Official Quant thread for CAT 2013

@next_big_thing : initially its a right angled traingle so it must retain its property as stated.
therefore after reducing 90 min side it will become 36 min side and applying Pythagoras theorem we will get 3rd side as 60 min so total comes out 2 be 144min.
For second question area of parking lot is initial traingle area - area new traingle.
area of first triangle is 1/2*48*90*15*15-1/2*48*36*15*15=.29 km^2.
@Asfakul said:
A trader cheats by 10% while selling and cheats by 20% while purchasing .He also offers a discount of 25% at cost price.find his profit /loss percent?Please explain approach ----- in Detail .
he buys 120 instead of 100 --> 20% profit

he sells 108 instead of 120 and gives 25 disc on 120...so he sells 108 at 90
here he incurs a loss of 1800/108 = 16.66

so overall profit/loss = 20-16.66-(20*16.66/100) = 0.008% profit

seems like i made a functional mistake somewhere....what is the OA??

What is the percentage change when 20/40 becomes 22/50 ???

Find the least number of all equal weight pieces which can be cut from three cakes of weights; 484g, 308g and 253g.

A. 90
B. 95
C. 100
D. 105
@abhishek.2011 said:
Find the least number of all equal weight pieces which can be cut from three cakes of weights; 484g, 308g and 253g.A. 90B. 95C. 100D. 105
95...

HCF = 11 so 44 + 28 + 23 = 95 pieces of weight 11.

regards
scrabbler

@abhishek.2011 said:
-1%
How? 50% became 44% so -12% hoga na?

regards
scrabbler

@abhishek.2011 said:
Find the least number of all equal weight pieces which can be cut from three cakes of weights; 484g, 308g and 253g.A. 90B. 95C. 100D. 105
95

divide each by hcf(11) and add
@Logrhythm said:
he buys 120 instead of 100 --> 20% profithe sells 108 instead of 120 and gives 25 disc on 120...so he sells 108 at 90here he incurs a loss of 1800/108 = 16.66so overall profit/loss = 20-16.66-(20*16.66/100) = 0.008% profit seems like i made a functional mistake somewhere....what is the OA??
@scrabbler ye wala dekhna...
@abhishek.2011 said:
Find the least number of all equal weight pieces which can be cut from three cakes of weights; 484g, 308g and 253g.A. 90B. 95C. 100D. 105
95?
HCF(484,308,253)=11
Number of pieces=(484+308+253)/11 =95 ?
@mohnish_khiani said:
What is the percentage change when 20/40 becomes 22/50 ???
initial= 20/40 = 1/2
final= 22/50=11/25

%age change= (final/initial -1) *100
=(11*2/25 -1)=-12%
12% decrease
@next_big_thing said:
This is a question from CAT 2010 paper. Can anyone plz solve it coz I am at a loss ??? -->A triangular garden is to be enclosed inside 3 straight fences. Raju started running at an uniform speed on the three sides of the proposed boundary of the garden & discovered that he was taking 48min, 102min, 90min to traverse the garden's three sides. However, in the latest colony meet, it was decided that the coverage area of the park should be reduced to accomodate a parking lot. Since the fence on the shortest boundary was already constructed, the length of the boundary covered by Raju in 90min was reduced by 60% & the longest was modified accordingly so that the park still remained triangular in shape.1) How much time will Raju take to run along the boundary of the garden thus formed? 120min, 148min, 128min, 160min, 144min2) If Raju's speed was 15metres/min, what is the approx area of the parking lot (in km^2)? 0.39, 0.28, 0.29, 0.45, 0.52Plz post the solution as well or else it wont be of any help.
ratio is the same as time covered :- 8:17:15 .... if u notice this is a right angle triangle
the side with 15 has to be reduced by 9cm , so new side would be 6m....
so 8,6 now the angle b/w two small sides would still be a right angle (this is my assumption) so that... and hence 8,6,10 so, 24*6 = 144min .... not sure..

for 2nd question, 1/2*(15*48*15)(90 - 36)*10^(-4) = 1.08*0.27 = 0.29 aprox.
@abhishek.2011 said:
Find the least number of all equal weight pieces which can be cut from three cakes of weights; 484g, 308g and 253g.A. 90B. 95C. 100D. 105
1/2 becomes 11/25

2*(11/25 - 1/2)*100 = 4*3 = 12% decrease
@next_big_thing said:
This is a question from CAT 2010 paper. Can anyone plz solve it coz I am at a loss ??? -->A triangular garden is to be enclosed inside 3 straight fences. Raju started running at an uniform speed on the three sides of the proposed boundary of the garden & discovered that he was taking 48min, 102min, 90min to traverse the garden's three sides. However, in the latest colony meet, it was decided that the coverage area of the park should be reduced to accomodate a parking lot. Since the fence on the shortest boundary was already constructed, the length of the boundary covered by Raju in 90min was reduced by 60% & the longest was modified accordingly so that the park still remained triangular in shape.1) How much time will Raju take to run along the boundary of the garden thus formed? 120min, 148min, 128min, 160min, 144min2) If Raju's speed was 15metres/min, what is the approx area of the parking lot (in km^2)? 0.39, 0.28, 0.29, 0.45, 0.52Plz post the solution as well or else it wont be of any help.
as 90 degree vertex is common side = 60 min
time 36+60+48=144
area = 1/2*15^2*48*54/10^6=0.29
@Logrhythm said:
he buys 120 instead of 100 --> 20% profithe sells 108 instead of 120 and gives 25 disc on 120...so he sells 108 at 90here he incurs a loss of 1800/108 = 16.66so overall profit/loss = 20-16.66-(20*16.66/100) = 0.008% profit seems like i made a functional mistake somewhere....what is the OA??
A trader cheats by 10% while selling and cheats by 20% while purchasing .He also offers a discount of 25% at cost price.find his profit /loss percent?

@Logrhythm said:
@scrabbler ye wala dekhna...

I interpreted the bold part above differently. Price instead of quantity. If quantity then your answer works.

He has to cheat by 20% on his cost price, I took (as we know nothing about the other person's CP) so he buys 100 ka worth stuff for 80. Then he raises the price from 100 to 110 and then gives a discount of 25% coming to 82.5. So what he bought for 80 he sold for 82.5 and hence profit is 3.125% .

Answer however would be different for different interpretations. I find these questions mildly awkward and ambiguous generally, can never be sure if one's interpretation is what the question-setter intended!

regards
scrabbler

@scrabbler said:
A trader cheats by 10% while selling and cheats by 20% while purchasing .He also offers a discount of 25% at cost price.find his profit /loss percent?I interpreted the bold part above differently. Price instead of quantity. If quantity then your answer works.He has to cheat by 20% on hiscost price, I took (as we know nothing about the other person's CP) so he buys 100 ka worth stuff for 80. Then he raises the price from 100 to 110 and then gives a discount of 25% coming to 82.5. So what he bought for 80 he sold for 82.5 and hence profit is 3.125% .Answer however would be different for different interpretations. I find these questions mildly awkward and ambiguous generally, can never be sure if one's interpretation is what the question-setter intended!regardsscrabbler
Exactly! I was getting diff answers for diff interpretations. Like If the quantity changes then answer is diff..OR if we apply (1+a%)(1+b%) then again ans changes...

Q. What is the ratio of number of divisors of N²º¹³ which lie in the range (1, 2013) to which lie in the range (N²º¹², N²º¹³) ?

A. 1 : 1
B. 1 : N
C. 1 : N²º¹²
D. 1 : N²º¹³


Source: Bodhi_vriksha FB Page
No OA
@ScareCrow28 said:
Q. What is the ratio of number of divisors of N²º¹³ which lie in the range (1, 2013) to which lie in the range (N²º¹², N²º¹³) ?A. 1 : 1B. 1 : NC. 1 : N²º¹²D. 1 : N²º¹³Source: Bodhi_vriksha FB PageNo OA
since it is a general question i think we can take any value of n and solve

lets take n=2
2^2013

factors in the range of (1,2013)=2^0,2^1.....2^10=11 factors

in the range of [2^2012,2^2013]=2 factos only

11:2
no OA is matching here

CAT 2008 Number System question if anyone is interested :


Numbers 1 to 40 are written on board. keep erasing any two Numbers, say (a,b) and replace by (a+b-1). Exactly one number will remain after some time..what is that?


@next_big_thing said:
This is a question from CAT 2010 paper. Can anyone plz solve it coz I am at a loss ??? -->A triangular garden is to be enclosed inside 3 straight fences. Raju started running at an uniform speed on the three sides of the proposed boundary of the garden & discovered that he was taking 48min, 102min, 90min to traverse the garden's three sides. However, in the latest colony meet, it was decided that the coverage area of the park should be reduced to accomodate a parking lot. Since the fence on the shortest boundary was already constructed, the length of the boundary covered by Raju in 90min was reduced by 60% & the longest was modified accordingly so that the park still remained triangular in shape.1) How much time will Raju take to run along the boundary of the garden thus formed? 120min, 148min, 128min, 160min, 144min2) If Raju's speed was 15metres/min, what is the approx area of the parking lot (in km^2)? 0.39, 0.28, 0.29, 0.45, 0.52Plz post the solution as well or else it wont be of any help.
Initially sides of triangles :
90,48,102(It is a right triangle)
90 is reduced by 60%=.4*90=36
so the new triangle will have sides 36,48, _/(36^2+48^2) or 36,48,60
Raju take to run along the boundary of the garden =36+48+60=144 min

Area of parking lot=.5 *15^2 * (90*48 - 36*48) /10^6
=.29 km^2
@Subhashdec2 said:
since it is a general question i think we can take any value of n and solvelets take n=22^2013factors in the range of (1,2013)=2^0,2^1.....2^10=11 factorsin the range of [2^2012,2^2013]=2 factos only11:2no OA is matching here
I am not sure of the range values here in the question, I am assuming it to be excluding the extremities.
Again in the second bold part it may be open brackets..so 0 factors in that range.
Not sure though.
@Subhashdec2 said:
since it is a general question i think we can take any value of n and solvelets take n=22^2013factors in the range of (1,2013)=2^0,2^1.....2^10=11 factorsin the range of [2^2012,2^2013]=2 factos only11:2no OA is matching here
what is N=13?