1) if p, s, and t are positive prime numbers, what is the value of p^3s^3t^3? (1) p^3st=728 (2) t=13 -----------------------
hi, using (1)... 728 = (2^3)*7*13 so p=2, t and s can be 7 or 13 so exact value of expression cant be found out...
using (2)... nothing can be said about the value of the expression given...as p and s are unknown...
combining both... we get p=2,s=7,t=13 so the given expression can be evaluated...
PS:i m unable to interpret the expression properly... if the given expression is (p)to the power(3s)to the power(3t)to the power(3) then it can be evaluated using both statements... if it is (p^3)*(s^3)*(t^3) then it can be evaluated using first statement in itself...
This is one of the questions which you have posted in the earlier Posts but i am not able to get the answer of the same..Can you please post the answer with the explanation for the same..
Here is one more......
In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?
This is one of the questions which you have posted in the earlier Posts but i am not able to get the answer of the same..Can you please post the answer with the explanation for the same..
Here is one more......
In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible? A) 24 B) 52 C) 96 D) 144 E) 648
Thanks & Regards Vaibhav Wadhera
Is the Ans B ?
Assuming that same people with diff medals is a separate victory circle
Ways to select any 3 ppl out of 4 = 4C3 => 4 Now, these 3 ppl can win in 4 formats:- GGG, GGS, GSS, GSB (G=Gold, S=Silver, B=Brone) GGG = only 1 arrangement => 1 GGS = 3 arrangements GSS = 3 arrangements GSB = 3! = 6 arrangements posssible So, total = 1+3+3+6 => 13 And this is posible for each of those 4 selection in the first line. So, 13*4 => 52..
IMO - E 1) 2C > 2J - 5... Insuff.. (C = Avg no. of book Carolyn reads, J = for jacob)
2) 5C = 5J +3 .. Insuff.
Together - Insuff..
2) During a 10-week summer vacation, was the average (arithmetic mean) number of books that Carolyn read per week greater than the average number of books that Jacob read per week? (1) Twice the average number of books that Carolyn read per week was greater than 5 less than twice the average number of books that Jacob read per week. (2) During the last 5 weeks of the vacation, Carolyn read a total of 3 books more than Jacob.
IMO - E During a 10-week summer vacation, was the average (arithmetic mean) number of books that Carolyn read per week greater than the average number of books that Jacob read per week?
(1) Twice the average number of books that Carolyn read per week was greater than 5 less than twice the average number of books that Jacob read per week. (2) During the last 5 weeks of the vacation, Carolyn read a total of 3 books more than Jacob.
1) 2C > 2J - 5... Insuff.. (C = Avg no. of book Carolyn reads, J = for jacob)
2) 5C = 5J +3 .. Insuff.
Together - Insuff..
Dont u think 1 is sufficient ?
2C > 2J - 5... (C = Avg no. of book Carolyn reads, J = for Jacob)
dividing it with 2 C > j - 2.5
So , as asked in the kostin was the average (arithmetic mean) number of books that Carolyn read per week greater than the average number of books that Jacob read per week?
Lets Suppose Jacob read / week, J = 20 books Then Carolyn reads >= 20 * 2 - 5 So, carolyn reads more than 35 books in 2 weeks. It can be 18/week or 19 or 20 or 21 and so onn. So insufficient
:cheers:
Dont u think 1 is sufficient ?
2C > 2J - 5... (C = Avg no. of book Carolyn reads, J = for Jacob)
dividing it with 2 C > j - 2.5
So , as asked in the kostin was the average (arithmetic mean) number of books that Carolyn read per week greater than the average number of books that Jacob read per week?
1) Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.which of the following is the measure of one of its angles? A. 30 B. 45 C. 60 D. 90 E.120
Area of gm = perpendicular * base 18 = perp. * 6 => perp. = 3. Now, its a triangle with perp. = 3 and hyp. = 6 So, Sin A = 1/2 => A = 30'
1) Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.which of the following is the measure of one of its angles? A. 30 B. 45 C. 60 D. 90 E.120
1) Of the three-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? A. 24 B. 36 C. 72 D. 144 E. 216 I think the answer option is not avl.......
If M = 3 digit, M^3 can be 7 or 8 digit If M^2 = 5 digit, M lies mainly b/w 100 to 300. Same condition as above.
Let M be smallest 3 digit no. = 100, M^2=10000 (5 digit) and M^3=1000000 (7 digit) If M is 300, M^2=90000 (5 digit) and M^3=27000000 (8 digit) So, we can say if it is 7 or 8 digit. hence E..
If M is a positive integer, then M^3 has how many digits? (1) M has 3 digits. (2) M^2 has 5 digits is there any shortcut.....
lets say ones and tens digit is same:- Ones place can have any no. from 1-9 = 9 ways Tens digit is same as ones = 1 way hundreds can have anything b/w 1-9 but not the no. chosen by ones = 8 ways. So, total possiblilties = 8*1*9 = 72 Now there are 3 possiblilities ones and tens can be same, tens and 100ths and ones and 100ths. So, 72*3 = 216, E is the ans..
1) Of the three-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two? A. 24 B. 36 C. 72 D. 144 E. 216 I think the answer option is not avl.......
lets say ones and tens digit is same:- Ones place can have any no. from 1-9 = 9 ways Tens digit is same as ones = 1 way hundreds can have anything b/w 1-9 but not the no. chosen by ones = 8 ways. So, total possiblilties = 8*1*9 = 72 Now there are 3 possiblilities ones and tens can be same, tens and 100ths and ones and 100ths. So, 72*3 = 216, E is the ans..
hi, im convinced now i tried to solve like 9C2*3!/2 and got 108 as solution tell me where i went wrong
hi, im convinced now i tried to solve like 9C2*3!/2 and got 108 as solution tell me where i went wrong
Hey Vijay, Bold part is incorrect .. If u have used that if p things out of n are alike then, total ways = n! / p!
Then, in that case, ur numerator is incorrect .. Extending your logic, 2 distinct digits can be chosen in 9C2 ways, 3rd digit is not repetitve, hence it has 2 options ..And these 3 digits can be arranged in 3 ! ways ...
Hence, numerator = 9C2 * 2 * 3 !
Of these, 2 digits are alike, hence total ways = 9C2 * 2 * 3 ! / 2 ! = 216 ...Ans ...
If x, y, and z are integers, and x (1) The mean of the set {x, y, z, 4} is greater than the mean of the set {x, y, z}. (2) The median of the set {x, y, z, 4} is less than the median of the set {x, y, z}.
A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
A container has 4 different varieties of fruits. In how many ways can you choose 6 fruits from the container ? ( Information on number of fruits in the container isn't available)
A container has 4 different varieties of fruits. In how many ways can you choose 6 fruits from the container ? ( Information on number of fruits in the container isn't available)