GMAT Question Pack 1 hard

[fangtray]

(1.00001)(0.99999) - (1.00002)(0.99998) =

a. 0
b. 10^-10
c. 3(10^-10)
d. 10^-5
e. 3(10^-5)

[GMATGuruNY]

(1.00001)(0.99999) - (1.00002)(0.99998) =

a. 0
b. 10^-10
c. 3(10^-10)
d. 10^-5
e. 3(10^-5)

1.00001 = 1+10ˉ�
.99999 = 1-10ˉ�
1.00002 = 1+2(10ˉ�)
.99998 = 1-2(10ˉ�)

Thus:
(1.00001)(0.99999) - (1.00002)(0.99998)

= (1+10ˉ�)(1-10ˉ�) - (1 + 2*10ˉ�)(1 - 2*10ˉ�) [Note the difference of two squares: (x+y)(x-y) = x²-y²]

= (1 - 10ˉ¹�) - (1 - 4*10ˉ¹�)

= 3*10ˉ¹�

The correct answer is C.

[fangtray]

(1.00001)(0.99999) - (1.00002)(0.99998) =

a. 0
b. 10^-10
c. 3(10^-10)
d. 10^-5
e. 3(10^-5)

1.00001 = 1+10ˉ�
.99999 = 1-10ˉ�
1.00002 = 1+2(10ˉ�)
.99998 = 1-2(10ˉ�)

Thus:
(1.00001)(0.99999) - (1.00002)(0.99998)

= (1+10ˉ�)(1-10ˉ�) - (1 + 2*10ˉ�)(1 - 2*10ˉ�) [Note the difference of two squares: (x+y)(x-y) = x²-y²]

= (1 - 10ˉ¹�) - (1 - 4*10ˉ¹�)

= 3*10ˉ¹�

The correct answer is C.

when i came across this problem on the exam.. i went the approach of 100001*10^-5..and ended up getting nowhere.. you only have 1 real shot at it in 2 minutes..any tips on how to spot which way to simplify?

[ihatemaths]

take 1.00000 = X so the problem can be expressed as (X + (1*10^-5)(X - (1*10^-5)[/color] - (X + (2*10^-5)(X-(2*10^-5)

next step apply (X+Y)*(X-Y)=X^2 + Y^2 seperatley for both the terms we would get

(X^2-(1*10^-5)^2) -(X^2 -(2*10^-5)^2) on simplification we get -> (4*10^-10)-(1*10^-10)= 3 * 10^-10

Ans is C

[ankita1709]

Step 1 - Make it simple: Multiply and divide by 10^10
That makes it (100001)(99999)-(100002)(99998)

Step 2 - Now look closely because the most complicated looking problems are sometimes the simplest
lets say a = 100001
b = 99999

which makes it a*b -(a+1)(b-1)
=>a-b+1
=>(100001-99999+1)*10^-10
=> 3*(10^-10)

Hope it helps!

[GMATGuruNY]

(1.00001)(0.99999) - (1.00002)(0.99998) =

a. 0
b. 10^-10
c. 3(10^-10)
d. 10^-5
e. 3(10^-5)

when i came across this problem on the exam.. i went the approach of 100001*10^-5..and ended up getting nowhere.. you only have 1 real shot at it in 2 minutes..any tips on how to spot which way to simplify?

Perform the same operation with easier numbers.

(1.1)(.9) - (1.2)(.8)

= .99 - .96 = .03 = 3 * 10ˉ².

The rightmost digits here are the same as those in the actual problem.
The result here is 3 times a negative power of 10.
By extension, the correct answer must also be 3 times a negative power of 10.
Here, we're multiplying (11*10^-1) by (9*10^-1), yielding 10ˉ².
In the actual problem, we're multiplying (100001*10ˉ�) by (99999*10ˉ�), implying that the final product must include 10ˉ¹�.
Thus, the correct answer must be C: 3 * 10ˉ¹�.

[mcdesty]

Here is how I would think about this one.

[[email protected]]

Hi All,

It looks like most of the posters in this thread are probably long since done with their GMAT studies, but for anyone who might come across this question, it actually has a really big shortcut built into it that will allow you to avoid most of the "long math":

The first part of the calculation...

(1.00001)(0.99999)

...will have 10 decimal places (5 decimal points x 5 decimal points = 10 total decimal points) and the last digit will be a 9 (1 x 9 = 9

The second part of the calculation....

(1.00002)(0.99998)

....will also have 10 decimal places (for the same reason that the first part has 10 decimal points) and the last digit will be a 6 (2 x 8 = 16)

From the answers, we know that we'll be dealing with 10 to some "negative power"; subtracting the second number from the first would give us...

._ _ _ _ _ _ _ _ _ 9
._ _ _ _ _ _ _ _ _ 6
__________________
._ _ _ _ _ _ _ _ _ 3

So, which answer has a "3" in it and implies 10 decimal points?

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

Interestingly enough, this official GMAT question is very similar to this official question: https://www.beatthegmat.com/operations-o ... 77054.html

Cheers,
Brent