Puys, some more...
2. How many positive integers less than 100 have exactly 4 odd factors and no even factors?
a>13
b>14
c>15
d>16
e>17
Puys, please explain ur methods
the OA are as follws:
1.E
2.C
I am getting 17 as the answer pls confirm
I am getting 17 as the answer pls confirm
Puys, some more...
1. Heights of women in a city follows a normal distribution with mean 160 cm and standard deviation of 6 cm. In a normal distribution, only 0.0063% of the population is not within 4 standard devistions of the mean. If 5 women are more than 184 cm tall, approximately how many women stay in the city?
a>16000
b>40000
c>80000
d> 100,000
e> 160,000
Normal distribution always follows symmetry ...
If 0.0063 % is not within 4 deviations from mean, half is below 4th deviation and half is above 4th deviation ...
Hence, 0.00315 % of the data is above 4th deviation ...
84 corresponds to 4 deviations above mean
Hence, total population is 5/0.00315 * 100 = 158730 ~ 160000 ..Ans E
Puys, some more...
2. How many positive integers less than 100 have exactly 4 odd factors and no even factors?
a>13
b>14
c>15
d>16
e>17
d2rockstar SaysI am getting 17 as the answer pls confirm
Yes , i Agree with Rockstar ...my answer also works out to 17 ..
For 4 odd factors, N has to be of the form N= a^1 * b^1 or simply a*b
OR a^3 , where a and b are odd prime nos ..
Let us list down prime nos :
3 can pair with 5,7,11,13,17,19,23,29,31 = 9 nos
5 can pair with 7,11,13,17,19 = 5 nos
7 can pair with 11,13 = 2 nos
Only 1 perfect cube of odd no within 100
3^3 = 1 no ...
Hence, total 17 nos within 100 have exactly 4 odd factors ...
If somebody does get 15 ...pls brief us ..
please post the explanations as well.
if 0I r/s
II rs
III s-r
If n is a multiple of 5 and n=p^2q, where p and q are prime numbers, which of the following must be a multiple of 25
a. p^2
b. q^2
c. pq
d. p^2q^2
e. p^3q
A set of 15 different integers has a median of 25 and range of 25. what is greatest possible integer that could be in this set?
1. 32
2. 37
3. 40
4. 43
5. 50
Puys, please help...
a juice manufacturer organized taste - testing sessions featuring four brands of orange juice, A, B , C and D. All customers who participated told the organizer which variety they they thought was the best. exactly 61% preerred brand A and exactly half as many prefereed brand B. Only 65 chose brand C. which of the foll could be the number of customers who liked brand D?
a> 8
b> 11
c>14
d>20
e>31
IMO: D
For C&D; together we have 8.5%
8.5%(n) = 65+d
n can be an integer only if d=20 among the given choices.
I agree. Had the exact same approach and the very same answer.
IMO: E
Normal distribution always follows symmetry ...
If 0.0063 % is not within 4 deviations from mean, half is below 4th deviation and half is above 4th deviation ...
Hence, 0.00315 % of the data is above 4th deviation ...
84 corresponds to 4 deviations above mean
Hence, total population is 5/0.00315 * 100 = 158730 ~ 160000 ..Ans E
please post the explanations as well.
if 0I r/s
II rs
III s-r
let us say r=1/2 and s=3/2, r/s=1/3. Pick other values like 0.9 and 1.9 for r and s, still, r/s
for r*s, pick r=0.9 and s=1.9, r*s = 1.71. So no good.
for s-r, pick the highest values for s and r lets say...1.9 and 0.9, s-r =1 not less than 1.any other value where r is more, s-r will be even more. So, no good.
If n is a multiple of 5 and n=p^2q, where p and q are prime numbers, which of the following must be a multiple of 25
a. p^2
b. q^2
c. pq
d. p^2q^2
e. p^3q
Let n=5^y
For multiple values of y, find p^2q format and get the values of p and q such that they are prime. For n to be multiple of 25, p needs to be 5 or 25 for various values of q. ex: 5^2 = p^2q, where p=5 and q=1, cant be chosen as q is not prime. 5^4 = p^2q, p=5, q=2. Good. 5^6 works, etc.
A set of 15 different integers has a median of 25 and range of 25. what is greatest possible integer that could be in this set?
1. 32
2. 37
3. 40
4. 43
5. 50
Lets start at the bottom of the choices, 50 cant be the highest number, because 50 -x = 25 where x is the least number of the range, is valid only when x =25, this cant be true as 25 is the median of the series.
If the highest number is 43, then 43 -x =25 means x=18.
So the first 7 numbers of the series could be 18,19,20,21,22,23,24 then 25, then.....on and on to 43. This series is possible. So 43 is the highest number. Eliminate the other choices as they are all less than 43 :-D
Here are my answers and explanations.
Normal distribution always follows symmetry ...
If 0.0063 % is not within 4 deviations from mean, half is below 4th deviation and half is above 4th deviation ...
Hence, 0.00315 % of the data is above 4th deviation ...
84 corresponds to 4 deviations above mean
Hence, total population is 5/0.00315 * 100 = 158730 ~ 160000 ..Ans E
@bhavin can you please elaborate the solution along with the Normal Distribution concept
thx
@bhavin can you please elaborate the solution along with the Normal Distribution concept
thx :grin:
vyomb:
Check out the attachment along with Bhavin's explanation to understand this one.
The number of ways in which 7 friends can be seated on 35 available seats such that no 2 friends seat together ?
I am confronted with 2 different answers for this.. plz share the approach..
Normal distribution always follows symmetry ...
If 0.0063 % is not within 4 deviations from mean, half is below 4th deviation and half is above 4th deviation ...
Hence, 0.00315 % of the data is above 4th deviation ...
84 corresponds to 4 deviations above mean
Hence, total population is 5/0.00315 * 100 = 158730 ~ 160000 ..Ans E
@bhavin can you please elaborate the solution along with the Normal Distribution concept
thx :grin:
vyomb:
Check out the attachment along with Bhavin's explanation to understand this one.
Thanks Vikram !!
Hey Vyomb,
Normal distribution is a bell shaped curved with high probability distribution closer to the mean and lower to the extremes ...
In statistics, probability distribution for continous functions like ND is given by z table ..( not expected on GMAT)
Just pasting my previous post for a better understanding:
34 % of the data falls within 1 standard deviation above the mean and 34 % data falls within 1 standard deviation below the mean...OR 68 % of the data is within 1 std deviation from mean..
OR in other words approx 32 % of the data is not within 1 deviation of the mean i.e 16 % is above 1 deviation and 16% is below 1 deviation
Likewise, for 2, 3 and 4 deviations from the mean ...
It is symmetric i.e 50% above mean and 50 % below mean ...So, if we are looking at either left or right tail, we need to discard half of the values of other extremes ...
So. if 0.0063 % is outside 4 devaitions, half is going to be outside 4 devaitions on the left tail and other half on the right tail ...we are only interested in the right tail, hence 0.00315 % is above 4 deviations ..
Hope this helps !!
My ans for the below problem
If n is a multiple of 5 and n=p^2q, where p and q are prime numbers, which of the following must be a multiple of 25
a. p^2
b. q^2
c. pq
d. p^2q^2
e. p^3q
is option d)p^2q^2
please post the explanations as well.
A set of 15 different integers has a median of 25 and range of 25. what is greatest possible integer that could be in this set?
1. 32
2. 37
3. 40
4. 43
5. 50
Vikram2010 SaysHere are my answers and explanations.
Why cant the answer be 50 ?
Median is the middle value of an arranged set ...where half of the values are equal to or below the median ...
Hence, the first 8 nos could be 25 , next 6 could be any no between 25 and 50 inclusive ...
For range to be 25, last no i.e highest poss no is 25 + 25 = 50
IMO ...Ans E
The number of ways in which 7 friends can be seated on 35 available seats such that no 2 friends seat together ?
I am confronted with 2 different answers for this.. plz share the approach..
Hey swap 25 ...just read the question ..
One clarification : Is it that nobody sits on adjacent seats OR 2 particular friends from 7 are never adjacent ?
I guess the sum is wanting the former ?
Why cant the answer be 50 ?
Median is the middle value of an arranged set ...where half of the values are equal to or below the median ...
Hence, the first 8 nos could be 25 , next 6 could be any no between 25 and 50 inclusive ...
For range to be 25, last no i.e highest poss no is 25 + 25 = 50
IMO ...Ans E
Bhavin,
First 8 numbers cannot be 25s, The question stem reads: A set of 15 different integers has a median of 25 and range of 25.
Bhavin,
First 8 numbers cannot be 25s, The question stem reads: A set of 15 different integers has a median of 25 and range of 25.
ohh ya ...i missed the word different
..Thanx !
Hey bhavin,
I thought that you would be the taker of this.. 😃 keep it up..
yeah question asks the former one i.e., nobody sits on adjacent seats..
Hey swap 25 ...just read the question ..
One clarification : Is it that nobody sits on adjacent seats OR 2 particular friends from 7 are never adjacent ?
I guess the sum is wanting the former ?
The number of ways in which 7 friends can be seated on 35 available seats such that no 2 friends seat together ?
I am confronted with 2 different answers for this.. plz share the approach..
Hey bhavin,
I thought that you would be the taker of this.. 😃 keep it up..
yeah question asks the former one i.e., nobody sits on adjacent seats..
well ..u have amazing source of questions !!
Really scratchy on this one !!
Tried various combinations from particular 2 not being together to nobody being together ...
Ok ...for nobody to be together ...this is what i cud think :
there need to be atleast 6 empty spaces between 7 ppl when they seat alternate ...OR degree of freedom is shortened by n-1 for n people
So we have 35 seats and 7 ppl ....so degree of freedon reduces (35-6)P7
i.e 29P7 = 29*28*27*26*25*24*23 ways of seating ...
Not sure on this ...if you are having OA pls do post !
I generalised by taking 2 egs ..
3 ppl and 7 chairs ---> 5*4*3 ways
3 ppl and 6 chairs ---> 4*3*2 ways ...
So, i generalised that for n people and m chairs total ways = Pn ways ..
Pls do correct fr errors !
P.S : took real long time to solve this one !
All correct. You rock buddy!! Thanks.
Vikram2010 SaysHere are my answers and explanations.
I want to share below problem:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT
a. x = w
b. x > w
c. x/y is an integer
d. w/z is an integer
e. x/z is an integer
I am providing the encrypted ans if in case i delay or forget to reply.
Ans: 27th char in below sequence:
acedbecdabcseystenaiwiearbcbyeadubbaesnweysaubdnkwebcd