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Joy Shaha: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu May 05, 2016 4:20 am; Thanked: 3 times

by Joy Shaha » Sun Sep 25, 2016 1:24 pm

Q. 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

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Source: Beat The GMAT — Problem Solving | Sun Sep 25, 2016 1:24 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Sep 26, 2016 7:59 am

The problem should read as follows:

If there are fewer than 8 zeroes between the decimal point and the first
nonzero digit in the decimal expansion of (t/1000)â�´, 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

The smallest value that has 7 zeroes to the right of the decimal point is 0.00000001.
Any value less than 0.00000001 will have MORE than 7 zeroes to the right of the decimal point.
Since (t/1000)â�´ cannot have more than 7 zeroes to the right of the decimal point, (t/1000)â�´ must be GREATER THAN OR EQUAL TO 0.00000001:
(t/1000)â�´ â‰¥ 0.00000001
(t/10Â³)â�´ â‰¥ 1/10â�¸
tâ�´/10Â¹Â² â‰¥ 1/10â�¸
10â�¸tâ�´ â‰¥ 10Â¹Â²
tâ�´ â‰¥ 10â�´.

None of the three options for t satisfies the constraint that tâ�´ â‰¥ 10â�´.

The correct answer is A.

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Sep 29, 2016 7:18 pm

Maybe an easier way:

If t is a single digit integer, then (t/1000) = .00t

If we raise that to the fourth power, we get (.00t)â�´. That will give us at least eight zeros (.00 four times is .00000000), so no single digit t will suffice.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Fri Nov 18, 2016 7:01 am

Joy Shaha wrote:Q. 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

We are given that the decimal expansion of (t/1000)^4 has fewer than 8 zeroes between the decimal point and the first nonzero digit. We are also given that 3, 5, and 9 are possible values of t. Let's test each Roman numeral:

I. 3

If t = 3, then (t/1000)^4 = (3/1000)^4 = (.003)^4 has twelve decimal places with the digits 81 (notice that 3^4 = 81). So there must be 10 zeros between the decimal point and the first nonzero digit 8 in the decimal expansion. This is not a possible value of t.

II. 5

If t = 5, then (t/1000)^4 = (5/1000)^4 = (.005)^4 has twelve decimal places with the digits 625 (notice that 5^4 = 625). So there must be 9 zeros between the decimal point and the first nonzero digit 6 in the decimal expansion.

This is not a possible value of t.

III. 9

If t = 9, then (9/1000)^4 = (9/1000)^4 = (.009)^4 has twelve decimal places with the digits 6561 (notice that 9^4 = 6561). So there must be 8 zeros between the decimal point and the first nonzero digit 6 in the decimal expansion. This is not a possible value of t.

Recall that we are looking for fewer than 8 zeros between the decimal point and the first nonzero digit in the decimal expansion. So none of the given numbers are possible values of t.

Answer: A

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Head of GMAT Instruction
[email protected]

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