BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Number

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 59
Joined: Thu May 05, 2016 4:20 am
Thanked: 3 times

Number

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
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
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)�, 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)� cannot have more than 7 zeroes to the right of the decimal point, (t/1000)� must be GREATER THAN OR EQUAL TO 0.00000001:
(t/1000)� ≥ 0.00000001
(t/10³)� ≥ 1/10�
t�/10¹² ≥ 1/10�
10�t� ≥ 10¹²
t� ≥ 10�.

None of the three options for t satisfies the constraint that t� ≥ 10�.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
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)�. That will give us at least eight zeros (.00 four times is .00000000), so no single digit t will suffice.
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1