z is a positive integer and a multiple of 2; p = 4^z, What is the reminder when p is divided by 10?
A) 10
B) 6
C) 4
D) 0
E) Cannot be Determined.
answer in red
4 ^ (2k) / 10 always gives 6 as the remainder as 6 
cyclicity !!
32. A set of numbers has the property that for any number t in the set, t + 2 is in the set. If 1 is in the set, which of the following must also be in the set?
I. 3 II. 1 III. 5
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
it is a set of all Odd integers , so answer in red
35) Line l is defined by the equation y - 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)
A) 0
B) 30
C) 60
D) 90
E) It cannot be determined from the information given.
35) Line l is defined by the equation y 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)
A) 0
B) 30
C) 60
D) 90
E) It cannot be determined from the information given.
Slope of line l is 5 and slope of line w is -1/5 ...If product of slopes of 2 lines is -1, then lines are perpendicular ..
Hence, line l is perp to line w ...
Line k does not intersect line l , hence it is either parallel or co-incident line ...
So, line k is also perp to line w ...Ans D ..
Line l is defined by the equation y - 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)
A) 0
B) 30
C) 60
D) 90
E) It cannot be determined from the information given.
product of slopes = -1 ... hence perpendicular
answer in red ;)
One more :
Six mobsters have arrived at the theater for the premiere of the film Goodbuddies. One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankies requirement is satisfied?
A6
B24
C120
D360
E720
One more :
Six mobsters have arrived at the theater for the premiere of the film "Goodbuddies." One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie's requirement is satisfied?
A 6
B 24
C 120
D 360
E 720
I might be a little too quick on this one.
IMO: D (360)
Approach:
Let A, B, C, D, J and F be our goons.
J=Joey, F=Frankie.
1---2---3---4---5---6
J ----------------------=> A,B,C,D,F can be arranged in 5 ! ways = 120
----J------------------ => F can be in 3,4,5,6 only. So 4! * 4 ways
---------J------------- => F can be in 4,5,6 only. So, 4! * 3 ways
-------------J--------- => F can be in 5,6 only. So, 4! * 2 ways
-----------------J----- => F can be in 6 only. So, 4! ways.
J cannot be in the 6th position as Frankie (F) cannot be behind him if Joey is the last in queue.
So overall number of ways is:
5! + 4! (4 + 3 + 2 + 1) = 120 + 240 = 360.
One more :
Six mobsters have arrived at the theater for the premiere of the film "Goodbuddies." One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie's requirement is satisfied?
A 6
B 24
C 120
D 360
E 720
Total no. of ways of arrangement = 6! = 720
In half of these Frankie will be standing behind Johnny and in th half Johnny behind Frankie.
Hence 720/2 = 360
One more :
Six mobsters have arrived at the theater for the premiere of the film Goodbuddies. One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankies requirement is satisfied?
A 6
B 24
C 120
D 360
E 720
hi,
i am getting 360 as the required number of ways...
plz confirm...
35) Line l is defined by the equation y 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)
A) 0
B) 30
C) 60
D) 90
E) It cannot be determined from the information given.
If a line do not intersect a particular line in a co-ordinate plane then the line has to be parallel to that particular line.
therefore slope of line K is equal to slope of line l=5
now angle tan inverse{(5+1/5)/0}=tan inverse(infinity)=90 degrees
Guys... Please post answers with permutations/combinations approach.
How many times will the number 7 be written when listing the integers from 1 to 1000?
1) 110
2) 111
3) 271
4) 300
5) 304
I think its D.. it does say bout t+2 but not about t-2.. there is no reason to believe that -3 should also be there. the set could start from -1 for all we know!!
32. A set of numbers has the property that for any number t in the set, t + 2 is in the set. If 1 is in the set, which of the following must also be in the set?
I. 3 II. 1 III. 5
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
Sorry if repost
If M=(4)^1/2 + (4)^1/3 + (4)^1/4, then value of M is -
1. less than 3
2. equal to 3
3. between 3 and 4
4. equal to 4
5. greater than 4
Guys... Please post answers with permutations/combinations approach.
How many times will the number 7 be written when listing the integers from 1 to 1000?
1) 110
2) 111
3) 271
4) 300
5) 304
I'll pick D
considering on unit and tens place
1-69 = 7
70-79 = 11
80-99 = 2
total = 20
Hence no. of 7s for 0-699 = 7 X 20 = 140
no. of 7s for 800-1000 = 2 X 20 = 40
no. of 7s from 700-799= 20 + (no. of 7's in hundred's place)= 20+100=120
Thf total = 140 + 40 + 120= 300
Sorry if repost
If M=(4)^1/2 + (4)^1/3 + (4)^1/4, then value of M is -
1. less than 3
2. equal to 3
3. between 3 and 4
4. equal to 4
5. greater than 4
Will pick E
M = 2 + 2^(2/3) + 2^(1/2)
we know sqrt 2 = 1.4
hence ..2^(2/3) will also be more than 1.4
M = 2 + (>1.4) + 1.4
hence M > 4
One More:
In the xy plane ,line L has positive slope and x-intercept 4. If the area of the triangle formed by line L and the two axes is 12, what is the y intercept of the line L?
No answer options.
I will post the answers tomm
One More:
In the xy plane ,line L has positive slope and x-intercept 4. If the area of the triangle formed by line L and the two axes is 12, what is the y intercept of the line L?
No answer options.
I will post the answers tomm
y intercept is -6
Darth Maul Saysy intercept is -6
provide your approach dude.. it will help all Puy's
pj02 Saysprovide your approach dude.. it will help all Puy's
too lazy to draw a figure man... but here goes..
one point is (4,0) as x intercept is 4
the other is (0, -y) as slope is positive so y intercept wud be -ve.
area of the triangle it forms with axes..
1/2 X 4 X y = 12
Y = 6
therefore y intercept = -6
Sorry if repost:
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2i3k5m7p, then i + k + m + p =
A. 4
B. 7
C. 8
D. 11
E. 12