Official Quant thread for CAT 2013

MBA CAT 2024
27268
@amresh_maverick said:
Find the sum of all the real values of 'x' that satisfy the equation:243^log81(x) -2x = 2^log16(x)+2 -8PS: log x and the no is base , very difficult to type log
OA>

sum =20


@amresh_maverick said:
Manish's happiness is given by a function a2b, where a is his daily consumption of ice creams and b is his daily consumption of chocolates. Each ice cream costs Rs. 20 and each chocolate costs Rs. 10. If he has Rs.1,000, how much should he spend on ice creams to maximise his happiness?
660


@amresh_maverick said:
If |a| I. 'a' is positive. II. 'b' is negative. III. 'c' is positive. a Only I b I and II c II and III d I, II and III e I and III
c II and III
27269
@AbhiFMS said:
Thank you puys for the prev question.I have another question in this attachment,again w.r.t to geometry basics.Do help in soving it too!


correct if i m wrong. :)
27270
@amresh_maverick said:
Manish €™s happiness is given by a function a2b, where a is his daily consumption of ice creams and b is his daily consumption of chocolates. Each ice cream costs Rs. 20 and each chocolate costs Rs. 10. If he has Rs.1,000, how much should he spend on ice creams to maximise his happiness?
500?

27271

@AbhiFMS said:
Thank you puys for the prev question.I have another question in this attachment,again w.r.t to geometry basics.Do help in soving it too!
50..solution in attachment..
27272
@amresh_maverick said:
OA>sum =20 660c II and III
bhai ye log wala ko kaise kara........
27273
@AbhiFMS said:
Thank you puys for the prev question.I have another question in this attachment,again w.r.t to geometry basics.Do help in soving it too!
50 ?

(r - 10)^2 + (r - 20)^2 = r^2
r^2 - 60r + 500 = 0
r = 50,10
r cannot be 10...so r = 50
27274

1> Four die are thown . In how many ways the sum =20
2> No of sol a + b+c=41 , where all are odd and non negative integers

27275
@AbhiFMS said:
Thank you puys for the prev question.I have another question in this attachment,again w.r.t to geometry basics.Do help in soving it too!
50....we can create a Pyth triplet with (x-20), (x-10) and x where x is the radius.

regards
scrabbler
27276
@amresh_maverick said:
OA>sum =20 660c II and III
sir yeh happiness waala explain karna....
27277
@Dexian said:
bhai ye log wala ko kaise kara........
I know the difficult part is see the log function

243^log81(x) -2x = 2^log16(x)+2 -8

3^(5/4)*log3(x) -2x = 4*2^(1/4)log2(x) -8
x^5/4 -2x = 4x^1/4 -8

x(x^1/4-2) = 4(x^1/4-2)
either x=4 or (x^1/4-2) =0 gives x=16

sum =16+4 =20
27278

a camel pursue an elephent and takes 5 leaps for every 7 leaps of the elephent, but 5 leaps of elephent are equal to 3 leaps of camel. what is the ratio of speed of camels and elephent

27279
@amresh_maverick said:
Manish €™s happiness is given by a function a2b, where a is his daily consumption of ice creams and b is his daily consumption of chocolates. Each ice cream costs Rs. 20 and each chocolate costs Rs. 10. If he has Rs.1,000, how much should he spend on ice creams to maximise his happiness?
we have 20a+10b =1000 or 2a + b =100

on this condition we need to maximize a^2b

so a+a+b =100
so a=100/3
amount spent on icecream = 100/3*20 = 666.6

27280
@vbhvgupta said:
a camel pursue an elephent and takes 5 leaps for every 7 leaps of the elephent, but 5 leaps of elephent are equal to 3 leaps of camel. what is the ratio of speed of camels and elephent
25 : 21? multiplied 1st statement by 5 and subbed second into it.

regards
scrabbler
27281
@amresh_maverick said:
1> Four die are thown . In how many ways the sum =202> No of sol a + b+c=41 , where all are odd and non negative integers
a+b+c=41
a=2x+1
b=2y+1
z=2z+1
2x+2y+2z=38
x+y+z=19
21c2=210?
27282
@amresh_maverick said:
1> Four die are thown . In how many ways the sum =20


35 ??
27283
@rnishant231 said:
we have 20a+10b =1000 or 2a + b =100on this condition we need to maximize a^2bso a+a+b =100so a=100/3 amount spent on icecream = 100/3*20 = 666.6
But can we have fractional values for a and b?? a = 33 and b = 34 should be the answer I guess...so 660?

regards
scrabbler
27284
@vbhvgupta said:
a camel pursue an elephent and takes 5 leaps for every 7 leaps of the elephent, but 5 leaps of elephent are equal to 3 leaps of camel. what is the ratio of speed of camels and elephent
5...7
3...5

so, 25:21
27285
@amresh_maverick said:
1> Four die are thown . In how many ways the sum =202> No of sol a + b+c=41 , where all are odd and non negative integers
5,5,5,5=1
6,4,5,5=24
6,6,4,4=6
6,6,5,3=12
6,6,6,2=4

47?


27286
@scrabbler said:
But can we have fractional values for a and b?? a = 33 and b = 34 should be the answer I guess...so 660?regardsscrabbler
exactly..Thanks..
27287
@vbhvgupta said:
a camel pursue an elephent and takes 5 leaps for every 7 leaps of the elephent, but 5 leaps of elephent are equal to 3 leaps of camel. what is the ratio of speed of camels and elephent
25:21