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

Redeem

DS exponent question

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 23
Joined: Thu Jun 01, 2017 9:36 pm
Followed by:1 members

DS exponent question

by amontobin » Mon Jul 17, 2017 10:35 am
If c=3.905 × 10^x and x is a negative integer, what is x?

(1) .00005 < c < .0005
(2) 10^−4 < c < 10^−3

What's a quick way to deal with negative exponents like this?
Top
Source: — Data Sufficiency |
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 Jul 17, 2017 1:04 pm
amontobin wrote:If c=3.905 × 10^x and x is a negative integer, what is x?

(1) .00005 < c < .0005
(2) 10^−4 < c < 10^−3
Test cases for x:
Case 1: x=3, with the result that c = 3.905 * 10¯³ = 0.003905.
Case 2: x=4, with the result that c = 3.905 * 10¯� = 0.0003905.
Case 3: x=5, with the result that c = 3.905 * 10¯� = 0.00003905.

Statement 1: 0.00005 < c < 0.0005
Only Case 2 satisfies this constraint, as illustrated by the digits highlighted in red below:
0.0000500 < 0.0003905 < 0.0005000.
Thus, x=4.
SUFFICIENT.

Statement 2: 0.0001 < c < 0.001
Only Case 2 satisfies this constraint, as illustrated by the digits highlighted in blue below:
0.0001000 < 0.0003905 < 0.0010000.
Thus, x=4.
SUFFICIENT.

The correct answer is D.
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/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Mon Jul 17, 2017 10:10 pm
amontobin wrote:If c=3.905 × 10^x and x is a negative integer, what is x?

(1) .00005 < c < .0005
(2) 10^−4 < c < 10^−3

What's a quick way to deal with negative exponents like this?
We have c = 3.905 × 10^x

Statement 1: 0.00005 < c < 0.0005

=> 5 x 10^-5 < c < 5 x 10^-4
5 x 10^-5 < 3.905 × 10^x < 5 x 10^-4

We see that 3.9 < 5, so the decision of less/more is among 10^-5, 10^x and 10^-4.

If we deal with the inequality 5 x 10^-5 < 3.905 × 10^x, we conclude that x must be at least -4.

Similarly, if we deal with the inequality 3.905 × 10^x < 5 x 10^-4 , we conclude that x can be at the most -4.

Thus, the only value of x that satisfies the conditions: "x must be at least -4" and "x can be at the most -4," is x = -4. Sufficient.

Statement 2: 10^−4 < c < 10^−3

=> 1 x 10^−4 < 3.905 × 10^x < 10 x 10^−4

The only value x can assume is x = -4. Sufficient.

The correct answer: D

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Mon Jul 17, 2017 10:37 pm
Statement 1 can be dealt in the following way too.
We have c = 3.905 X 10^x

Statement 1: 0.00005 < c < 0.0005

=> 5 x 10^-5 < c < 5 x 10^-4
5 x 10^-5 < 3.905 x 10^x < 5 x 10^-4
=> 5 x 10^-5 < 39 x 10^(x-1) < 50 x 10^-5

We did this so that the non-exponent parts can be easily compared. We see that they are arranged in an ascending order.

Thus, x-1 = -5

x = -5 + 1 = -4.

Hope this helps.

-Jay
Top
Post new topic Post Reply
• Page 1 of 1