Official Quant thread for CAT 2013

MBA CAT 2024
27928
@ananyboss said:
Hi,Can anyone explain this ?Q - In an Exam, the average was found to bex marks. After deducing error the average marks of 94 students get reduced from 84 to 64.The average then came down by 18.8 marks, the number of candidates who took the exam were ?Ans -- 100.all I can figure out is reduction = 94 x (20 )i.e.18.8 = 94 x ( 20 )

ALSO
since you have already understood the reduction
it is a reduction over n students
94*20/n=18.8
n=100
27929
A circle circumscribes an equilateral triangle and is inscribed inside another equilateral triangle.Fnd the ratio of area of bigger triangle to the smaller one.

I don't have the OA for this question.

how to solve this ?
27930
@nole said:
A circle circumscribes an equilateral triangle and is inscribed inside another equilateral triangle.Fnd the ratio of area of bigger triangle to the smaller one.I don't have the OA for this question.how to solve this ?
for bigger triangle it is the incircle=area1/s =sqrt(3)*a^2/4 * 2/3a=a/2sqrt(3)for smaller triangle it is the circumcircle = b*b*b/4area2=b^3/sqrt(3)b^2=b/sqrt(3)
a/2(sqrt)3 =b/sqrt(3)
a/b=2
a^2/b^2=4:1
27931
@nole said:
A circle circumscribes an equilateral triangle and is inscribed inside another equilateral triangle.Fnd the ratio of area of bigger triangle to the smaller one.I don't have the OA for this question.how to solve this ?
Area=abc /4R
assume equilateral triangle of 2,2,2 area =_/3
R=abc/4_/3=2/_/3

for the outer triangle as centroid diviides in 2:1 ratio and coincides with circum center in Equilateral triangle

Distance from Center to bottom side is R=2/_/3
Height of outer traingle is 3R=2_/3
area is 4_/3
ration of areas=4:1
ďťżďťż
27932

A circle is inscribed in an isosceles trapezoid with lengths of its parallel side as 75 and 108 units. Find the diameter of the circle.

attached image

27933
@amresh_maverick said:
A circle is inscribed in an isosceles trapezoid with lengths of its parallel side as 75 and 108 units. Find the diameter of the circle.attached image
90 ?
27934
@amresh_maverick said:
A circle is inscribed in an isosceles trapezoid with lengths of its parallel side as 75 and 108 units. Find the diameter of the circle.attached image
Let r s p and q be the lengths of tangents from R S P and Q
r+s=p+q
s+p=75
r+q=108
p+q=s+r=PQ=RS=(108+75)/2 =
make a perpendicular from S to RQ.
let the point be T
RT=(108-75)/2
ST^2=SR^2-RT^2=1/4 (4*108*75)
ST^2=25*9 *4 *9
ST=5*3*2*3
diameter=ST=90
27935
@Subhashdec2 said:
Let r s p and q be the lengths of tangents from R S P and Qr+s=p+qs+p=75r+q=108p+q=s+r=PQ=RS=(108+75)/2 =make a perpendicular from S to RQ.let the point be TRT=(108-75)/2ST^2=SR^2-RT^2=1/4 (4*108*75)ST^2=25*9 *4 *9ST=5*3*2*3diameter=ST=90
@royy said:
90 ?
@amresh_maverick said:
A circle is inscribed in an isosceles trapezoid with lengths of its parallel side as 75 and 108 units. Find the diameter of the circle.attached image
OA : 90
27936
@psk.becks said:
2ND IS PRETY STARIGHT FORWARD ...MY TAKE ON THE FIRST ONE......TO MAXIMIZE THE NO. OF SINGLE SMOKERS WE HAVE TO MINIMIZE THE NO. OF THOSE WHO SMOKE ALL THREE.... AND PUT THOSE WHO SMOKE TWO = 0LET THE NO. OF PEOPLE BE 100AND NO. OF PEOPLE WHO SMOKE ALL THREE BE X...SO SMOKERS = A+B+C+X= 50A+B+C+3X = 92 --> 2X = 42 x=21 SO A+B+C CAN BE MAXIMUM 29 (WHEN THERE ARE 100 PEOPLE)CONVERTING TO THE CASE OF 35029*350/229*7/2 ---WHICH IS NOT POSSIBLE SO DECREASE THE VALUE OF A+B+C= 28HENCE TOTAL NO..= 98
Question for reference
In a colony, there are 350 residents. The number of residents who smoke cigar, hookah and cigarette as a percentage of the total number of residents is at least 40%, at least 30% and at least 22% respectively.a) If 50% of the residents do not smoke, then at most how many residents smoke exactly one of cigar, cigarette and hookah?a) 70 b) 175 c) 98 d) 91

Hey... Just a small correction to your calculation... the value you got of 29 is correct... but thats 29% of 100 ... so while scaling up u need to take 29% of 350... which comes out to be 101.5... then clear the half person to get... max value as 101..... you instead approximated early to 28% and that's where u go wrong.....
So ans should be 101.... but thats not there in any option.. :(

Here's the distribution: 66 ppl only cigar 31 ppl only hookah 4 pl only cigarette... 73 pl all three.. and one person both cigar and hookah.... that makes it 175...

your views pls

27937
@nole Draw the figure, the smaller triangle is madeby joining the mid points of the bigger triangle. So that means the ratio of sides is 1:2 hence the ratio of areas is 1:4
27938
@rkshtsurana What is left shift operator??
Plz explain me the concept.
27939

If 100 cats eat 100 rats in 100 hours then in how much time 10 cats eat 1000 rats??


27940
@albiesriram said:
a) 216b) 432c) 648d) 400e) 1944
Wots the answer for this one ? I am getting 648 ? Question reference: reply no 27245 Page1363 ..
27941
@Asfakul said:
If 100 cats eat 100 rats in 100 hours then in how much time 10 cats eat 1000 rats??
10000
27942
@Asfakul said:
If 100 cats eat 100 rats in 100 hours then in how much time 10 cats eat 1000 rats??
100 c 100 r 100 h
10 c 1000 r 100*100/10 *1000/100 =10000 hours
27943
@MBAVichar said:
Wots the answer for this one ? I am getting 648 ? Question reference: reply no 27245 Page1363 ..
rest 3 digit not containing 1
9c2 *3!/2! =36*3=108
rest 3 containing 1
9c2*3!= 36*6=324
432
27944
@Subhashdec2 said:
rest 3 digit not containing 19c2 *3!/2! =36*3=108rest 3 containing 19c2*3!= 36*6=324432
Why have u taken 9C2.... its not a combination question... arrangement matters... 1585 is different no from 1558.....
it shud be 9P2..... then same logic as your... we get 648..
27945
what is the minimum value |x-1|+|x-2|+|x-3|........+|x-10|??
27946
@Gsathe89 said:
what is the minimum value |x-1|+|x-2|+|x-3|........+|x-10|??
25?
27947
@Gsathe89 said:
what is the minimum value |x-1|+|x-2|+|x-3|........+|x-10|??
min value will always occur at 10/2

so 2(1+2+3+4) = 20 ??

EDIT: 2(1+2+3+4)+5 = 25