OG 2017 - If there are fewer than

[fiza gupta]

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

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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

[Matt@VeritasPrep]

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.

[MartyMurray]

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.

[ygcrowanhand]

Hi GMATters,

Here's my video explanation of this question: https://youtu.be/VnLRYs2jd5w

Enjoy!

Rowan