GRE Question of The Day

liveletlive
#1. May 19th, 2006, at 3:04 PM.

20

Lee
#2. May 19th, 2006, at 3:26 PM.

if O is the centre of the triangle, then angle AOB =2*angle C =120.

then, arc AEB = 240/3= 80.
arc AE= arc EB= 80/2 = 40, because the triangle is equilateral.

arc EF = 240/4 = 60

therefore, EF - EB = 80 - 60 =20, so the answer is 1.

Could anyone suggest an easier method? Where can we see the answers?

pragya
#3. May 19th, 2006, at 4:03 PM.

e) cannot be determined from the given data

pragya
#4. May 19th, 2006, at 4:11 PM.

sorry..the answer is 20… the figure was not given in the mail, hence had arrived at the earlier conclusion

angle COB =120
angle COF = 90 (the sides of the square are tangents to the circle)
thus, angle FOB = angle COB- angle COF = 30

for a complete circle the length is 240, thus for an arc subtended by a 30 degree angle is 20

Viren
#5. May 19th, 2006, at 5:18 PM.

Thanks Pragya, thats easy to follow

abhishek
#6. May 19th, 2006, at 6:16 PM.

hey It can also be like this

arc cfb=240/3=80 &ar cf=240/4=60 from geometry.THus bf=80-60=20

Vikas
#7. May 19th, 2006, at 7:58 PM.

A) 20

mahesh
#8. May 19th, 2006, at 10:20 PM.

20
by the way pragya u method was excellent

Chelo
#9. May 19th, 2006, at 10:36 PM.

Yeah, the problem puzzled me a little initially but pragya gave an excellent approach!

pragya
#10. May 20th, 2006, at 7:37 PM.

nutboltoo
#11. May 21st, 2006, at 12:33 AM.

initially it sounded difficult……….thanks pragya

chandan
#12. May 22nd, 2006, at 11:09 PM.

yep… 20 is rite…. but a different method c if u find it easier…

1st join DF thru O(which is centre)… then join AO and BO…
angle AOB is 120… and angle OBA=OAB=30deg…
thus, angle BOF=angle AOD=30deg….
so length of arc BF=radius of arc * angle subtended at the centre(here its 30 deg)

so ans is 20inches..

gre1600
#13. May 22nd, 2006, at 11:22 PM.

Dear Chandan,
No doubt it was another good approach. but not the first choice.

Sorry If I am not shating others views.

pari
#14. October 13th, 2008, at 2:27 PM.

i would suggest finding ans by elimination method.
known : EF+FC+CD+DE= 240 (circumference)
so EF=240/4=60
we need to find BF which is EF-EB. that is 60- EB .if B is mid point of E and F then EF=EB=30. then answer will be 60-30=30. but clearly its seen in the fig that B is more than half way between E and F so EF-EB must be <30. so only option is a) 20.

abhi
#15. October 16th, 2008, at 9:49 AM.

arc AEB = 80 inches
arc DEF = 120 inches
so,DA + BF = 40.
From symmetry, DA = BF = 20 inches.

aritra
#16. October 20th, 2008, at 10:52 PM.

Half of circum: 240/2 = 120 = length of DEF
length of AEB = 240 /3 = 80
BF = (120 - 80)/2 = 20 Ans. A.