1. A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $10.00?
(A) 40
(B) 60
(C) 90
(D) 120
(E) 240
2. If A is the center of the circle shown above and AB=BC=CD, what is the value of x?
(A) 15
(B) 30
(C) 45
(D) 60
(E) 75
3. In each production lot for a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size B. If 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?
(A) 15 (B) 25 (C) 30
(D) 35 (E) 40
4. If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
(A) 100 (B) 120 (C) 140 (D) 150 (E) 160
5.The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?
(A) 1,350?
(B) 1,200 + 400?
(C) 1,200 + 300?
(D) 1,200 + 200?
(E) 1,200 + 150?
6.In ?PQS above, if PQ =3 and PS = 4, then
(A)
(B) 12/5
(C)
(D)
(E)
Hi madhav...I am getting different answer..my approach is as follows
i am using area of sector formula...i,e (theta/360) * pi * r^2
theta is the angle of the sector...
For Question 5
-----------------------------
Rectangle Area = 30*40 = 1200
Semi-circle area excluding shaded area = (Outer Circle Area - Inner Circle Area)
==> (180/360)*pi *30^2 - (180/360)*pi*10^2
==>Total Area = 1200+400pi....
pls correct me if I am wrong..
For 2nd Question
--------------------------
AB=BC=CD=DA= r ..This becomes a rhombus...
Take centre of BD as O....
AC^2 = AD^2 + CD^2 = r^2 + r^2 = 2* (r^2)
From this...... AC=root(2) * r...AO becomes (root(2)*r)/2 = r/root(2)...
Similarly..BO = r/root(2)....
Tan(x) = AO/BO = 1..x = Tan Inverse of(1) = 45degrees
For Question 5
-----------------------------
Rectangle Area = 30*40 = 1200
Semi-circle area excluding shaded area = (Outer Circle Area - Inner Circle Area)
==> 20*20*pi - 10*10*pi = 300pi
Total Area = 1200+300pi....
For 2nd Question
--------------------------
AB=BC=CD=DA= r ..This becomes a rhombus...
Take centre of BD as O....
AC^2 = AD^2 + CD^2 = r^2 + r^2 = 2* (r^2)
From this...... AC=root(2) * r...AO becomes (root(2)*r)/2 = r/root(2)...
Similarly..BO = r/root(2)....
Tan(x) = AO/BO = 1..x = Tan Inverse of(1) = 45degrees
For Question 5
-----------------------------
Rectangle Area = 30*40 = 1200
Semi-circle area excluding shaded area = (Outer Circle Area - Inner Circle Area)
==> 20*20*pi - 10*10*pi = 300pi
Total Area = 1200+300pi....
dude !!!
For Question 5
-----------------------------
Rectangle Area = 30*40 = 1200
Semi-circle area excluding shaded area = (Outer Circle Area - Inner Circle Area)
==> 20*20*pi - 10*10*pi = 300pi => This will give area for complete circle...whereas we need for a semi-circle....this should be 300pi/2 = 150pi
Total Area = 1200+300pi....
===================
Hi MSD,
Let hourly wage of John or Mary be 'J' dollars/hour
John worked on the job for 10 hrs ..So Amount John got is=10J
Mary worked for 2 hours less than John....So Amount Mary got is = 8J
Initial amount given to John and Mary each is = x dollars
Mary gave john y dollars of her payment so that they receive the same hourly wage
so John's amount ==> 10J = x + y(Amount from Mary)
Mary's Amount ==> 8J = x - y(Since Mary gave y dollars to John)
Since both recieve the same hourly wage....
(x+y)/10 = (x-y)/8
solving both
we get x = 9y
Hope you got the answer
Yes Vicky....I missed it..its a semi-circle...so area will be half..thanks Dude...
Hi Bunty,
I dont think you need to use Sector formula here...its a simple Semi-circle...so area of circle is enough....Anyways i took it as a circle....see the below post of Vicky...he has corrected my mistake above...
Q2. If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?
(1)More than 1/2 of the 10 employees are women.
(2)The probability that both representatives selected will be men is less than 1/10
I think ans E.
Total selection is 10C2
P= p is the probability that both representatives selected will be women
Is p>1/2
(1)More than 1/2 of the 10 employees are women.
Ie no: of women may be n=6,7,8,8,9 at extreme 10
So required probability, p=nC2/10C2
Consider each value of n.
When n=6 , p=6C2/10C2=1/3 p
When n=7 , p=7C2/10C2=7/15 p
When n=8 , p=8C2/10C2=1/3 p>1/2
So A alone not sufficient
(2)The probability that both representatives selected will be men is less than 1/10
Let a be the no: of men
So aC2/10C2 Solving aIe a=1,2,3
So B alone not sufficient
Taking together when a=3 , p when a=2 , p>1/2
So both not sufficient..
Anyone to validate my reasoning
dude !!!
For Question 5
-----------------------------
Rectangle Area = 30*40 = 1200
Semi-circle area excluding shaded area = (Outer Circle Area - Inner Circle Area)
==> 20*20*pi - 10*10*pi = 300pi => This will give area for complete circle...whereas we need for a semi-circle....this should be 300pi/2 = 150pi
Total Area = 1200+300pi....
===================
But guys OA is E
Help needed with SETS question -
I came across this question..
Q-1 In a group of 68 students, each student is registered for at least one of three classes History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
A. 19
B. 13
C. 10
D. 8
E. 7
OA is 10...My ans was 13.
I am using the following method -
AUBUC = A + B + C -AB - BC - CA + ABC + none.
ok, here A = history, b=math, c=english
As per question -
68 = 25 + 25 + 34 - a - b - c + 3
68 - 50 - 34 - 3 = -a -b -c
68 - 87 = - a - b - c
thus a + b + c = 19...
Now since this 19 has 3 included three times we need to elimate 3 thats included twice. So we do 19 - 3*2 => 19 - 6 or 13
but the answer is 10. Why ??? In the ques (another sets ques) below the above method did work.
Help needed with SETS question -
I came across this question..
Q-1 In a group of 68 students, each student is registered for at least one of three classes History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
A. 19
B. 13
C. 10
D. 8
E. 7
OA is 10...My ans was 13.
I am using the following method -
AUBUC = A + B + C -AB - BC - CA + ABC + none.
ok, here A = history, b=math, c=english
As per question -
68 = 25 + 25 + 34 - a - b - c + 3
68 - 50 - 34 - 3 = -a -b -c
68 - 87 = - a - b - c
thus a + b + c = 19...
Now since this 19 has 3 included three times we need to elimate 3 thats included twice. So we do 19 - 3*2 => 19 - 6 or 13
but the answer is 10. Why ??? In the ques (another sets ques) below the above method did work.
a+b+c=19..thats correct. but this contains three times ABC. So u need to deduct three times ABC to get the answer which is ONLY 2 langs.
in the second question, question asked for MORE THAN ONE = TWO + THREE. in which case, you will deduct two times ABC to get the answer.
a+b+c=19..thats correct. but this contains three times ABC. So u need to deduct three times ABC to get the answer which is ONLY 2 langs.
in the second question, question asked for MORE THAN ONE = TWO + THREE. in which case, you will deduct two times ABC to get the answer.
Thanks for the explanation. But I am a bit confused.
The first ques asks - how many students are registered for exactly two classes ? (asking two classes, so how do i figure out how much to deduct)? what if it asked 3 classes or one.
In the other one it was more than one of the three products. This means two or three. Isnt the above one two. I can't figure out the difference.
Thanks for the explanation. But I am a bit confused.
The first ques asks - how many students are registered for exactly two classes ? (asking two classes, so how do i figure out how much to deduct)? what if it asked 3 classes or one.
In the other one it was more than one of the three products. This means two or three. Isnt the above one two. I can't figure out the difference.
exactly two is = (AB)+(BC)+(AC) but not ABC..
to calculate exactly two classes, we hv to deduct 3 times ABC from (AB)+(BC)+(AC)..bcoz each one contains one time ABC.
more than one is = (AB)+(BC)+(AC) including one time ABC
to calculate more than one, we hv to deduct 2 times ABC from (AB)+(BC)+(AC)
this is better explained by venn diagrams.
ashishjha100 SaysBut guys OA is E
Thats what I marked in my previous post :
5.The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?
(A) 1,350?
(B) 1,200 + 400?
(C) 1,200 + 300?
(D) 1,200 + 200?
(E) 1,200 + 150?
30*40 + (pi*(20)(20) - pi*(10)(10))/2 => 1200 + 150pi
ashishjha100 SaysPls help with reasoning...........
For 2nd Question
--------------------------
AB=BC=CD=DA= r ..This becomes a rhombus...
Take centre of BD as O....
AC^2 = AD^2 + CD^2 = r^2 + r^2 = 2* (r^2)
From this...... AC=root(2) * r...AO becomes (root(2)*r)/2 = r/root(2)...
Similarly..BO = r/root(2)....
Tan(x) = AO/BO = 1..x = Tan Inverse of(1) = 45degrees
Hey jpmadhav...ABCD is a rhombus and not a square...
statement in bold is incorrect...angle ADC is not 90 degrees and pythogaras rule is not applicable..
we get 2 eq triangles in form of ABC and ADC .
angle ABD = 1/2 angle ABC
= 1/2 * 60
x = 30
hope this helps..
exactly two is = (AB)+(BC)+(AC) but not ABC..
to calculate exactly two classes, we hv to deduct 3 times ABC from (AB)+(BC)+(AC)..bcoz each one contains one time ABC.
more than one is = (AB)+(BC)+(AC) including one time ABC
to calculate more than one, we hv to deduct 2 times ABC from (AB)+(BC)+(AC)
this is better explained by venn diagrams.
Thanks a lot for the explanation dude. Will follow what you said.
Q2. If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?
(1)More than 1/2 of the 10 employees are women.
(2)The probability that both representatives selected will be men is less than 1/10
I think ans E.
Total selection is 10C2
P= p is the probability that both representatives selected will be women
Is p>1/2
(1)More than 1/2 of the 10 employees are women.
Ie no: of women may be n=6,7,8,8,9 at extreme 10
So required probability, p=nC2/10C2
Consider each value of n.
When n=6 , p=6C2/10C2=1/3 p
When n=7 , p=7C2/10C2=7/15 p
When n=8 , p=8C2/10C2=1/3 p>1/2
So A alone not sufficient
(2)The probability that both representatives selected will be men is less than 1/10
Let a be the no: of men
So aC2/10C2 Solving aIe a=1,2,3
So B alone not sufficient
Taking together when a=3 , pwhen a=2 , p>1/2
So both not sufficient..
Anyone to validate my reasoning
In the point (1) you have mentioned 1/3 as being P1/2. If we indeed get P
Hello,
Someone please help me with the following question:
Q.1 A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5B. 1.75C. 2.0 D. 2.5 E. 3
Thanks
MSD
msd_2008 SaysIn the point (1) you have mentioned 1/3 as being P1/2. If we indeed get P
it was a typing mistake
8C2/10C2 = 28/45 =.633 so p>1/2
Hello,
Someone please help me with the following question:
Q.1 A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5B. 1.75C. 2.0 D. 2.5 E. 3
Thanks
MSD
i think ans is C........if it is correct i'll give reasoning.....
Originally Posted by msd_2008 View Post
Hello,
Someone please help me with the following question:
Q.1 A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5B. 1.75C. 2.0 D. 2.5 E. 3
Thanks
MSD
ashishjha100 Saysi think ans is C........if it is correct i'll give reasoning.....
i guess the correct answer should be D.msd_2008 ,can you please verify