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

Redeem

Math problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Tue Mar 16, 2010 12:53 pm

Math problem

by priyasaibaba » Thu Apr 22, 2010 12:13 pm
Can anyone help to solve this problem?

Is X close to 10^(-2) or 10^(-3)?
(1) x is closer to 10^-4 than to 10^-1.
(2) x is closer to 10^-3 than to 10^-1.

A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


Thanks,
Priya
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Thu Apr 22, 2010 7:52 pm
IMO A

s1) on number line x will have a value more than the avg of 10^-4 and 10^-1 which is actually closer to 10^-3
suff
s2) insuff
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pm
Location: Milpitas, CA
Thanked: 447 times
Followed by:88 members

by Rahul@gurome » Thu Apr 22, 2010 9:36 pm
Let X = 10^y.
So the question becomes Is y close to -2 or to -3?
(1) y is closer to -4 than to -1.
(2) Y is closer to -3 than to -1.

Consider statement (1) alone.
If y is closer to - 4 than to -1, then there can be two cases.
Either y < -4 or - 4<y<-1.
If y < -4 obviously it will be closer to -3 than to -2.
If -4<y<-1 and y is closer to - 4, it means distance between y and -4 on the number line is less than the distance between y and -1.
Now distance between -4 and -1 is -1-(-4) = 3.
Half of this is 1.5.
So y-(-4) < 1.5
Or y+4<1.5
Or y < -2.5.
Take an example. Let y = -2.6 which is less than -2.5.
Distance between -2.6 and -2 is -2- (-2.6) = 0.6
Distance between -2.6 and -3 is -2.6 - (-3) = 0.4
So we see that -2.6 is closer to -3 than to -2.
So we can conclude that any number closer to -4 than to -1 is also closer to -3 than to -2.
So (1) is sufficient.
Consider (2)
Again there can be two cases.
First that y < -3 and second -3<y<-1.
In the first case it will be closer to -3 than to -2.
In the second case we will have that distance between y and -3 is less than the distance between y and -1.
Distance between -3 and -1 = 2
Half of this is 1.
So y-(-3) < 1
Or y<-2
Take y = -2.2 for example.
Dist between -2.2 and -2 is 0.2. and between -2.2 and -3 is 0.8.
Here y is closer to -2 than to -3.
Since nothing definite can be said we say that (2) is not sufficient.

The correct answer is A.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Fri Apr 23, 2010 12:54 am
Thanked: 1 times

by neodemion » Fri Apr 23, 2010 1:05 am
I might be totally mistaken, but I believe that both of the previous responses are wrong.

if you draw the situation:

--|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

having that:
10^-1 = 0.1
10^-2 = 0.01
10^-3 = 0.001
10^-4 = 0.0001

You can see that the last three points are located within the 0.01 - 0 range.. therefore even 0.03 is closer to any of them than to 10^-1... I believe that we have not enought data to solve the problem. Both of them are not sufficient.
Top
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Fri Apr 23, 2010 12:54 am
Thanked: 1 times

by neodemion » Fri Apr 23, 2010 1:15 am
Probably you can also see it better with integers..

the problem is the same as:

is X closer to 100 or to 10?

(a) x is closer to 1 than to 1000

(b) x is closer to 10 than to 1000
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Thu Mar 25, 2010 4:50 am

by Nilakshi1001 » Fri Apr 23, 2010 2:02 am
My answer:

To find x is closer to which value, let's take the average of 0.01 and 0.001 which is 0.0055, meaning 5.5X10^-3.

Taking first condition, x is closer to 10^-4 than to 10^-1. The average of 0.0001 and 0.1 is 0.1001/2, i.e. 0.05005 which is 5.005X10^-2. Condition 1 gives us x<5.005X10^-2. Thus, the condition is insufficient.

Second condition gives us x is closer to 10^-3 than to 10^-1. Using this we get x < 0.101/2 = 0.0505 = 5.05X10^-2. the condition is insufficient.

.......... 10^-4....................10^-3..........................10^-2.......................10^-1.......
---------------------------------5.005X10^-2-------------------------------
============5.05X10^-2============

----------5.5X10^-3---------

using both the statement also, we cannot find out the answer.

Thus, my answer is E.
Top
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Fri Apr 23, 2010 5:26 am
Moved to DS forum!
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
Master | Next Rank: 500 Posts
Posts: 114
Joined: Mon Sep 22, 2008 3:51 am
Thanked: 8 times
GMAT Score:680

by Fiver » Fri Apr 23, 2010 6:13 am
Agree with A.

Is x close to 1/100 or to 1/1000?

St1] x is closer to 10^-4 than to 10^-1.
The value midway of 10^-1 and 10^-4 is 10^-2.5 and to comply to st1] x has to be > 10^-2.5
This makes x closer to 10^-3 than to 10^-2.
Suff.

St2] x is closer to 10^-3 than to 10^-1.
Applying the same logic as above x>10^-2.
Hence x could be for e.g. 10^-2.1, which makes it closer to 10^-2 or any value greater than 10^-2.5, which makes it closer to 10^-3.
Insuff.
Top
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Fri Apr 23, 2010 12:54 am
Thanked: 1 times

by neodemion » Fri Apr 23, 2010 6:45 am
Fiver, the midway of 10^-1, which is equal to 0.1, and 10^-4, which is equal to 0.0001 is not 10^-2.5, which is equal to 0.0032. The midway is (0.1 + 0.0001) / 2 = 0.05005

Besides, the simplification proposed by Rahul is wrong.
Top
Master | Next Rank: 500 Posts
Posts: 114
Joined: Mon Sep 22, 2008 3:51 am
Thanked: 8 times
GMAT Score:680

by Fiver » Fri Apr 23, 2010 7:31 am
neodemion wrote:Fiver, the midway of 10^-1, which is equal to 0.1, and 10^-4, which is equal to 0.0001 is not 10^-2.5, which is equal to 0.0032. The midway is (0.1 + 0.0001) / 2 = 0.05005

Besides, the simplification proposed by Rahul is wrong.
You are right. My approach is fundamentally flawed.
Top
Legendary Member
Posts: 752
Joined: Sun May 17, 2009 11:04 pm
Location: Tokyo
Thanked: 81 times
GMAT Score:680

by tohellandback » Fri Apr 23, 2010 11:42 am
IMO E

1) INSUFF: the point x can lie in region m,9m,90m and also 900m upto <500m

2) INSUFF:same reasoning..the point x can lie in region m,9m,90m and also 900m upto <495m

combined:same reasoning
Attachments
Presentation1.ppt
(108.5 KiB) Downloaded 699 times
The powers of two are bloody impolite!!
Top
Master | Next Rank: 500 Posts
Posts: 301
Joined: Sun Mar 21, 2010 3:18 pm
Thanked: 4 times

by ansumania » Sun Apr 25, 2010 7:14 pm
hi,

is there a convenient way of analyzing the data?

pl. provide...

regards,

Ansuman
Top
Post new topic Post Reply
• Page 1 of 1