If M= (4)^1/2+(4)^1/3+(4)^1/4. What is the value of M?
Can anyone tell me a simple approach to this problem.....Explanations would be appreciated...
Simplest way.... take Log both sides.
Simplest way.... take Log both sides.
Please explain what is meant by - (Two groups are considered different if at least one group member is different.) - The "different" here is Senior/Junior 'OR' different partners?
Also please solve this by publishing the steps/equation.
A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different.)
a. 48 b. 100 c. 120 d. 288 e. 600
The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hrs and a standard deviation of 6 hrs. The number of hours that Pat, a resident of Town X, watcched Television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
a. 30 b. 20 c. 18 d. 12 e. 6
Please explain what is meant by - (Two groups are considered different if at least one group member is different.) - The "different" here is Senior/Junior 'OR' different partners?
Also please solve this by publishing the steps/equation.
A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different.)
a. 48 b. 100 c. 120 d. 288 e. 600
1. Number of groups without single senior partner = 6!/3!*3! = 6*5*4/6 = 20
2. Total number of groups = 10!/7!*3! = 10*9*8/6 = 15*8 = 120
Number of groups with at least one senior partner = Total number of groups - Number of groups without single senior partner = 120 - 20 = 100
Please confirm!
The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hrs and a standard deviation of 6 hrs. The number of hours that Pat, a resident of Town X, watcched Television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
a. 30 b. 20 c. 18 d. 12 e. 6
Pat's hours would be between 21 (mean) - 12(2*Standard deviation) = 9 and 21(mean) - 6(1*standard deviation) = 15 so can be 15
Answer is D
100 is the Answer. Thanks .
I have a question based on Geometry but I do not see an option to draw figures in the posts. So let me try and create a word problem statement for it:
Given, a semi-circle with its diameter on the x-axis and center at O(0,0). Points P (-sqrt(3), 1) and Q (s, t) lie on this circle with center O. Given Angle(POQ) = 90 degrees. What is the value of s?
a. 1/2 b. 1 c. sqrt(2) d. sqrt(3) e. sqrt(2)/2
Correct answer stated is b. 1. Can someone explain?
Also, since I am new to PG, pls let me know if we have provision in the PG editor to draw geometric figures!!
I have a question based on Geometry but I do not see an option to draw figures in the posts. So let me try and create a word problem statement for it:
Given, a semi-circle with its diameter on the x-axis and center at O(0,0). Points P (-sqrt(3), 1) and Q (s, t) lie on this circle with center O. Given Angle(POQ) = 90 degrees. What is the value of s?
a. 1/2 b. 1 c. sqrt(2) d. sqrt(3) e. sqrt(2)/2
Correct answer stated is b. 1. Can someone explain?
Also, since I am new to PG, pls let me know if we have provision in the PG editor to draw geometric figures!!
Angle of PO with X axis is 30 degrees, angle POQ is 90, so angle between QO and X axis is 60.
Radius is 2 (30-60-90 triangle), so distance between t and X axis is sqrt(3) i.e. t is sqrt(3) and distance between s and Y axis is 1 so s is 1.
h(100)+1 = 2*50! + 1, so its going to be prime, so answer e.
Please confirm
Can you please steps with which you arrived at the answer? I just don't seem to get it!
Thanks.
Can you please steps with which you arrived at the answer? I just don't seem to get it!
Thanks.
I am not sure which step is unclear to you -
For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n inclusive, if p is the smallest prime factor of h(100) +1, then p is
a) between 2 & 10
b) between 10 & 20
c) between 20 & 30
d) between 30 & 40
e) greater than 40.
From given information
h(100) = 2*4*6*....*100 + 1 (right?)
h(100) = 2*(1*2*3*....*50) + 1 (factored 2 out of product)
h(100) = 2*50! + 1 = Even + Odd , specifically it is going to contain trailing 0s (because it has 2 and 50 in product so would definitely be ___00 format and add 1 to it would be like ____001)
For a) primes would be 1,3,5,7
For b) primes would be 11,13,17,19
For c) primes would be 23,29
For d) primes would be 31, 37,
For e) unlimited number of primes beyond 40 (41,47...)
2*50! is evenly divisible by all primes from a to d but adding 1 to it would make it indivisible(try it add 1 to p*q where p is any prime of your choice and q is any other positive integer.) So it is E
This looks a simple prob and can be easily solved using linear eqns...I got the correct ans using that approach but when i applied a diffrent approach m getting wrong ans. Can anyone please explain wat is wrong with my approach?
Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and
average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the
average weight of the boxes in the shipment is to be reduced to 14 pounds by removing
some of the 20-pound boxes, how many 20-pound boxes must be removed?
A. 4
B. 6
C. 10
D. 20
E. 24
Solving method - avg wright is reduced by 4 pounds , which is equivalent to reducing 4 pounds from each of 30 boxes.. hence total weight reduced is 30 *4 = 120 pounds.
But since we have only removed 20 pound boxes, this weight shud correspond to no of 20 pound boxes removed. hence total no of 20 pound boxes removed should be 30*4 / 20 = 6 (Which infact is not the correct ans). Can someone please help.
This looks a simple prob and can be easily solved using linear eqns...I got the correct ans using that approach but when i applied a diffrent approach m getting wrong ans. Can anyone please explain wat is wrong with my approach?
Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and
average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the
average weight of the boxes in the shipment is to be reduced to 14 pounds by removing
some of the 20-pound boxes, how many 20-pound boxes must be removed?
A. 4
B. 6
C. 10
D. 20
E. 24
Solving method - avg wright is reduced by 4 pounds , which is equivalent to reducing 4 pounds from each of 30 boxes.. hence total weight reduced is 30 *4 = 120 pounds.
But since we have only removed 20 pound boxes, this weight shud correspond to no of 20 pound boxes removed. hence total no of 20 pound boxes removed should be 30*4 / 20 = 6 (Which infact is not the correct ans). Can someone please help.
What is correct answer?
Originally there are 24 boxes with 20 pound weight and 6 boxes with 10 pound weight
24 x 20 + 6 x 10 = 480 + 60 = 540
Average 540 / 18 = 30 (matched with what is in problem)
Now say n 20 pound boxes are removed -
(24 - n) x 20 + 6 x 10 = 14 x (30 - n)
480 - 20 n + 60 = 420 - 14 n
540 - 420 = 120 = 6 n
6n = 120 meaning n = 20, so 20 boxes of 20 pounds removed would give
4 x 20 + 6 x 10 = 140
Average is 14.
Answer is D
Is above right? What about previous answers? What are your sources of these problems?
Thanks a lot .. D is perhaps the correct answer. :)
Its one of the questions from actual GMAT.
a) Using statement a alone ,the question can't be answered as AD=20 does not give u relation between BC and CD
b) Using statement B alone ,the question can't be answered as AB =CD does not give u any information about BC
c) Using both the statement the question can not be answered as 2x+BC =20
Hence the answer is E
A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red?
(1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2 : 1.
(2) Of the first 6 marbles removed, 4 are red.
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.
a) Using statement A the question can be answered . from this statement one can deduct that 6 red balls and 3 blue balls are removed . so number of red balls can be found out
b) Using statement B the question can not be answered as no information can be deducted for the three balls
Hence the answer is A
Came across this question..in one of the GMAT paper tests...
I don't really find this solvable.. can someone please help?
In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r = ?
A. 6
B. 5
C. 4
D. 3
E. 2
It should be 5 (option B) , u have to plot the circle on a x, y axis ....when u plot it u will come to know that since (4,-3) lies outside the circle r 4 , since its an integer
6Came across this question..in one of the GMAT paper tests...
I don't really find this solvable.. can someone please help?
In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r = ?
A. 6
B. 5
C. 4
D. 3
E. 2
Came across this question..in one of the GMAT paper tests...
I don't really find this solvable.. can someone please help?
In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r = ?
A. 6
B. 5
C. 4
D. 3
E. 2
Distance between (-2,-3) and (-2,1) square root of( (-2 -- 2)^2 + (-3-1)^2) which is 4
Distance between (-2,-3) and (4,-3) square root of( (-2-4)^2 + (-3--3)^2) which is 6
r is integer distance between 4 and 6 so it must be 5
Thanks... got it! 😃
Came across this question..in one of the GMAT paper tests...
I don't really find this solvable.. can someone please help?
In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r = ?
A. 6
B. 5
C. 4
D. 3
E. 2
The pure math way to do this is the distance formula done by PS25. Personally I would just shift the circle.
Think of the circle with center (0,0). The center is offset by -2,-3. So adding 2 to x and 3 to y for all these points means
a) Center is at (0,0)
b) (0,4) is within the circle
c) (6,0) lies outside the circle
Hence, from the options, 5 is the radius of the circle.