If there are fewer than 8 zeroes between the decimal point and the first nonzero digit in the decimal expansion of (t/1000)^4, which of the following numbers could be the value of t?
I. 3
II. 5
III. 9
A) None
B) I only
C) II only
D) III only
E) II and III
OA:A
OG 2017 - If there are fewer than
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- fiza gupta
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Hi fiza gupta,
This question was discussed here:
https://www.beatthegmat.com/number-t292641.html#782186
GMAT assassins aren't born, they're made,
Rich
This question was discussed here:
https://www.beatthegmat.com/number-t292641.html#782186
GMAT assassins aren't born, they're made,
Rich
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We know that (t/1000)� = t� / 1000�.
t�/1000� = t� * .000000000001
We only want at most seven leading zeros, so t� must be at least five digits long. But 3� = 81, 5� = 625, and 9� = 6561, so none of these are long enough, t > 9, and the answer is A.
t�/1000� = t� * .000000000001
We only want at most seven leading zeros, so t� must be at least five digits long. But 3� = 81, 5� = 625, and 9� = 6561, so none of these are long enough, t > 9, and the answer is A.
- MartyMurray
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You could start by breaking (t/1000)� down to t� x (1/1000)�.
Now let's become clear about (1/1000)�.
Every time you divide 1 by 1000, you move the 1 three more decimal places to the right of the decimal.
1/1000 = 0.001
0.001/1000 = 0.000001
0.000001/1000 = 0.000000001
0.000000001/1000 = 0.000000000001
So (1/1000)� = 0.000000000001, which has 11 zeros between the decimal and the first non-zero digit.
Dividing a 2 digit number, say 27, divided by 1000� generates a decimal that has 10 zeros between the decimal and the first non-zero digit, as is case in 0.000000000027.
To generate a number that has 7 or fewer zeros between the decimal and the first non-zero digit, you need to divide by (1/1000)� a number with five or more digits, such as 11,111, which when divided by (1/1000)� generates 0.000000011111.
The smallest five digit number is 10,000, which equals 10�.
So any number smaller than 10 will not work for t.
The correct answer is A.
Now let's become clear about (1/1000)�.
Every time you divide 1 by 1000, you move the 1 three more decimal places to the right of the decimal.
1/1000 = 0.001
0.001/1000 = 0.000001
0.000001/1000 = 0.000000001
0.000000001/1000 = 0.000000000001
So (1/1000)� = 0.000000000001, which has 11 zeros between the decimal and the first non-zero digit.
Dividing a 2 digit number, say 27, divided by 1000� generates a decimal that has 10 zeros between the decimal and the first non-zero digit, as is case in 0.000000000027.
To generate a number that has 7 or fewer zeros between the decimal and the first non-zero digit, you need to divide by (1/1000)� a number with five or more digits, such as 11,111, which when divided by (1/1000)� generates 0.000000011111.
The smallest five digit number is 10,000, which equals 10�.
So any number smaller than 10 will not work for t.
The correct answer is A.
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
- ygcrowanhand
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Hi GMATters,
Here's my video explanation of this question: https://youtu.be/VnLRYs2jd5w
Enjoy!
Rowan
Here's my video explanation of this question: https://youtu.be/VnLRYs2jd5w
Enjoy!
Rowan
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PS have you seen the new GMAT Work and Rates guide? Comes with a free 8-video course.
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Learn more about Private GMAT Tutoring at: https://privategmattutor.london