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

Redeem

PS Queries - Need expert help One day left for the GMAT

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 107
Joined: Tue Jun 05, 2012 3:25 am
Thanked: 1 times
Followed by:13 members

PS Queries - Need expert help One day left for the GMAT

by soni_pallavi » Wed Oct 31, 2012 10:22 pm
Dear All

Plz help with the following questions

q1)Tanya prepared 4 different letters to be sent to 4 different addresses.For each letter,she prepared an envelope with its correct address.If the 4 letterd are to be put into the 4 envelopes at random what is the probability that only one letter will be put into the envelope with its correct address.

q2)If n denotes a number to the left of 0 on the numberv line such that teh square of n is less than 1/100 then the reciprocal of n must be...


Ans..Less than 10 (plz explain how?)

q3)For every integer k from 1 to 10 inclusive kth term is given by (-1)^k+1(1/2^k).If T is the sum of the first 10 terms then T is

Ans Between 1/4 and 1/5 (Plz explain how)
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Wed Oct 31, 2012 10:48 pm
soni_pallavi wrote:Dear All

Plz help with the following questions

q1)Tanya prepared 4 different letters to be sent to 4 different addresses.For each letter,she prepared an envelope with its correct address.If the 4 letterd are to be put into the 4 envelopes at random what is the probability that only one letter will be put into the envelope with its correct address.
Let the envelopes be E1, E2, E3, E4 and the corresponding letters be L1, L2, L3, L4.
Suppose L1 goes to E1 and the other letters do not go in their corresponding envelopes.
So, E2 will have either L3 or L4
If E2 has L3, E3 will have L4, E4 will have L2.
If E2 has L4, E3 will have L2, E4 will have L3.
So, for L1 going to E1 we have 2 arrangements where other letters are not going into right envelopes.
Similarly for L2 going to E2 or L3 going to E3 or L4 going to E4, we have 2 arrangements each.

There are 2 * 2 * 2 * 2 = 8 ways in which only one letter goes to right envelope.

Total number of all possible arrangements of letters in any envelopes is 4! = 24.

Required probability is 8/24 = [spoiler]1/3[/spoiler].
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Wed Oct 31, 2012 10:54 pm
soni_pallavi wrote:Dear All

q2) If n denotes a number to the left of 0 on the numberv line such that teh square of n is less than 1/100 then the reciprocal of n must be...

Ans..Less than 10 (plz explain how?)
The Question is:

if n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be

a. less than -10
b. between -1 and -1/10
c. between -1/10 and 0
d. between 0 and 1/10
e. greater than 10

Explanation:

n is to the left of 0 on the number line, i.e. n < 0
As n² < 1/100, n lies between -1/10 and 1/10

Hence, -1/10 < n < 0
--> 1/n < -10

The correct answer is A.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Wed Oct 31, 2012 10:56 pm
soni_pallavi wrote:Dear All

q3)For every integer k from 1 to 10 inclusive kth term is given by (-1)^k+1(1/2^k).If T is the sum of the first 10 terms then T is

Ans Between 1/4 and 1/5 (Plz explain how)
Question is:

For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (-1)^(k+1) x (1/2^k). If "T" is the sum of the first 10 terms in the sequence, then T is:

A. greater than 2
B. between 1 and 2
C. between 1/2 and 1
D. between 1/4 and 1/2
E. less than 1/2

Explanation:

We know that the sum of n terms of a geometric series is given by:
S(n) = a(1 - r�)(1 - r), where a is the first term, r is the common ratio of the geometric progression and n = number of terms.

Here, a = 1/2, r = -1/2, n = 10
T = 1/2[1 - (-1/2)^10]/[1 + 1/2]
= 1/2[1 - 1/1024]/[3/2]
= 1/2 * 1023/1024 * (2/3)
= (1023/1024) * (1/3)
Now (1023/1024) = 1 approx, so T = 1/3, which lies between 1/4 and 1/2.

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Post new topic Post Reply
• Page 1 of 1