D.

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