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three different PS questions

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by EddieU » Wed Jun 15, 2011 6:41 pm
maybe it's the because of the late time why I can't get these questions right:


Image

Q.1: What percent of the people surveyed use product A or product B or both, but not product C ?
(A) 12.5%
(B) 17.5%
(C) 30%
(D) 40%
(E) 60%

Correct answer: C.

Q.2:
Image


Q.3: If x, y, and z are positive integers and 3x = 4y = 7z, then the least possible value of x + y + z is
(A) 33
(B) 40
(C) 49
(D) 61
(E) 84

Correct answer: D.

Thank you in advance,
E.
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by Anurag@Gurome » Wed Jun 15, 2011 7:53 pm
Solution for Q1. No. of people who use only product A = 400 - (125 + 75 + 125) = 75
No. of people who use only product B = 400 - (125 + 75 + 100) = 100
No. of people who use product A or B = 125

Therefore, no of people who use product A or B, but not C = 75 + 100 + 125 = 300
So, percent of the people who use product A or B, but not C = 300/1000 * 100 = [spoiler]30%[/spoiler]

The correct answer is C.
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by newgmattest » Wed Jun 15, 2011 8:06 pm
Hi,

Can you please post/draw in Q2, where is chord for which we are looking for length?

Thanks.
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by Anurag@Gurome » Wed Jun 15, 2011 8:25 pm
Solution for Q3.

Let 3x = 4y = 7z = n
Then x = n/3, y = n/4, and z = n/7
So, x + y + z = n/3 + n/4 + n/7 = 61n/84
Since x, y, and z are positive integers, so x + y + z will also be a positive integer.
For x + y + z to be minimum, n should be 84, which implies minimum value of x + y + z should be 61.

The correct answer is D.
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by smackmartine » Wed Jun 15, 2011 9:06 pm
newgmattest wrote:Hi,

Can you please post/draw in Q2, where is chord for which we are looking for length?

Thanks.
Q2) IMO B
Image
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by EddieU » Thu Jun 16, 2011 1:04 pm
smackmartine wrote:
newgmattest wrote:Hi,

Can you please post/draw in Q2, where is chord for which we are looking for length?

Thanks.
Q2) IMO B
Image

I have this question from an old GMAT paper test, it's a retired ps question. I was also confused how the cord is lined...and yes, the answer is correct. Thank you.


quick question though: How did you get 70pi? I did not quite understand the way you calculated the number. The arc's formula is Arc/360 and in our case 80/360 (that's how at least I started to solve the problem) but where did you get the 90 from?

Thanks,
E.
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by smackmartine » Thu Jun 16, 2011 5:04 pm
EddieU wrote:
smackmartine wrote:
newgmattest wrote:Hi,

Can you please post/draw in Q2, where is chord for which we are looking for length?

Thanks.
Q2) IMO B
Image

I have this question from an old GMAT paper test, it's a retired ps question. I was also confused how the cord is lined...and yes, the answer is correct. Thank you.


quick question though: How did you get 70pi? I did not quite understand the way you calculated the number. The arc's formula is Arc/360 and in our case 80/360 (that's how at least I started to solve the problem) but where did you get the 90 from?

Thanks,
E.
80 cm and 60 cm are the radii of two circles and NOT THE LENGTH OF THE ARCS. We have to calculate the both the arcs using these radii.

Length of an arc = 2( pi ) *Radius* (central angle/360), where central angle is angle projected by two ends of the arc at the center of the circle. In this case central angle is 90 degrees in both the circles.

Therefore, Length of the arcs = Length of the arc of circle with radius 80 cm + Length of the arc of circle with radius 60 cm
= 2( pi ) *80* (90/360) + 2( pi ) *60* (90/360)
= 2( pi ) *80* (1/4) + 2( pi ) *60* (1/4)
= 2( pi ) *20 + 2( pi ) *15
= 40( pi ) + 30( pi )
= 70( pi )

Hope its clear now.
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by winniethepooh » Thu Jun 16, 2011 5:37 pm
Thanks smackmartine.
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