Since we are talking about increase by a FACTOR of 5, i will take it as 5a
Any examples to prove otherwise?
Vishal84 SaysIf i say that it takes 2 years for a to increase by a factor of 5, will the final value after 2 years be 5a or 6a?
excellent explanation!!! Simply Fabulous!!
I dont think it will change anything......please see the explanation below:
Let the nos be a->e, we know e=3a+20,
so R={a,b,55,c, 3a+20}
summing all nos
4a+b+c+75 = 55*5 (since mean is 55)
4a+b+c = 200
Range for R will be e-a (largest - smallest) = 3a+20-a = 2a+20
Our task is to maximise the range, i.e., find Max value of 2a+20
using the first eqn 4a+b+c=200.
Max value of a will be achieved by minimising values of b and c.
Min value of c will be 55(equal to the median)
Min value of b will be a (since it cannot be less than a)
thus, 4a+a+55=200
a=29
Range becomes, 58+20 = 78
Values of a
In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over forty have master's degrees?
(1) Exactly 100 of the employees are college graduates.
(2) Of the employees forty years old or less, 25 percent have master's degrees.
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.
I guess the answer is A
Hi guys,
this is how i looked at the above problem... please let me know if this approach is correct or has some unforeseen flaws.
1. from the figure we have ABDC to be a cyclic quadrilateral.
2. there are 2 possiblities for AD
a. it is the diameter of the circle.
b. it is NOT the diameter.
3. the data given states that AB=CD
considering the above points, we have 2 possiblities for the quadrilateral
a. it is a rectangle (or a square)
b. it is an isoceles trapezium
now... looking at the options we see that D is the only one that holds true for both the above cases. hence the answer should be D.
Hi,
My understanding is that the naming convention is not right in the fig which u have pasted .ie it should be either clockwise or anticlockwise. In both the cases AC and BD would have been the diagonals and not the sides like u have shown.
Now come to the question
It is given that AB=CD which clearly implies that AB and CD are 2 equal chords of the circle and hence they should be equidistant from the centre.It is one of the basic properties of circle.
Therefore the line joining the pts A & D ie AD must be parallel to the line joining the pts B & C ie BC(since from the center, the lines AB and CD are equidistant) or may be equal also.
Therefore we can infer that ABCD would be either a rectangle or square or isosceles trapezium as u have said. In all the 3 cases the diagonals AC and BD would be equal. Hence for me the answer would be Option C ie AC=BD.
PS. Opposite angles of a isosceles trapezium are not equal. Only the base angles are equal. The opposite angles add up to 180 degree just like any cyclic quadilateral. If the opposite angles of the isosceles trapezium were equal, then there would be no diff of it wid a rectangle or square.
Hi,
My understanding is that the naming convention is not right in the fig which u have pasted .ie it should be either clockwise or anticlockwise. In both the cases AC and BD would have been the diagonals and not the sides like u have shown.
Now come to the question
It is given that AB=CD which clearly implies that AB and CD are 2 equal chords of the circle and hence they should be equidistant from the centre.It is one of the basic properties of circle.
Therefore the line joining the pts A & D ie AD must be parallel to the line joining the pts B & C ie BC(since from the center, the lines AB and CD are equidistant) or may be equal also.
Therefore we can infer that ABCD would be either a rectangle or square or isosceles trapezium as u have said. In all the 3 cases the diagonals AC and BD would be equal. Hence for me the answer would be Option C ie AC=BD.
PS. Opposite angles of a isosceles trapezium are not equal. Only the base angles are equal. The opposite angles add up to 180 degree just like any cyclic quadilateral. If the opposite angles of the isosceles trapezium were equal, then there would be no diff of it wid a rectangle or square.
hi,
thanks for the reply... actually the figure that i have given is a quote of the original question... so unless that is wrong... the quadrilateral is ABDC as mentioned. the rest of the logic is applicable...
in case the diagram is incorrect, and the quadrilateral is indeed ABCD... then ur logic is applicable... but if the quadrilateral is ABDC as given in the original question, then option C is incorrect.
I know that the opposite angles of a trapezium are not equal... considering the figure given, u will notice that the angles mentioned are the base angles of the isoceles trapezium... n hence the logic holds...
hope that clarifies the point.
hello all,
I have been preparing for gmat for couple of months now and I am taking gmat in 1 month now.
I have been consistently scoring 47 in quant, I need to increase the score but I am not able to do so.
Guys,please suggest any good source of gmat Quant questions...
Hi,
My understanding is that the naming convention is not right in the fig which u have pasted .ie it should be either clockwise or anticlockwise. In both the cases AC and BD would have been the diagonals and not the sides like u have shown.
Now come to the question
It is given that AB=CD which clearly implies that AB and CD are 2 equal chords of the circle and hence they should be equidistant from the centre.It is one of the basic properties of circle.
Therefore the line joining the pts A & D ie AD must be parallel to the line joining the pts B & C ie BC(since from the center, the lines AB and CD are equidistant) or may be equal also.
Therefore we can infer that ABCD would be either a rectangle or square or isosceles trapezium as u have said. In all the 3 cases the diagonals AC and BD would be equal. Hence for me the answer would be Option C ie AC=BD.
PS. Opposite angles of a isosceles trapezium are not equal. Only the base angles are equal. The opposite angles add up to 180 degree just like any cyclic quadilateral. If the opposite angles of the isosceles trapezium were equal, then there would be no diff of it wid a rectangle or square.
same case as mine hence AC=BD
Excuse me for the font color. I am not able to change it.
Q. Someone plans to invest $10,000 in an account paying 3% annual interest and compounded semi-annually. How much must he invest in another account paying 5% annual interests and compounded quarterly so that his annual income from the 2 accounts in the first year are the same
Does annual income mean the total amount or the interest?
Q. The mean of a list of numbers is m and the deviation (not sure here) is n. It is known that 68% of the numbers are within m and n, what is the percentage of the numbers that are less (or more) than m+n?
Q. A total of $200,000 was deposited at a fixed annual interest rate which is compounded quarterly. What is the interest of the first month?
1) The interest in the second month is 1 percent more than first month
2) The interest in the second month is $2 more than first month
Q. Someone plans to invest $10,000 in an account paying 3% annual interest and compounded semi-annually. How much must he invest in another account paying 5% annual interests and compounded quarterly so that his annual income from the 2 accounts in the first year are the same
Does annual income mean the total amount or the interest?
Q. The mean of a list of numbers is m and the deviation (not sure here) is n. It is known that 68% of the numbers are within m and n, what is the percentage of the numbers that are less (or more) than m+n?
Q. A total of $200,000 was deposited at a fixed annual interest rate which is compounded quarterly. What is the interest of the first month?
1) The interest in the second month is 1 percent more than first month
2) The interest in the second month is $2 more than first month
Excuse me for the font color. I am not able to change it.
Q. Someone plans to invest $10,000 in an account paying 3% annual interest and compounded semi-annually. How much must he invest in another account paying 5% annual interests and compounded quarterly so that his annual income from the 2 accounts in the first year are the same
Does annual income mean the total amount or the interest?
I guess Annul income is the interest earned per year.
In the first plan, its 10150 + 101.50 + 50.75 = 10302.25. The interest earned is 302.25.
if the investment amount is X , then X * (1+ 0.00125)^4 = 10302.25.
Do provide the options.
Q. A total of $200,000 was deposited at a fixed annual interest rate which is compounded quarterly. What is the interest of the first month?
1) The interest in the second month is 1 percent more than first month
2) The interest in the second month is $2 more than first month
I didn't understand, how the interest for the 1st month and 2nd month be different. I am considering the 1st month as the 1st month after commencing of the deposit. As the interest is compounded quaterly, I guess the interest should be same for the each quarter.
Am I missing something?
Excuse me for the font color. I am not able to change it.
Q. Someone plans to invest $10,000 in an account paying 3% annual interest and compounded semi-annually. How much must he invest in another account paying 5% annual interests and compounded quarterly so that his annual income from the 2 accounts in the first year are the same
Does annual income mean the total amount or the interest?
Q. The mean of a list of numbers is m and the deviation (not sure here) is n. It is known that 68% of the numbers are within m and n, what is the percentage of the numbers that are less (or more) than m+n?
Q. A total of $200,000 was deposited at a fixed annual interest rate which is compounded quarterly. What is the interest of the first month?
1) The interest in the second month is 1 percent more than first month
2) The interest in the second month is $2 more than first month
whts the source? somehow dnt sound gmat like and ambiguous at best.
for the Q2, im not sure what are you nt sure of? and if you are not sure of the question itself better stay away :D
honest advice: watch your source of questions for GMAT, makes a HUGE difference.
Maxim possible range-to maintain the condition we can keep X= 12--lowest to attain maxi range
second no=13 iii=55 given=mean=median, and fourth no again we should keep 55, again to maintain the condition.
12, 13, 55, 55, 130
range=118
What is the largest integer 'n' such that 43! is divisible by 2^n?
Post your approach to solve this....
Thanks in advance.
What is the largest integer 'n' such that 43! is divisible by 2^n?
Post your approach to solve this....
Thanks in advance.
This is a standard CAT question.
What needs to be calculated is the sum of: ( here[] means greatest integer function )
=21
=10
=5
=2
=1
Thus max n = 21+10+5+2+1 = 39
K..thanks sausi007. But theoretically how this method works?....Sorry it may be a basic question.
What is the largest integer 'n' such that 43! is divisible by 2^n?
Post your approach to solve this....
Thanks in advance.
Ok so I will try to give you the correct approach and also the logic behind it. I do not think that the solution by sausi is logical, although it gives you the answer. So lemme give it a shot.
Lets take an example of 10! instead of 43!
First thing you have to understand is what the question means. It means you have to find the number of 2's which come when you factorise 43! or 10! in our case.
Lets see how:
10! = 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10
= 1 X 2 X 3 X (2X2) X 5 X (2X3) X 7 X (2X2X2) X 9 X (2X5)
So now you can count the 2's manually. There are 8 of them.
So basically you can divide 10! by 2^8. You cannot go beyond that. You CAN NOT divide 10! by 2^9 because we dont have as many twos.
So now the question boils down to finding the number of twos in the factorisation. for this we do the following.
Now in the factorisation of 10, you will see 2 five times. 10/2 = 5. Because every second factor will have a two in it for any number. So till 10 you will get 5 2's.
Similarily after every 4th number you will have an extra 2. So in this case 10/4 = 2.5 = 2
Similarily after every 8th number you will have an extra 2. In this case 10/8= 1.xx = 1
So basically you accounted for all twos that are appearing. 5+2+1 = 8
SO the general formula becomes: lets say X is your number, you do this:
+ + + ....+
So basically the box [] are to approximate the figures to nearest lower integer value as we did in the example. And as soon as you get 1, you can stop there.
For 43!, the solution will be:
43/2 = 21.5 = 21 or =21
= = 10
=5
=2
=1
STOP
Answer is 39
If they asked you for 3^n
you would do:
=14
=4
so on...
If they asked you for lets say 6,
then you would do it for 3...because 6=2X3
And number of 3's will be less than no. of 2's. So find the 3's and the extra 2's will be useless...so that will be the answer.
Generally its asked for 10's or in other words they will ask how many trailing zeroes 43! will have, which basically means whats the max n for 10^n
Iin that case 10=2X5
So just find it for 5 and you are good.
Hope that helps!
Check out my website and blog. Lotsa more stuff like this there. And videos too.
GMATing: Realizing your B-School dream!!How I got a 770!!
Ya.....Thanks dude.....
Mohan Kumar T SaysYa.....Thanks dude.....
Use the thanks button! 😉
There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is?....
Ok so I will try to give you the correct approach and also the logic behind it. I do not think that the solution by sausi is logical, although it gives you the answer. So lemme give it a shot.
Lets take an example of 10! instead of 43!
First thing you have to understand is what the question means. It means you have to find the number of 2's which come when you factorise 43! or 10! in our case.
Lets see how:
10! = 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10
= 1 X 2 X 3 X (2X2) X 5 X (2X3) X 7 X (2X2X2) X 9 X (2X5)
So now you can count the 2's manually. There are 8 of them.
So basically you can divide 10! by 2^8. You cannot go beyond that. You CAN NOT divide 10! by 2^9 because we dont have as many twos.
So now the question boils down to finding the number of twos in the factorisation. for this we do the following.
Now in the factorisation of 10, you will see 2 five times. 10/2 = 5. Because every second factor will have a two in it for any number. So till 10 you will get 5 2's.
Similarily after every 4th number you will have an extra 2. So in this case 10/4 = 2.5 = 2
Similarily after every 8th number you will have an extra 2. In this case 10/8= 1.xx = 1
So basically you accounted for all twos that are appearing. 5+2+1 = 8
SO the general formula becomes: lets say X is your number, you do this:
+ + + ....+
So basically the box [] are to approximate the figures to nearest lower integer value as we did in the example. And as soon as you get 1, you can stop there.
For 43!, the solution will be:
43/2 = 21.5 = 21 or =21
= = 10
=5
=2
=1
STOP
Answer is 39
If they asked you for 3^n
you would do:
=14
=4
so on...
If they asked you for lets say 6,
then you would do it for 3...because 6=2X3
And number of 3's will be less than no. of 2's. So find the 3's and the extra 2's will be useless...so that will be the answer.
Generally its asked for 10's or in other words they will ask how many trailing zeroes 43! will have, which basically means whats the max n for 10^n
Iin that case 10=2X5
So just find it for 5 and you are good.
Hope that helps!
Check out my website and blog. Lotsa more stuff like this there. And videos too.
GMATing: Realizing your B-School dream!!How I got a 770!!
Why do you say the solution is not logical?? :shock::shock::shock:
The solution given by you is absolutely correct, just that you have elaborated the steps involved.
@Mohan: Pick up Arun Sharma, the number system chapter deals with a host of these kind of problems.