GMAT Problem Solving Discussions

[reddy.harikisho]

Originally Posted by jackgreat

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 -A∩B - B∩C - C∩A + A∩B∩C + 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.

[In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
A) 5
B) 10
C) 15
D) 20
E) 25 ]

[Here 85 = 50 + 30 + 20 -a -b -c + 5 thereby a + b + c = 20 and we did 20 - 5*2 thus 10 answer.] [Here 5 was included 3 times but we subtracted twice only.]

a+b+c=19..thats correct. but this contains three times A∩B∩C. So u need to deduct three times A∩B∩C 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 A∩B∩C to get the answer.

[jackgreat]

Originally Posted by reddy.harikisho

a+b+c=19..thats correct. but this contains three times A∩B∩C. So u need to deduct three times A∩B∩C 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 A∩B∩C 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.

[reddy.harikisho]

Originally Posted by jackgreat

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 = (A∩B)+(B∩C)+(A∩C) but not A∩B∩C..
to calculate exactly two classes, we hv to deduct 3 times A∩B∩C from (A∩B)+(B∩C)+(A∩C)..bcoz each one contains one time A∩B∩C.

more than one is = (A∩B)+(B∩C)+(A∩C) including one time A∩B∩C
to calculate more than one, we hv to deduct 2 times A∩B∩C from (A∩B)+(B∩C)+(A∩C)

this is better explained by venn diagrams.

[vicky.verma]

Originally Posted by ashishjha100

But 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

[bhavin422]

Originally Posted by ashishjha100

Pls help with reasoning...........

Originally Posted by jpmadhav

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..

[jackgreat]

Originally Posted by reddy.harikisho

exactly two is = (A∩B)+(B∩C)+(A∩C) but not A∩B∩C..
to calculate exactly two classes, we hv to deduct 3 times A∩B∩C from (A∩B)+(B∩C)+(A∩C)..bcoz each one contains one time A∩B∩C.

more than one is = (A∩B)+(B∩C)+(A∩C) including one time A∩B∩C
to calculate more than one, we hv to deduct 2 times A∩B∩C from (A∩B)+(B∩C)+(A∩C)

this is better explained by venn diagrams.

Thanks a lot for the explanation dude. Will follow what you said.

[msd_2008]

Originally Posted by ashishjha100

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<1/2
When n=7 , p=7C2/10C2=7/15 p<1/2
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 <1/10
Solving a<3.5
Ie a=1,2,3

So B alone not sufficient

Taking together when a=3 , p<1/2
when 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 P<1/2 and just after that you've mentioned 1/3 as being P>1/2. If we indeed get P<1/2 in all cases....then the answer should actually be A and not E.

[msd_2008]

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. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5

Thanks
MSD

[ashishjha100]

Originally Posted by msd_2008

In the point (1) you have mentioned 1/3 as being P<1/2 and just after that you've mentioned 1/3 as being P>1/2. If we indeed get P<1/2 in all cases....then the answer should actually be A and not E.

it was a typing mistake

8C2/10C2 = 28/45 =.633 so p>1/2

[ashishjha100]

Originally Posted by msd_2008

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. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5

Thanks
MSD

i think ans is C........if it is correct i'll give reasoning.....