Algebra
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- John fran kennedi
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Hello guys, I have just practiced the GMAT, as we can see on this image , I get confused to solve this. I have seen the answer explanation , but I don't understand well. I don't know whether because I don't get the question well or not.
In the answer explanation ( OG 2016) page 245, it states
=10,000(0.0012)-100(0.0012)
=12,12 - 0,12
I don't know why it's 12,12, not 12.
I do need your help to make me understand. Thanks in advance
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- Brent@GMATPrepNow
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(10� - 10²)(0.00121212...) = 10�(0.00121212...) - 10²(0.00121212...)A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 - 10^2) (0.0012)?
Note: There is a bar over "12" in 0.0012.
(A) 0
(B) 0.12 (with the bar over the 12)
(C) 1.2
(D) 10
(E) 12
= 12.121212... - 0.121212...
= 12 (since the decimal parts, in blue, are identical, they cancel out]
Answer: E
Cheers,
Brent
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- Brent@GMATPrepNow
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We can also apply some number sense here.A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 - 10^2) (0.0012)?
Note: There is a bar over "12" in 0.0012.
(A) 0
(B) 0.12 (with the bar over the 12)
(C) 1.2
(D) 10
(E) 12
(10� - 10²)(0.00121212...) = (10,000 - 100)(0.00121212...)
= 9900(0.00121212...)
= (a bit less than 10,000)(0.00121212...)
Well, (10,000)(0.00121212...) = 12.121212
So, (a bit less than 10,000)(0.00121212...) = a bit less than 12.121212...
Check the answer choices:
A) 0
B) 0.121212...
C) 1.2
D) 10
E) 12
E is the best match
Cheers,
Brent
- John fran kennedi
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Another idea here: since (xy/99) = .xyxyxyxy..., we can say that
.0012121212... =
.12121212... * (1/100) =
12/99 * 1/100 =
12/9900
Now we have
(10� - 10²) * 12/9900 =
9900 * 12/9900 =
12
and we're set!
.0012121212... =
.12121212... * (1/100) =
12/99 * 1/100 =
12/9900
Now we have
(10� - 10²) * 12/9900 =
9900 * 12/9900 =
12
and we're set!
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- ceilidh.erickson
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A common mistake that students make on a problem like this is to subtract the exponents. But of course we cannot subtract the exponents when we're subtracting terms with the same base.
More on this here: https://www.beatthegmat.com/fdp-problem- ... tml#763953
More on this here: https://www.beatthegmat.com/fdp-problem- ... tml#763953
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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- Scott@TargetTestPrep
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Remember that the notation [12] means there is a bar over the 12, indicating that the decimal is non-terminating.A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 - 10^2) (0.0012)?
Note: There is a bar over "12" in 0.0012.
(A) 0
(B) 0.12 (with the bar over the 12)
(C) 1.2
(D) 10
(E) 12
Now, let's start the problem by factoring out 10^2 from (10^4 - 10^2). This gives us:
(10^4 - 10^2) (0.00[12])
10^2 (10^2 - 1)(0.00[12])
We can distribute 0.00[12] with the two quantities in the parentheses. This gives us:
10^2(0.[12] - 0.00[12])
100(0.[12] - 0.00[12])
12.[12] - 0.[12] = 12
Answer: E
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