1.A certain company assigns employees to offices in such a way that some of the offices
can be empty and more than one employee can be assigned to an office. In how many
ways can the company assign 3 employees to 2 different offices?
A. 5
B. 6
C. 7
D. 8
E. 9
2.Which of the following fractions has a decimal equivalent that is a terminating decimal?
A.10/189
B.15/196
C.16/225
D.25/144
E.39/128
3.This year Henry will save a certain amount of his income, and he will spend the rest.
Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
Ans: 1/(2r+3)
Pls help with reasoning.......
1.A certain company assigns employees to offices in such a way that some of the offices
can be empty and more than one employee can be assigned to an office. In how many
ways can the company assign 3 employees to 2 different offices?
A. 5
B. 6
C. 7
D. 8
E. 9
2.Which of the following fractions has a decimal equivalent that is a terminating decimal?
A.10/189
B.15/196
C.16/225
D.25/144
E.39/128
3.This year Henry will save a certain amount of his income, and he will spend the rest.
Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
Ans: 1/(2r+3)
Pls help with reasoning.......
Q.1
There are total 3 employees and 2 offices. Following are the possible ways of arranging them
Office A - 1; Office B - 2 (total 3 ways of doing this since there are 3 different individuals involved)
Office A - 2; Office B - 1 (again, total 3 ways of doing this)
Office A - 3; Office B - 0
Office A - 0; Office B - 3
Hence total number of ways is 8
Q.3
Let I be Henry's income and S be his savings
Thus, expense = I - S
It is mentioned that Henry receives 1+r dollars for each dollar he saves. Hence, Henry will have S(1+r) = S+Sr dollars
As per the condition given in the problem
S+Sr = 1/2(I - S)
2S+2Sr = I - S
3S+2Sr = I; S(3+2r) = I
S = I/(3+2r)
So fraction of the income that he should save is 1/(2r+3)
Regards
MSD
Hi Pugs,
Can someone please give the explanation to the answers of these two attached questions. These are from OG11.
Thanks in advance.
1.The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 1 percent, what was the annual interest rate last year?
A. 1% B. 1.1% C. 9.1% D. 10% E. 10.8%
2.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'
Question(1):-
Let Interest last year be "x". This year's interest is x(10/100) + x
--> (x/10) + x --> 11x/10
When the interest this year is 1/100, how much was it last year?
Cross multiply --> (1*x*10)/(100*11*x) * 100 %
--> 1/110 * 100 %
--> 9.09% --> 9.1%
Question (2):-
Area of a the parallelogram = bh = 18 (b given as 6)
--> 6*h = 18 --> h = 3 (h is a perpendicular drawn to the base)
the triangle formed as a result will have sides 6, 3 and x (right angled triangle)
find x using Pythagoras theorem --> x = 3*sqrt3
This will give the three sides to be the ratio 6:3:3sqrt3
--> 2:1:sqrt3
--> this is a 90-30-60 triangle
Therefore the angle must be 30 degrees. (Draw the figure to understand why it can't be 60)
Hope this helps!
1.The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 1 percent, what was the annual interest rate last year?
A. 1% B. 1.1% C. 9.1% D. 10% E. 10.8%
2.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'
Hi Arch,
I guess the only angle we can get from the data is 30.
Here goes the explanation...
Since we have a right angled triangle with
hypotenuse= 6
opposite side = 3
adjacent side = 3*root(3)
tan(angle) = opposite side/ adjacent side
==> tan(angle) = 3/3*root(3) = 1/root(3)
hence angle = tanInverse(1/root(3)) = 30 degrees...
correct me if i was wrong....
Yes i concur.. I just meant drawing the figure will give a clearer picture =]
Hi Arch,
I guess the only angle we can get from the data is 30.
Here goes the explanation...
Since we have a right angled triangle with
hypotenuse= 6
opposite side = 3
adjacent side = 3*root(3)
tan(angle) = opposite side/ adjacent side
==> tan(angle) = 3/3*root(3) = 1/root(3)
hence angle = tanInverse(1/root(3)) = 30 degrees...
correct me if i was wrong....
Hi.. Can anyone help me with these questions?! Thanks a ton!
(I) A large cube 10cm on a side is composed of smaller cubes 1 cm on a side. The large cube is printed red on its outside surfaces and then all the cubes are mixed in a drum. If one cube is selected randomly, which of the following is the approximate probability that the cube will have at least one red face?
(A) 1:6 (B) 1:5 (C) 1:4 (D) 1:3 (E) 1:2
(II) Let a and b be integers where bb. If (a + 2)/(b-1)>0, which of the following is not a possible value for a?
(A) -1 (B) -3 (C) -4 (D) -6 (E) -8
In the rectangular coordinate system, points (4, 0) and ( 4, 0) both lie on circle
C. What is the
maximum possible value of the radius of C ?
A. 2
B. 4
C. 8
D. 16
E. There is no finite maximum value
Can some one help with this ?
C. What is the
maximum possible value of the radius of C ?
A. 2
B. 4
C. 8
D. 16
E. There is no finite maximum value
Can some one help with this ?
In the rectangular coordinate system, points (4, 0) and ( 4, 0) both lie on circle
C. What is the
maximum possible value of the radius of C ?
A. 2
B. 4
C. 8
D. 16
E. There is no finite maximum value
Can some one help with this ?
My pick is B.......wats OA?
My take is Choice (E).
In the rectangular coordinate system, points (4, 0) and ( 4, 0) both lie on circle
C. What is the
maximum possible value of the radius of C ?
A. 2
B. 4
C. 8
D. 16
E. There is no finite maximum value
Can some one help with this ?
*arch* SaysMy take is Choice (E).
Can you pls explain your answer
The points (4,0) & (-4,0) can be any given points on the circle. They need not necessarily be opposite ends of the diameter of the circle and might be end points of a chord in a circle, etc.
Hence, it is not possible to determine the radius of the circle with the information given.
Hope this helps!
harneet.m.kaur SaysCan you pls explain your answer
To find the radius we also need the CENTER of the circle.
Hi.. Can anyone help me with these questions?! Thanks a ton!
(I) A large cube 10cm on a side is composed of smaller cubes 1 cm on a side. The large cube is printed red on its outside surfaces and then all the cubes are mixed in a drum. If one cube is selected randomly, which of the following is the approximate probability that the cube will have at least one red face?
(A) 1:6 (B) 1:5 (C) 1:4 (D) 1:3 (E) 1:2
(II) Let a and b be integers where bb. If (a + 2)/(b-1)>0, which of the following is not a possible value for a?
(A) -1 (B) -3 (C) -4 (D) -6 (E) -8
Hi *Arch*,
I just got stumped by the first question, somehow didn't get it at all.
My reasoning for the 2nd one is here -
(II) b0
Hence, an expression having negative denominator can be positive iff numerator is also negative as -ve/-ve = +ve
a+2 can become less than zero by all the above values except a=-1. So, (A) is the answer. Please let me know if I am right.
Yes the Answers are 1:2 and -1 for the first and second questions respectively.
Thanks a ton for your explanations!
Puys,
Please help me solve the following problems:
1. The number of ways in which three letters be posted in four letter
boxes in a village, if all the three letters are not posted in the same letter box.
A) 64 B) 60 C) 81 D) 78 E) None of these
2. A jar contains 16 marbles, of which 4 are red, 3 are blue and the rest
are yellow. If 2 marbles are to be selected at random from the jar,
one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?
A.3/64 B.1/20 C.1/16 D.1/12 E.1/8
3. Each signal that a certain ship can make is comprised of 3 different
flags hanging vertically in a particular order. how many unique signals can be made by using 4 different flags?
A.10 B.12 C.20 D.24 E.36
4. Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
A.4 B.6 C.8 D.10 E.12
5. A photographer will arrange 6 people of different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
A.5 B.6 C.9 D.24 E.36
Regards
MSD
Here are my answer choices:-
1 (B)
2 (B) - doubtful
3 (D) - doubtful
4 (E)
5 (A)
What are the OAs?!
Puys,
Please help me solve the following problems:
1. The number of ways in which three letters be posted in four letter
boxes in a village, if all the three letters are not posted in the same letter box.
A) 64 B) 60 C) 81 D) 78 E) None of these
2. A jar contains 16 marbles, of which 4 are red, 3 are blue and the rest
are yellow. If 2 marbles are to be selected at random from the jar,
one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?
A.3/64 B.1/20 C.1/16 D.1/12 E.1/8
3. Each signal that a certain ship can make is comprised of 3 different
flags hanging vertically in a particular order. how many unique signals can be made by using 4 different flags?
A.10 B.12 C.20 D.24 E.36
4. Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
A.4 B.6 C.8 D.10 E.12
5. A photographer will arrange 6 people of different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
A.5 B.6 C.9 D.24 E.36
Regards
MSD
Puys,
Please help me solve the following problems:
1. The number of ways in which three letters be posted in four letter
boxes in a village, if all the three letters are not posted in the same letter box.
A) 64 B) 60 C) 81 D) 78 E) None of these
2. A jar contains 16 marbles, of which 4 are red, 3 are blue and the rest
are yellow. If 2 marbles are to be selected at random from the jar,
one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?
A.3/64 B.1/20 C.1/16 D.1/12 E.1/8
3. Each signal that a certain ship can make is comprised of 3 different
flags hanging vertically in a particular order. how many unique signals can be made by using 4 different flags?
A.10 B.12 C.20 D.24 E.36
4. Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
A.4 B.6 C.8 D.10 E.12
5. A photographer will arrange 6 people of different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
A.5 B.6 C.9 D.24 E.36
Regards
MSD
What r the OAs......if my choices r correct i'll give reasoning......
Hello Guys..
Need your help in the answers for the following questions:
Q1. 6 hrs from now, the population of a colony of bacteria will be 2.56 x 10 to the power 7. If the population of the bacteria colony doubles every 3 hrs, how many hours ago did the population surpass 100,000 ?
A. 9
B. 18
C. 21
D. 27
E. 33
Q2. If r+s+p > 1, is p > 1 ?
(1) p > r+s-1
(2) 1 -(r+S) > 0
i seem to be contradicting with the answers proposed and would like your help in confirming that.:bigear: