Official Quant thread for CAT 2013

@sujamait said:
A potter asked his two sons to sell some pots inthe market. The amount received for each potwas same as the number of pots sold. The twobrothers spent the entire amount on somepackets of potato chips and one packet of bananachips. One brother had the packet of banana chipsalong with some packets of potato chips, whilethe other brother just had potato chips. Eachpacket of potato chips costs 10/- and the packetof banana chips costs less than 10/-. Thepackets of chips were divided between the twobrothers so each brother received equal numberof packets. How much money should one brothergive to the other to make the division financiallyequitable?
Is it 4, for 36, 3*10 + 6 = 36
20 - 16 = 4 ?
It was a pure hit and trial
@sujamait said:
A potter asked his two sons to sell some pots inthe market. The amount received for each potwas same as the number of pots sold. The twobrothers spent the entire amount on somepackets of potato chips and one packet of bananachips. One brother had the packet of banana chipsalong with some packets of potato chips, whilethe other brother just had potato chips. Eachpacket of potato chips costs 10/- and the packetof banana chips costs less than 10/-. Thepackets of chips were divided between the twobrothers so each brother received equal numberof packets. How much money should one brothergive to the other to make the division financiallyequitable?
shud be 2 in that case to make it equitable.
@rachit_28
@sujamait said:
A potter asked his two sons to sell some pots inthe market. The amount received for each potwas same as the number of pots sold. The twobrothers spent the entire amount on somepackets of potato chips and one packet of bananachips. One brother had the packet of banana chipsalong with some packets of potato chips, whilethe other brother just had potato chips. Eachpacket of potato chips costs 10/- and the packetof banana chips costs less than 10/-. Thepackets of chips were divided between the twobrothers so each brother received equal numberof packets. How much money should one brothergive to the other to make the division financiallyequitable?
My take 4
@sujamait said:
A potter asked his two sons to sell some pots inthe market. The amount received for each potwas same as the number of pots sold. The twobrothers spent the entire amount on somepackets of potato chips and one packet of bananachips. One brother had the packet of banana chipsalong with some packets of potato chips, whilethe other brother just had potato chips. Eachpacket of potato chips costs 10/- and the packetof banana chips costs less than 10/-. Thepackets of chips were divided between the twobrothers so each brother received equal numberof packets. How much money should one brothergive to the other to make the division financiallyequitable?
2 Rs
@sujamait said:
A potter asked his two sons to sell some pots inthe market. The amount received for each potwas same as the number of pots sold. The twobrothers spent the entire amount on somepackets of potato chips and one packet of bananachips. One brother had the packet of banana chipsalong with some packets of potato chips, whilethe other brother just had potato chips. Eachpacket of potato chips costs 10/- and the packetof banana chips costs less than 10/-. Thepackets of chips were divided between the twobrothers so each brother received equal numberof packets. How much money should one brothergive to the other to make the division financiallyequitable?(5) 7
Number of pots = n
Amount received for each pot = n

Packets of potato = p , Cost of potato = 10, Banana cost = b ( b

p + 1 was equally divided among brothers [ p has to be odd]

so, A has (1 + (p-1)/2) [1 banana + rest potato] and B has (p + 1)/2 [all potatoes]

Money with A = b + 5*(p-1) = 5p + (b-5)
Money with B = 5*(p + 1) = 5p + 5

Difference between the amount = (10 - b)

Sum of the money = 10*p + b = n^2

p = odd only
p = 1, b = 6 => n = 4
p = 3, b = 6 => n = 6
p = 19, b= 6 => n = 14
p = 25, b= 6 => n = 16

b is always 6 somehow :wow: .. (Need to prove it :splat: => since p is odd -> second last digit is odd, and since second last digit is odd, the perfect square must end in 6 :), hence b = 6 )

=> money to be given = 2 ?
@sujamait said:
A potter asked his two sons to sell some pots inthe market. The amount received for each potwas same as the number of pots sold. The twobrothers spent the entire amount on somepackets of potato chips and one packet of bananachips. One brother had the packet of banana chipsalong with some packets of potato chips, whilethe other brother just had potato chips. Eachpacket of potato chips costs 10/- and the packetof banana chips costs less than 10/-. Thepackets of chips were divided between the twobrothers so each brother received equal numberof packets. How much money should one brothergive to the other to make the division financiallyequitable?
Amount received = x²
Potato chips bought = 2p - 1

Amount spent = 20p + a - 10, where a
So, one brother paid 10p and other one paid 10p - 10 + a
=> One will pay (10 - a)/2 to other one

x² = 20p - 10 + a
Unit digit of x² is 'a' (so unit digit can not be 0) and tens digit is always odd

Now, all the perfect square having tens digit as odd have unit digit as 6

=> a = 6

So, money to be paid = (10 - 6)/2 = 2
Find the complex number having the least possible argument and satisfying z-5i............I dont have the oa.......so plz post your solutions with approach
@19rsb said:
Find the complex number having the least possible argument and satisfying z-5i
Is it |z - 5i |

It is a circle with center at x = 0, y = 5 and radius as 3

So, the compex number with the least argument is the intersection point of tangent from origin and the circle.

I made the diagram, and it turns out that the angle with y axis is = tan inverse (3/4) = A

=> Complex number = (4sinA) + (4cosA)*i = (4/5)*(3 + 4i) ?
@deedeedudu said:
2 Rs
@YouMadFellow said:
Number of pots = nAmount received for each pot = nPackets of potato = p , Cost of potato = 10, Banana cost = b ( bp + 1 was equally divided among brothers [ p has to be odd]so, A has (1 + (p-1)/2) [1 banana + rest potato] and B has (p + 1)/2 [all potatoes]Money with A = b + 5*(p-1) = 5p + (b-5)Money with B = 5*(p + 1) = 5p + 5 Difference between the amount = (10 - b)Sum of the money = 10*p + b = n^2p = odd only p = 1, b = 6 => n = 4p = 3, b = 6 => n = 6p = 19, b= 6 => n = 14p = 25, b= 6 => n = 16b is always 6 somehow .. (Need to prove it => since p is odd -> second last digit is odd, and since second last digit is odd, the perfect square must end in 6 , hence b = 6 ) => money to be given = 2 ?
@chillfactor said:
Amount received = x²Potato chips bought = 2p - 1Amount spent = 20p + a - 10, where a So, one brother paid 10p and other one paid 10p - 10 + a=> One will pay (10 - a)/2 to other onex² = 20p - 10 + aUnit digit of x² is 'a' (so unit digit can not be 0) and tens digit is always oddNow, all the perfect square having tens digit as odd have unit digit as 6=> a = 6So, money to be paid = (10 - 6)/2 = 2
Given that product of a two-digit number AB and 74 is a three-digit number EEE, where A, B and E are
distinct non zero digits. What is the value of €˜E €™?
A. 9
B. 7
C. 6
D. 8
E. None of these

@sujamait said:
Given that product of a two-digit number AB and 74 is a three-digit number EEE, where A, B and E aredistinct non zero digits. What is the value of €˜E €™?A. 9B. 7C. 6D. 8E. None of these
888/74=12

d.8
@sujamait said:
Given that product of a two-digit number AB and 74 is a three-digit number EEE, where A, B and E aredistinct non zero digits. What is the value of €˜E €™?A. 9B. 7C. 6D. 8E. None of these
D. 8

74*12 = 888

Total number of bananas with three friends €“ Moti, Sumit and Manky €“ is 10. The sum of the reciprocals of
the number of bananas with the three friends is 1. If the number of bananas with each of the three friends is
an integer, which of the following could be the difference between the number of bananas with Moti and
Sumit?
A. 2
B. 3
C. 0
D. 1
E. Either (A) or (C) (2

@sujamait said:
Total number of bananas with three friends €“ Moti, Sumit and Manky €“ is 10. The sum of the reciprocals ofthe number of bananas with the three friends is 1. If the number of bananas with each of the three friends isan integer, which of the following could be the difference between the number of bananas with Moti andSumit?A. 2B. 3C. 0D. 1E. Either (A) or (C) (2
e)
1/4+1/4+1/2
@grkkrg said:
D. 874*12 = 888
@krum said:
e)1/4+1/4+1/2
@sujamait said:
Given that product of a two-digit number AB and 74 is a three-digit number EEE, where A, B and E aredistinct non zero digits. What is the value of €˜E €™?A. 9B. 7C. 6D. 8E. None of these
(37 * 2) * 12 = 888
If 'a' is an odd natural number and 'b' is an even natural number, what is the total number of solutions of the
equation ab = 2a + b + 598?
A. 16
B. 12
C. 5
D. 6
E. 8 (2

@sujamait said:
If 'a' is an odd natural number and 'b' is an even natural number, what is the total number of solutions of theequation ab = 2a + b + 598?A. 16B. 12C. 5D. 6E. 8 (2
12?
@sujamait said:
If 'a' is an odd natural number and 'b' is an even natural number, what is the total number of solutions of theequation ab = 2a + b + 598?A. 16B. 12C. 5D. 6E. 8 (2
B. 12?

ab = 2a + b + 598
(2k-1)(2p) = 4k-2 + 2p + 598
4kp - 2p = 4k -2 + 2p + 598
4k(p-1) = 4p + 596
k(p-1) = p + 149
k = (p+149)/(p-1)
k = 1 + 150/(p-1)
Find p to get positive integral values for k
150 = 2*3*5^2
Total factors = 2*2*3 = 12
@sujamait said:
If 'a' is an odd natural number and 'b' is an even natural number, what is the total number of solutions of theequation ab = 2a + b + 598?A. 16B. 12C. 5D. 6E. 8 (2

4mn+2n=4m+2+2n+598
4mn=4m+600
mn=m+150
m(n-1)=150=2*3*5^2

B.12